Patent Publication Number: US-9430816-B2

Title: Image processing method, image processing system, image processing device, and image processing program capable of removing noises over different frequency bands, respectively

Description:
TECHNICAL FIELD 
     The present invention relates to an image processing method, an image processing system, an image processing device, and an image processing program. 
     BACKGROUND ART 
     In the image processing technology, a technology for reducing noise contained in an image is essential to sharp reproduction of a captured image. A typical technology for reducing noise is disclosed, for example, in Non-patent Literature 1. The Non-patent Literature 1 discloses a noise removal method using total-variation (T-V) norm regularization. Hereinafter, the method is referred to as a T-V method for short. 
       FIG. 19  illustrates an image processing method using the conventional T-V method. 
       FIG. 20  is a flow chart illustrating the image processing method using the conventional T-V method. 
     An input image F is supplied to a skeleton component/residual component separation unit  101 . 
     The skeleton component/residual component separation unit  101  separates the supplied image F to a skeleton component U T-V  composed of a strong edge and a flat area and a residual component V T-V  composed of a texture and a noise. In other words, the input image F is represented according to the following formula (1), i.e., is represented by a sum of the skeleton component U T-V  and the residual component V T-V .
 
 F=U   T-V   +V   T-V   (1)
 
     The skeleton component U T-V  can be obtained by minimizing a total variation norm J (U T-V ) of the U T-V  that is represented by the following formula (2).
 
 J ( U   T-V )=∫|∇ U   T-V   |dxdy   (2)
 
     Meanwhile, in the formula, x represents a pixel location of the skeleton component U T-V  in a horizontal direction, and y represents a pixel location of the skeleton component U T-V  in a vertical direction. 
     The minimization problem can be solved by iteration of the Chambolle&#39;s projection method. Alternatively, a subgradient method using a subgradient of a T-V norm can be used instead of the Chambolle&#39;s projection method. 
     Where k represents an iteration count,
 
 U   T-V   (k)  
 
represents a skeleton component at a time of a k th  iteration, and β represents a value to be set based on a standard deviation of a noise of a target image,
 
 U   T-V   (0)   =F  
 
is set as an initial value where k=0 (step S 1 ).
 
     As represented by the following formula (3), a skeleton component at a time of a k+1 th  iteration, i.e.,
 
 U   T-V   (k+1)  
 
is calculated using the subgradient method (step S 2 ).
 
     
       
         
           
             
               
                 
                   
                     
                       
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                     ⁢ 
                     
                       
                         where 
                         ⁢ 
                         
                             
                         
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                             ( 
                             0 
                             ) 
                           
                         
                       
                       = 
                       F 
                     
                     , 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         α 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       = 
                       
                         β 
                         
                           k 
                           + 
                           1 
                         
                       
                     
                     , 
                     and 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       g 
                       ⁡ 
                       
                         ( 
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                         ) 
                       
                     
                     = 
                     
                       
                         ⅆ 
                         
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                         ⅆ 
                         X 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     A stop condition for stopping the iteration will be described below. Where a height of the input image is M, a width thereof is N, and a m-line n-row element of the residual component at the time of the k th  iteration, i.e.,
 
 V   T-V   (k)  
 
it is possible to stop the iteration (step S 3 ), using a standard deviation σ noise  of a noise of the target image estimated in advance, when the following formula is satisfied.
 
                       1   MN     ⁢       ∑       1   ≤   m   ≤   M     ,     1   ≤   n   ≤   N                 ⁢       (     v     m   ,   n       (   k   )       )     2         ≈     σ   noise   2             (   4   )               
Here, the formula (4) is true provided that the residual component, i.e.,
 
 V   T-V   (k)  
 
is the noise. Alternatively, it is possible to stop the iteration (step S 3 ) when
 
                       ∑       1   ≤   m   ≤   M     ,     1   ≤   n   ≤   N                 ⁢            v     m   ,   n       (     k   +   1     )       -     v     m   ,   n       (   k   )                &lt;   ɛ           (   5   )               
is satisfied using a threshold ε. In other words, in the above formula (5), a result of the k th  iteration, i.e.,
 
 V   T-V   (k)  
 
is compared with the k+1 th  iteration, i.e.,
 
 V   T-V   (k+1)  
 
and, if a fluctuation amount is sufficiently small, it is considered that a solution is converged.
 
     Further, the iteration is stopped at a time also when the iteration count k reaches the maximum value, i.e., iteration count k max  (step S 4 ). Where the iteration count takes a value less than k, and
 
 U   T-V   (k)  
 
is not converged, the subgradient method continues provided k=k+1 (step S 5 ).
 
     In thus obtained skeleton component U T-V  and residual component V T-V , the skeleton component U T-V  is output as a denoised image Z according to the following formula (6) (step S 6 ).
 
 Z=U   T-V   (6)
 
       FIG. 21  illustrates an improved image processing method of the image processing method using the T-V method of  FIG. 19 . That is, in the improved method, a noise component of the residual component that was separated by the skeleton component/residual component separation unit  101  is attenuated to be synthesized with the skeleton component. 
       FIG. 22  is a flow chart illustrating the image processing method of  FIG. 21 . 
     The residual component V T-V  separated by the skeleton component/residual component separation unit  101  is supplied to a noise suppression unit  102 , where the residual component V T-V  is subjected to an effect of a function f for attenuating the noise component according to the following formula (7) (step S 7 ). The skeleton component U T-V  is synthesized with the residual component (i.e., texture component) f (V T-V ), of which noise component being attenuated, to be output as the image Z containing less noise (step S 6 ). Meanwhile, step  1  to step  5  are identical to those of the image processing method using the T-V method of  FIG. 19 . Therefore, descriptions thereof are omitted here.
 
 Z=U   T-V   +f ( V   T-V )  (7)
 
     Examples of the function f include soft evaluation threshold processing illustrated in  FIG. 23( a ) , hard evaluation threshold processing illustrated in  FIG. 23( b ) , and factor processing illustrated in  FIG. 23( c ) . The function f, however, is not limited to those examples. Where an input value is x, an output value is f(x), and a threshold is r in the function f, the soft evaluation threshold processing illustrated in  FIG. 23( a )  is represented by the following formula (8). 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       soft 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         τ 
                       
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               sign 
                               ⁡ 
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
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                               ( 
                               
                                 
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                                    
                                 
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                               if 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                  
                                 x 
                                  
                               
                             
                             &gt; 
                             τ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Here, a sign function in the formula (8) is a function for outputting a plus/minus sign. 
     The hard evaluation threshold processing illustrated in  FIG. 23( b )  is represented by the following formula (9). 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       hard 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         τ 
                       
                       ) 
                     
                   
                   = 
                   
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                           x 
                         
                         
                           
                             
                               if 
                               ⁢ 
                               
                                   
                               
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                                  
                                 x 
                                  
                               
                             
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                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Further, when γ is set to a proper coefficient, factor processing illustrated in  FIG. 23( c )  is represented by the following formula (10).
 
 f   factor ( x ,γ)=γ×x  (10)
 
     Still further, it is possible to combine the soft evaluation threshold processing or the hard evaluation threshold processing with the factor processing according to a formula (11).
 
 f   factor-soft ( x ,γ,τ)= f   soft ( f   factor ( x ,γ),τ)
 
 f   soft-factor ( x ,τγ)= f   factor ( f   soft ( x ,τ),γ)  (11)
 
     In the formula (11), a function is constituted using the soft evaluation threshold processing. However, as a matter of course, it is also possible to constitute an equivalent function using the hard evaluation threshold processing. 
     CITATION LIST 
     Non-Patent Literature 
     [Non-Patent Literature 1] 
     
         
         L. Rudin, S. Osher, E. Fatemi, “Nonlinear Total Variation based noise removal algorithms,” Physica D vol. 60, 1992, pp. 259-268. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     The technology of Non-patent Literature 1 is directed to iteration-type processing in which the above described Chambolle&#39;s projection method is repetitively applied until a solution is converged. Therefore, there is a problem of a high calculation cost. 
     The T-V method is capable of removing a high frequency noise. The T-V method, however, has such a problem that the method is not suitable to remove a low frequency noise that is generated due to unevenness of a distribution density of noise particles and that disperses in a relatively wide area in comparison with a case of the high frequency noise. The low frequency noise is generated by distribution density unevenness of noise particles in a wide area of, for example, a range between several pixels and several tens of pixels. The T-V norm with respect to the low frequency noise becomes small. Therefore, such area is considered as a flat area (i.e., an area without noise). More specifically, the T-V method is no use for the low frequency noise in principle. 
     The present invention was made to solve the above described problem. A purpose of the present invention is to provide an image processing method capable of effectively and smoothly removing noises over different frequency bands and an image processing device. 
     Solution to Problem 
     The present invention is directed to an image processing method including: generating an initial denoised image with a reduced noise while preserving an edge in an input image; controlling an iterative operation performed based on energy defined in advance based on an initial residual component calculated from the input image and the initial denoised image; and separating the initial denoised image to a skeleton component and a residual component by the controlled iterative operation to generate the skeleton component as an output image. 
     The present invention is directed to an image processing device including: an initial denoised image generation unit generating an initial denoised image by a noise removal method for storing an edge component in an input image; a skeleton component/residual component separation unit separating the initial denoised image to a skeleton component and a residual component by an iterative operation based on energy defined in advance and generating the skeleton component as an output image; and a control unit controlling the iterative operation based on the initial residual component. 
     Advantageous Effect of Invention 
     According to the present invention, it is possible to effectively and smoothly remove noises over different frequency bands. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is an explanatory chart illustrating an image processing method according to a first embodiment. 
         FIG. 2  is a flow chart illustrating exemplary steps of the image processing method according to the first embodiment. 
         FIG. 3( a )  is an original image containing noise.  FIG. 3( b )  is an image resulting from an application of noise removal processing to the original image of  FIG. 3( a )  by using Wavelet Shrinkage method. 
         FIG. 4  is another explanatory chart illustrating the image processing method according to the first embodiment. 
         FIG. 5  is a flow chart illustrating exemplary steps of the image processing method according to the first embodiment. 
         FIG. 6  is a block diagram illustrating an exemplary configuration of an image processing device according to the first embodiment. 
         FIG. 7  is a block diagram illustrating another exemplary configuration of the image processing device according to the first embodiment. 
         FIG. 8  is an explanatory chart illustrating an image processing method according to a second embodiment. 
         FIG. 9  is a flow chart illustrating exemplary steps of the image processing method according to the second embodiment. 
         FIG. 10  is a block diagram illustrating an exemplary configuration of an image processing device according to the second embodiment. 
         FIG. 11  is an explanatory chart illustrating an image processing method according to a third embodiment. 
         FIG. 12  is a flow chart illustrating exemplary steps of the image processing method according to the third embodiment. 
         FIG. 13  is a block diagram illustrating an exemplary configuration of an image processing device according to the third embodiment. 
         FIG. 14  is an explanatory chart illustrating the image processing method according to the third embodiment. 
         FIG. 15  is an explanatory chart illustrating an image processing method according to a fourth embodiment. 
         FIG. 16( a )  is an original image.  FIG. 16( b )  is an image resulting from an application of a wavelet transform to the original image of  FIG. 16( a ) .  FIG. 16( c )  is an image resulting from recursive three applications of the wavelet transform to the original image of  FIG. 16( a ) . 
         FIG. 17  is a flow chart illustrating exemplary steps of the image processing method according to the fourth embodiment. 
         FIG. 18  is a block diagram illustrating an exemplary configuration of an image processing device according to the fourth embodiment. 
         FIG. 19  is an explanatory chart illustrating the conventional image processing method. 
         FIG. 20  is a flow chart illustrating exemplary steps of the conventional image processing method. 
         FIG. 21  is an explanatory chart illustrating another conventional image processing method. 
         FIG. 22  is a flow chart illustrating exemplary steps of another conventional image processing method. 
         FIG. 23( a )  is a graph illustrating an input/output response of soft evaluation threshold processing.  FIG. 23( b )  is a graph illustrating an input/output response of hard evaluation threshold processing.  FIG. 23( c )  is a graph illustrating an input/output response of factor processing. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
     A first embodiment of the present invention will be described below. 
       FIG. 1  is a functional block diagram illustrating an image processing method according to the first embodiment of the present invention. 
     The image processing method according to the first embodiment of the present invention is characterized in including an initial denoised image generation unit  103  generating an initial denoised image by a light-weight noise removal method for storing an edge component in an input image, an iteration control unit  104  controlling a skeleton component/residual component separation unit positioned in its downstream based an initial residual component separated from the input image in the initial denoised image generation unit  103 , and the skeleton component/residual component separation unit  101  separating the input image to a skeleton component and a residual component as shown in  FIG. 19 . 
     Meanwhile, the skeleton component/residual component separation method for separating an image to a skeleton component and a residual component will be described below exemplifying the T-V method described in the above conventional method. However, the skeleton component/residual component separation method is not limited to this. 
       FIG. 2  is a flow chart illustrating the image processing method according to the first embodiment. 
     Hereinafter, a flow of the processing will be described. 
     An input image F is supplied to the initial denoised image generation unit  103 . 
     The initial denoised image generation unit  103  applies a light-weight noise removal method for storing the edge component to the input image F, thereby generating an initial denoised image U init  (step S 8 ). Where an initial residual component composed of a texture and a noise is noted by V init , the following formula (12) is true.
 
 F=U   init   +V   init   (12)
 
     Thus generated initial denoised image U init  is supplied to the skeleton component/residual component separation unit  101 . Also, thus separated initial residual component V init  is supplied to the iteration control unit  104 . 
     The light-weight noise removal method for storing the edge component in step S 8  will be described below. Examples of the light-weight noise removal method include the Wavelet Shrinkage (WS) method and the Bilateral Filter (BF). These methods have high edge preservability and require a calculation cost lower than that of the T-V method. 
     In the WS method, a two-dimensional wavelet transform is applied to an image, and a high frequency component of a wavelet transform coefficient is attenuated in a zero direction. Then, an inverse two-dimensional wavelet transform is further applied to the image to reconfigure the image, thereby obtaining a noise-reduced image. Where the wavelet transform coefficient is w, a post-Shrinkage wavelet transform coefficient is w′, and an attenuation amount is λ, an attenuation processing is represented by, for example, the following formula (13) and formula (14). 
     
       
         
           
             
               
                 
                   
                     w 
                     ′ 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               sign 
                               ⁡ 
                               
                                 ( 
                                 w 
                                 ) 
                               
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                    
                                   w 
                                    
                                 
                                 - 
                                 λ 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               if 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                  
                                 w 
                                  
                               
                             
                             &gt; 
                             λ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     ′ 
                   
                   = 
                   
                     { 
                     
                       
                         
                           w 
                         
                         
                           
                             
                               if 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                  
                                 w 
                                  
                               
                             
                             &gt; 
                             λ 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     A sign function in the formula (13) is a function for outputting the plus/minus sign. 
     In a normal image, almost all the wavelet transform coefficients having small absolute values are noise components. Therefore, setting of the proper attenuation amount λ and attenuation of the wavelet transform coefficient ensure reduction of a noise component contained in the image. Further, since the wavelet transform coefficient having a large absolute value representing the edge component remains, an edge in the input image is finally preserved. 
     The BF is a weighted smoothing filter-derived filter, which realizes a noise removal method capable of preserving the edge by using the below mentioned two indexes for determining a filter coefficient. 
     The first index is a spatial distance between a to-be-denoised target pixel and its neighboring pixels. The pixels spatially proximity to the target pixel are deemed to have a high correlation with the target pixel and thus given a large weight factor for the filter coefficient. To the contrary, spatially distant pixels are deemed to have a low correlation with the target pixel and thus given a small weight factor for the filter coefficient. 
     The second index is a difference between a pixel value of the to-be-denoised target pixel and pixel values of its neighboring pixels. It is deemed that a correlation with the target pixel becomes higher as the difference between pixel values becomes smaller. Therefore, the weight factor of the filter coefficient is set larger. To the contrary, it is deemed that the correlation with the target pixel becomes lower as the difference between pixel values becomes larger. Therefore, the weight factor of the filter coefficient is set smaller. 
     Specifically, according to an effect of the second index, an area where the pixel values are almost uniform, i.e., a flat area, takes a roll of a typical weighted smoothing filter. This ensures noise removal. To the contrary, according to the effect of the second index, an area where the difference between the pixel values is large, i.e., an area containing the edge, the weight factor of the filter coefficient other than the target pixel is small. This ensures preservation of the edge. 
     A calculation cost of each of the WS method and the BF is smaller than that of the T-V method. However, a visual artifact may occur in a post-processing image in the WS method. This is exemplified in  FIG. 3 .  FIG. 3( a )  is an image containing noise.  FIG. 3( b )  is an image from which noise was removed by the WS method. In  FIG. 3( b ) , unnatural degradation that does not exist in the original image is seen throughout the image. Further, in principle, it is not possible for the BF to remove isolated noise that is referred to as a pepper noise. However, the WS method and the BF in the present embodiment are only used to generate an initial denoised image. The artifact that occurs in the WS method and the isolated noise that is unremovable by the BF method will be removed by processing performed thereafter in the present invention. Therefore, this is not a problem in the present invention. Further, the conventional WS method requires strict setting of the attenuation amount for reducing the occurrence of the artifact. In the present invention, however, since the artifact that occurs in the WS method can be removed by the processing that will be performed thereafter, it is possible to simplify the setting of the attenuation amount in the WS method. 
     The iteration control unit  104  controls the iteration count of the T-V method based on the initial residual component V init  supplied from the initial denoised image generation unit  103 . 
     A standard deviation σ init  is calculated based on the initial residual component V init  supplied from the initial denoised image generation unit  103  in the following manner (step S 9 ). In step S 9 , where the m-line n-row element of the initial residual component V init  is
 
 V   m,n   (init)  
 
the standard deviation σ init  is calculated according to the following formula (15).
 
     
       
         
           
             
               
                 
                   
                     σ 
                     init 
                   
                   = 
                   
                     
                       
                         1 
                         MN 
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             
                               1 
                               ≤ 
                               m 
                               ≤ 
                               M 
                             
                             , 
                             
                               1 
                               ≤ 
                               n 
                               ≤ 
                               N 
                             
                           
                           
                               
                           
                         
                         ⁢ 
                         
                           
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                               v 
                               
                                 m 
                                 , 
                                 n 
                               
                               
                                 ( 
                                 init 
                                 ) 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     In the conventional T-V method, a parameter β in the formula (3) and a maximum iteration count k max  of a fixed value are used. In the present embodiment, however, each parameter is corrected based on a standard deviation σ noise  of noise that was estimated in advance and the standard deviation σ init  calculated in step S 9  (step S 10 ). 
     For example, a parameter β′ represented by the following formula (16) is used, the parameter β′ being calculated based on the standard deviation σ noise  of the noise estimated in advance and the standard deviation σ init  calculated in step S 9 . 
     
       
         
           
             
               
                 
                   
                     β 
                     ′ 
                   
                   = 
                   
                     
                       
                          
                         
                           
                             σ 
                             noise 
                           
                           - 
                           
                             σ 
                             init 
                           
                         
                          
                       
                       
                         σ 
                         noise 
                       
                     
                     × 
                     β 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     In other words, in the formula (16), in a case where σ init  is close to σ noise , the parameter β′ exists close to a converged solution of the T-V method. This ensures improvement of a converging speed. More specifically, narrowing of a to-be-searched area in a single iteration ensures improvement of the converging speed. 
     Further, a maximum iteration count k′ max  is determined according to the following formula (17) using the conventional maximum iteration count k a , a minimum iteration count k min  determined in advance, the standard deviation σ noise  of the noise estimated in advance, and the standard deviation σ init  of the initial residual component V init  (step S 10 ). 
     
       
         
           
             
               
                 
                   
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                       ⁢ 
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                   = 
                   
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                             m 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                         
                         , 
                         
                           min 
                           ⁡ 
                           
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                                 k 
                                 
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                                   ⁢ 
                                   
                                       
                                   
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                                   x 
                                 
                               
                               , 
                               
                                 round 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       k 
                                       
                                         ma 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         x 
                                       
                                     
                                     × 
                                     
                                       
                                          
                                         
                                           
                                             σ 
                                             noise 
                                           
                                           - 
                                           
                                             σ 
                                             init 
                                           
                                         
                                          
                                       
                                       
                                         σ 
                                         noise 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Here, a max function is a function for outputting a larger one of two input values, a min function is a function for outputting a smaller one of two input values, and a round function is a rounding function for rounding a value to an integer value. In the formula (17), in a case where values are close to each other between the standard deviation σ noise  of the noise estimated in advance and the standard deviation σ init  of V init , i.e., in a case where a better initial solution is obtained, the iteration count of the T-V method is reduced. To the contrary, in a case where values are not close to each other between the standard deviation σ noise  of the noise estimated in advance and the standard deviation σ init  of V init , i.e., in a case where a better initial solution could not be obtained, the iteration count of the T-V method is kept to a value close to k max . 
     The skeleton component/residual component separation unit  101  applies the T-V method to the initial denoised image U init  that was supplied from the initial denoised image generation unit  103  as the initial solution to separate a resulting image to a skeleton component U T-V  composed of a strong edge and a flat area and a residual component V T-V  composed of a texture and a noise according to the following formula (18) based on the iteration stop condition set by the iteration control unit  104 .
 
 U   init   =U   T-V   +V   T-V   (18)
 
     The processing performed by the skeleton component/residual component separation unit  101  according to the present embodiment sets, different from the conventional method, the initial value as follows in step S 1 .
 
 U   T-V   (0)   =U   init  
 
     Further, in an iteration stop determination of step S 3 , the skeleton component/residual component separation unit  101  uses the following formula (19) as the iteration stop condition instead of the formula (4) of the conventional method. 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       MN 
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           
                             1 
                             ≤ 
                             m 
                             ≤ 
                             M 
                           
                           , 
                           
                             1 
                             ≤ 
                             n 
                             ≤ 
                             N 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               v 
                               
                                 m 
                                 , 
                                 n 
                               
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               v 
                               
                                 m 
                                 , 
                                 n 
                               
                               
                                 ( 
                                 init 
                                 ) 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                   ≈ 
                   
                     σ 
                     noise 
                     2 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     According to the formula (19), similar to the iteration stop condition of the conventional T-V method, the iteration of the T-V method can be controlled based on σ noise . In a case where the standard deviation σ init  of V init  is close to σ noise , narrowing of the to-be-searched area realizes a high-speed processing since the solution of the T-V method is converged with less iteration count. Further, in the iteration stop determination of step S 4 , k′ max  set in step S 10  is used instead of k max  of the conventional method. Meanwhile, the processing in each of steps S 2  and S 5  is equivalent to the corresponding one of the conventional method. Therefore, descriptions thereof are omitted here. 
     With the skeleton component U T-V  being considered as an image from which noise was removed, a denoised image Z is obtained according to the following formula (20) (step S 6 ).
 
 Z=U   T-V   (20)
 
     As a matter of course, in the present embodiment, it is also possible to synthesize the residual component V T-V  of which noise component is attenuated with the skeleton component U T-V  according to a formula (21) and to output the denoised image Z. The image processing method of the present invention has a configuration illustrated in  FIG. 4  and is shown by a flow chart of  FIG. 5 . The skeleton component/residual component separation unit  101  supplies the residual component V T-V  separated by the skeleton component/residual component separation unit  101  to a noise suppression unit  102 , where the effect of the function f for attenuating a noise component is applied to the residual component V T-V  according to the following formula (21) (step S 7 ). Then, a residual component f(V T-V ), of which noise component being attenuated, is synthesized with the skeleton component U T-V  supplied from the skeleton component/residual component separation unit  101 . A resulting image is output as the denoised image Z (step S 6 ).
 
 Z=U   T-V   +f ( V   T-V )  (21)
 
     Next, a specific image processing device to which the image processing method according to the first embodiment is applied will be described.  FIG. 6  is an exemplary configuration of the image processing device according to the first embodiment. 
     An image processing device  1000  applies noise removal processing to an input image  1  and outputs the resulting image as an output image  2 . 
     The image processing device  1000  includes an initial denoised image generation unit  3 , an initial residual component storage memory  4 , a standard deviation calculation unit  5  of the initial residual component, a standard deviation storage memory  6  of the initial residual component, a parameter calculation unit  7  of the subgradient method, a parameter storage memory  8  of the subgradient method, an iteration control unit  9  of the subgradient method, and a skeleton component/residual component separation unit  10 . 
     When given the input image  1 , in step S 8 , the initial denoised image generation unit  3  applies a light-weight noise removal method for storing the edge component to the input image  1  to generate an initial denoised image. 
     The initial residual component storage memory  4  stores the initial residual component separated from the input image  1  by initial denoised image generation unit  3 . 
     The standard deviation calculation unit  5  of the initial residual component refers to the initial residual component storage memory  4  in order to calculate the standard deviation of the initial residual component according to the procedure described in step S 9 . 
     The standard deviation storage memory  6  of the initial residual component stores the standard deviation of the initial residual component that was calculated by the standard deviation calculation unit  5  of the initial residual component. 
     The parameter calculation unit  7  of the subgradient method refers to the standard deviation storage memory  6  of the initial residual component in order to calculate the parameter β′ of the subgradient method and the maximum iteration count parameter k′ max  of the subgradient method according to the procedure described in step S 10 . 
     The parameter storage memory  8  of the subgradient method stores the parameter of the subgradient method that was calculated by the parameter calculation unit  7  of the subgradient method. 
     The iteration control unit  9  of the subgradient method refers to the initial residual component storage memory  4  and the parameter storage memory  8  of the subgradient method in order to control the iteration of the sugradient method in the skeleton component/residual component separation unit  10  according to the procedures described in step S 3  and step S 4 . 
     Under the control of the iteration control unit  9  of the subgradient method, the skeleton component/residual component separation unit  10  executes the subgradient method using the initial denoised image supplied from the initial denoised image generation unit  3  as the initial solution, separates the initial denoised image to the skeleton component and the residual component, and outputs the skeleton component as the output image  2  according to the procedures described in steps S 1 , S 2 , S 3 , S 4 , and S 5 . 
     Meanwhile, the configuration of the image processing device illustrated in  FIG. 6  is a mere example. Any other configuration may be employed so far as the device realizes the equivalent function with the configuration. 
     Further, a function of the image processing device  1000  can be realized by a computer. In other words, each of the components constituting the image processing device, i.e., the initial denoised image generation unit  3 , the initial residual component storage memory  4 , the standard deviation calculation unit  5  of the initial residual component, the standard deviation storage memory  6  of the initial residual component, the parameter calculation unit  7  of the subgradient method, the parameter storage memory  8  of the subgradient method, the iteration control unit  9  of the subgradient method, and the skeleton component/residual component separation unit  10 , can be formed into a program for causing a central processing unit (CPU) of the computer to realize the above described functions. 
     In sum, a function of each of the components constituting the image processing device can be realized by a computer, i.e., in the form of a program. This applies not only to the first embodiment but also to other embodiments. 
     Further, the image processing device  1000  may also be configured, similar to an image processing device  1001  illustrated in  FIG. 7 , to generate the output image  2  by synthesizing the residual component, of which noise component being attenuated, and the skeleton component. 
     The image processing device  1001  includes, similar to the image processing device  1000 , the initial denoised image generation unit  3 , the initial residual component storage memory  4 , the standard deviation calculation unit  5  of the initial residual component, the standard deviation storage memory  6  of the initial residual component, the parameter calculation unit  7  of the subgradient method, the parameter storage memory  8  of the subgradient method, the iteration control unit  9  of the subgradient method, and the skeleton component/residual component separation unit  10 . The above components perform processing as those of the image processing device  1000 . Therefore, descriptions thereof are omitted here. 
     The image processing device  1001  includes, in addition to the image processing device  1000 , a noise suppression unit  11  and a synthesizing unit  12 . 
     The noise suppression unit  11  suppresses the noise component from the residual component that is supplied from the skeleton component/residual component separation unit  10  according to a procedure of step S 7 . 
     The synthesizing unit  12  synthesizes the skeleton component and the residual component (i.e., texture component), of which noise component being attenuated, to thereby generate the output image  2 . The skeleton component is supplied from the skeleton component/residual component separation unit  10 , and the residual component is supplied from the noise suppression unit  11 . 
     The configuration of the image processing device illustrated in  FIG. 7  is a mere example. Any other configuration may be employed so far as the device realizes the equivalent function with the configuration. 
     According to an aspect of the first embodiment, the light-weight noise removal method for storing the edge component is used to generate the initial denoised image, and thus obtained image is set to the initial solution of the T-V method. Further, the iteration count of the T-V method is controlled based on the residual component that was separated from the input image. This reduces the iteration count of the Chambolle&#39;s projection method required until the solution is converged. As a result, a calculation time is shortened. 
     Second Embodiment 
     A second embodiment of the present invention will be described below. 
       FIG. 8  is a functional block diagram illustrating an image processing method according to the second embodiment of the present invention. 
     The image processing method according to the second embodiment of the present invention is characterized by including the initial denoised image generation unit  103  that generates the initial denoised image by the light-weight noise removal method for storing the edge component in the input image, the iteration control unit  104  that controls the skeleton component/residual component separation unit  101  positioned in its downstream based on the initial residual component separated from the input image in the initial denoised image generation unit  103 , the skeleton component/residual component separation unit  101  that separates the image to the skeleton component and the residual component as illustrated in  FIG. 19 , and a noise suppression unit  201  that suppresses the initial residual component separated from the input image in the initial denoised image generation unit  103  and noise of the residual component separated from an initial denoised image in the skeleton component/residual component separation unit that separates the image to the skeleton component and the residual component based on the T-V method based on a standard deviation of the initial residual component that was separated from the input image in the initial denoised image generation unit  103 . 
     Meanwhile, the skeleton component/residual component separation method for separating the image to the skeleton component and the residual component will be described below using the conventional T-V method. However, this should not be construed in a limiting sense. 
       FIG. 9  is a flow chart illustrating the image processing method according to the second embodiment of the present invention. 
     A flow of the processing will be described below. 
     The input image F is supplied to the initial denoised image generation unit  103 . 
     The initial denoised image generation unit  103  applies the light-weight noise removal method for storing the edge component to the input image F, thereby generating the initial denoised image U init  (step S 8 ). The initial denoised image generation unit  103  further separates the initial residual component V init  composed of a texture and a noise from the input image F. The light-weight noise removal method for storing the edge component is identical to that of the first embodiment. Therefore, a description thereof is omitted here. Thus generated initial denoised image U init  is supplied to the skeleton component/residual component separation unit  101 . The second embodiment differs from the first embodiment in that the separated initial residual component V init  is supplied not only to the iteration control unit  104  but also to the noise suppression unit  201 . 
     The iteration control unit  104  controls the iteration of the T-V method based on the initial residual component V init  supplied from the initial denoised image generation unit  103 . The steps S 9  and S 10  for the iteration control method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. The second embodiment differs from the first embodiment in that a standard deviation σ init  of the initial residual component V init  calculated in step S 9  is supplied to the noise suppression unit  201 . 
     The skeleton component/residual component separation unit  101  applies the T-V method to the initial denoised image U init  supplied from the initial denoised image generation unit  103  as the initial solution. Then, the skeleton component/residual component separation unit  101  separates the image to the skeleton component U T-V  composed of a strong edge and a flat area and the residual component V T-V  composed of a texture and a noise based on the iteration stop condition set by the iteration control unit  104 . The steps S 1 , S 2 , S 3 , S 4 , and S 5  for the separating method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. The residual component V T-V  is supplied to the noise suppression unit  201 . 
     The noise suppression unit  201  causes the function f for attenuating the noise component to work on the residual component V init  that was supplied from the initial denoised image generation unit  103  and the residual component V T-V  that was supplied from the skeleton component/residual component separation unit  101  based on the standard deviation σ init  of the residual component V init  supplied from the iteration control unit  104 , thereby generating the residual component f(V init , V T-V ) with attenuated noise component (step S 11 ). 
     In step S 11 , the function f is configured based on the formula (11) as a basic formula. For example, it is possible to configure the function f, using thresholds τ 1  and τ 2  and coefficients γ 1  and γ 2 , by applying a combination of the soft evaluation threshold processing and the factor processing to each of the residual components V init  and V T-V  according to the following formula (22).
 
 f ( V   init   ,V   T-V )= f   soft-factor ( V   init ,τ 1 ,γ 1 )+ f   soft-factor ( V   T-V ,τ 2 ,γ 2 )  (22)
 
     Here, τ 1  and τ 2  are set as follows using the standard deviation σ noise  of the noise of the target image estimated in advance and the standard deviation σ init  of the initial residual component supplied from the iteration control unit  104 .
 
τ 1   =a   1 ×σ init  
 
τ 2   =a   2 ×(σ noise −σ init )  (23)
 
Here, a 1  and a 2  represent coefficients.
 
     Also, where γ 1 =0 is satisfied, it is also possible to attenuate, as illustrated in  FIG. 2  according to the first embodiment, the noise component only from the residual component V T-V  separated by the skeleton component/residual component separation unit  101 . In this case, also, the second embodiment differs from the first embodiment in that the attenuation amount of the noise component is set based on the standard deviation σ init  of the initial residual component V init  supplied from the iteration control unit  104 . 
     As a matter of course, an order may be reversed with respect to the soft evaluation threshold processing and the factor processing, and/or the hard evaluation threshold processing may be combined therewith. The function f is not limited to the formula (22). Any function may be employed instead of the function f so far as the processing has an equivalent effect. 
     Finally, according to the following formula (24), the skeleton component U T-V  that is supplied from the skeleton component/residual component separation unit  101  is synthesized with the residual component (i.e., texture component) f(V init , V T-V ), of which noise component being attenuated, supplied from the noise suppression unit  201  to thereby obtain the denoised image Z (step S 6 ).
 
 Z=U   T-V   +f ( V   init   ,V   T-V )  (24)
 
     Based on the above described operation, the image processing method of the present invention generates the denoised image. 
     Next, an image processing device to which the image processing method of the second embodiment is applied will be described.  FIG. 10  illustrates an exemplary configuration of the image processing device according to the second embodiment. 
     An image processing device  1002  removes noise from the input image  1  to output it as the output image  2 . 
     The image processing device  1002  includes, similar to the image processing device  1001  of  FIG. 7 , the initial denoised image generation unit  3 , the initial residual component storage memory  4 , the standard deviation calculation unit  5  of the initial residual component, the standard deviation storage memory  6  of the initial residual component, the parameter calculation unit  7  of the subgradient method, the parameter storage memory  8  of the subgradient method, the iteration control unit  9  of the subgradient method, the skeleton component/residual component separation unit  10 , and the synthesizing unit  12 . Processing of each of these components is identical to each corresponding one of the image processing device  1001 . Therefore, descriptions thereof are omitted here. 
     The image processing device  1002  further includes a noise suppression unit  13  that executes processing different from processing of the image processing device  1001 . 
     The noise suppression unit  13  suppresses the noise component according to a procedure of step S 11  from the initial residual component that is obtainable by referring to the initial residual component storage memory  4  and the residual component that is supplied from the skeleton component/residual component separation unit  10  based on the standard deviation of the initial residual component that is obtainable by referring to the standard deviation storage memory  6  of the initial residual component. 
     A configuration of the image processing device illustrated in  FIG. 10  is a mere example. Any other configuration may be employed so far as the device realizes the equivalent function with the configuration. 
     According to an aspect of the second embodiment, it is possible to smoothly remove noise while better preserving the edge and the texture by synthesizing not only the residual component that was separated by the T-V method but also the initial residual component that was separated upon generation of the initial denoised image, of which noise component being attenuated, with the skeleton component based on the residual component that was separated upon generation of the initial denoised image. 
     Third Embodiment 
     A third embodiment of the present invention will be described below. 
     In the third embodiment, an image processing method having better edge preservability than that of the image processing method of the first embodiment will be described below. 
     It is possible to realize the smooth noise removal while preserving the edge and the texture also according to the first embodiment and the second embodiment. However, in those embodiments, there may be a case where the noise is excessively suppressed by the T-V method depending on an image, which invites degradation of the resolution feeling. Therefore, in the third embodiment, an image processing method in which the noise is capable of being removed smoothly as well as capable of preventing excessive suppression of noise will be described. 
       FIG. 11  is a functional block diagram illustrating the image processing method according to the third embodiment of the present invention. 
     The image processing method according to the third embodiment of the present invention is characterized by including the initial denoised image generation unit  103  that generates the initial denoised image based on the WS method, the iteration control unit  104  that controls the skeleton component/residual component separation unit positioned in its downstream based on the initial residual component that was separated from the input image in the initial denoised image generation unit  103 , the skeleton component/residual component separation unit  101  that separates the image to the skeleton component and the residual component as illustrated in  FIG. 19 , a restriction space creation unit  304  that creates a space for restricting the skeleton component generated by the skeleton component/residual component separation unit  101  based on the wavelet transform coefficient that is calculated in the course of the generation of the initial denoised image and the noise attenuation amount in the initial denoised image generation unit  103 , and a projection unit  306  that projects the wavelet transform coefficient of the skeleton component generated in the skeleton component/residual component separation unit  101  to a restriction space that is created in the restriction space creation unit  304 . 
     Meanwhile, the skeleton component/residual component separation method for separating the image to the skeleton component and the residual component will be described below referring to the conventional T-V method. However, this should not be construed in a limiting sense. 
       FIG. 12  is a flow chart illustrating the image processing method according to the first embodiment. 
     Hereinafter, a flow of processing will be described. 
     The input image is supplied to the initial denoised image generation unit  103 . 
     The initial denoised image generation unit  103  generates the initial denoised image using the WS method. 
     Initially, the wavelet transform unit  301  applies the wavelet transform to the supplied input image (step S 12 ), and supplies a wavelet transform coefficient to a Shrinkage unit  302  and the restriction space creation unit  304 , respectively. 
     The Shrinkage unit  302  applies the Shrinkage to the wavelet transform coefficient supplied from the wavelet transform unit  301  (step S 13 ). For example, the processing according to each of the formula (13) and the formula (14) is applicable as a form of the Shrinkage. Further, the Shrinkage unit  302  supplies a post-Shrinkage wavelet transform coefficient to the inverse wavelet transform unit  303  and supplies an attenuation amount X of the Shrinkage to the restriction space creation unit  304 . 
     The inverse wavelet transform unit  303  applies the inverse wavelet transform to the post-Shrinkage wavelet transform coefficient that was supplied from the Shrinkage unit  302  (step S 14 ) to obtain the initial denoised image U init  and the residual component V init . Then, the inverse wavelet transform unit  303  supplies thus obtained initial denoised image U init  to the skeleton component/residual component separation unit  101  as well as supplies thus obtained initial residual component V init  to the iteration control unit  104 . 
     The restriction space creation unit  304  creates a restriction space S using the wavelet transform coefficient that was supplied from the wavelet transform unit  301  and the attenuation amount λ that was supplied from the Shrinkage unit  302  (step S 15 ). 
     Where a height of the input image is M, a width thereof is N, a coordinate position in a vertical direction in the image is m, a coordinate position in a horizontal direction in the image is n, and a wavelet transform coefficient is w, a restriction space S is represented by the following formula (25).
 
 S={s   m,n   εR   M×N   :∀m,n ,( WT ( s )) m,n   ε[W   m,n   −   ,W   m,n   + ]}
 
 W   m,n   −   =w   m,n   −c×λ,  
 
 W   m,n   +   =w   m,n   +c×λ   (25)
 
     Meanwhile, in the formula, the WT(•) represents the wavelet transform, and c represents a coefficient. The formula (25) shows that, when the wavelet transform is applied to the restriction space S, a wavelet transform coefficient thereof exists within a range of =c×λ of the wavelet transform coefficient of the input image. 
     Thus created restriction space S is supplied to the projection unit  306 . 
     The iteration control unit  104  controls the iteration of the T-V method based on the noise component V init  that is supplied from the inverse wavelet transform unit  303 . Steps S 9  and S 10  for the iteration control method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. 
     The skeleton component/residual component separation unit  101  applies the T-V method to the initial denoised image U init  that was supplied as an initial solution from the initial denoised image generation unit  103 . Then, the skeleton component/residual component separation unit  101  separates the image to the skeleton component U T-V  and the residual component V T-V  composed of a texture and a noise based on the iteration stop condition set by the iteration control unit  104 . Steps S 1 , S 2 , S 3 , S 4 , and S 5  for separating method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. The skeleton component/residual component separation unit  101  supplies thus obtained skeleton component U T-V  to a wavelet transform unit  305 . 
     The wavelet transform unit  305  applies the wavelet transform to the skeleton component U T-V  that was supplied from the skeleton component/residual component separation unit  101  (step S 16 ) and supplies a wavelet transform coefficient to the projection unit  306   
     The projection unit  306  uses the restriction space S that was supplied from the restriction space creation unit  304  and the wavelet transform coefficient that was supplied from the wavelet transform unit  305  to perform projection processing according to the following formula (26) (step S 17 ).
 
 t   m,n ′=max(min( t   m,n   ,W   m,n   + ), W   m,n   − )  (26)
 
     Meanwhile, t is the wavelet transform coefficient resulting from the application of the wavelet transform to the skeleton component U T-V  that was output from the wavelet transform unit  305 , and t′ is the wavelet transform coefficient output as a result of the application of the projection processing to the restriction space S. 
     More specifically, in the third embodiment, the wavelet transform coefficient of the output image Z is restricted to be varied within the range of ±c×λ of a wavelet transform coefficient w m,n  of the input image F. This ensures prevention of noise from the excessive suppression. 
     Further, the projection unit  306  supplies a post-projection wavelet transform coefficient according to the formula (26) to an inverse wavelet transform unit  307 . 
     The inverse wavelet transform unit  307  applies the inverse wavelet transform to the wavelet transform coefficient that was supplied from the projection unit  306  (step S 18 ) to thereby obtain the noise-removed output image. 
     Based on the above described operation, the image processing method of the present invention generates the denoised image. 
     Next, a specific image processing device for executing the image processing method according to the third embodiment will be described.  FIG. 13  illustrates an exemplary configuration of the image processing device according to the third embodiment. 
     An image processing device  1003  applies image processing to the input image  1  and outputs the image as the output image  2 . 
     The image processing device  1003  includes, similar to the image processing device  1000  of  FIG. 7 , the initial residual component storage memory  4 , the standard deviation calculation unit  5  of the initial residual component, the standard deviation storage memory  6  of the initial residual component, the parameter calculation unit  7  of the subgradient method, the parameter storage memory  8  of the subgradient method, the iteration control unit  9  of the subgradient method, the skeleton component/residual component separation unit  10 , a restriction space creation unit  14 , a restriction storage memory  15 , and a restriction processing unit  16 . Processing performed by each of the components is identical to each corresponding one of the image processing device  1000 . Therefore, descriptions thereof are omitted here. 
     The initial denoised image generation unit  3  carries out initial denoised image generation using the WS method according to the procedures of steps S 12 , S 13 , and S 14 . Then, the initial denoised image generation unit  3  supplies the wavelet transform coefficient and the attenuation amount that are obtainable in the course of the initial denoised image generation to the restriction space creation unit  14 . 
     The restriction space creation unit  14  creates a restriction space according to the procedure of step S 15  based on the wavelet transform coefficient and the attenuation amount that are supplied from the initial denoised image generation unit  3 . 
     The restriction processing unit  16  restricts a variation range of the skeleton component according to the procedures of steps S 16 , S 17 , and S 18  based on the skeleton component supplied from the skeleton component/residual component separation unit  10  and the restriction space supplied from the restriction space creation unit  14 . 
     The configuration of the image processing device illustrated in  FIG. 13  is a mere example. Any other configuration may be employed so far as the device realizes the equivalent function with the configuration. 
     According to the third embodiment, a problem of degradation of the resolution feeling caused by the excessive suppression of noise by the T-V method is solved, and therefore, the smooth noise removal becomes possible while the edge and the texture are better preserved. 
     Meanwhile, a combination of the third embodiment and the second embodiment ensures realization of the image processing method by which the edge and the texture are better preserved. The configuration of which is illustrated in  FIG. 14 . A description of processing thereof is omitted here. 
     Fourth Embodiment 
     A fourth embodiment of the present invention will be described below. 
       FIG. 15  is a functional block diagram illustrating an image processing method according to the fourth embodiment of the present invention. 
     The fourth embodiment is directed to an image processing method having a better low-frequency noise removal performance than the image processing method according to the first embodiment. 
       FIG. 15  illustrates a flow of processing in a case of applying the wavelet transform to a multiresolution image of a three-layer structure. However, the processing can be applied also to a structure other than the three-layer structure.  FIG. 16  illustrates an example of the multiresolution wavelet transform.  FIG. 16( a )  illustrates an original image.  FIG. 16( b )  illustrates an image in which the wavelet transform is applied to a first layer.  FIG. 16( c )  illustrates an image in which the wavelet transform is applied to a third layer. In  FIG. 16( b ) , L represents a low frequency side, and H represents a high frequency side. A combination of L and H expresses a subband. For example, LH means that the horizontal direction is on the low frequency side and the vertical direction is on the high frequency side. A recursive application of the wavelet transform to the LL component in  FIG. 16( b )  realizes the multiresolution wavelet transform as illustrated in  FIG. 16( c ) . Hereinafter, in the multiresolution wavelet transform, the LL component in a k th  layer is noted by LL k . Each of a LH component, a HL component, and a HH component of the k th  layer is noted in a similar manner. 
     The LL component of the multiresolution wavelet transform takes a roll of the wavelet transform coefficient as well as a reduced image of the original image. For example, the LL component in the third layer when the multiresolution wavelet transform was executed for the three-layer structure is a reduced image reduced to 8 times of the original image in both of the horizontal direction and the vertical direction, resulting in having a resolution reduced to 64 times of the original image. Since the T-V method is noise removal processing for an image area, the T-V method is executable with respect to the wavelet transform coefficient of the LL component. The LL component in a deep layer is deemed as being composed of the low frequency component of the original image. Therefore, execution of the denoise processing in the deep layer ensures removal of the low frequency noise. 
       FIG. 17  is a flow chart illustrating the image processing method according to the fourth embodiment. 
     Hereinafter, a flow of the processing will be described. 
     The input image F is supplied to a wavelet transform unit  401 . 
     The wavelet transform unit  401  applies the wavelet transform to the supplied input image F and supplies a LL 1  component of the wavelet transform coefficient to a wavelet transform unit  402 . The LL 1  component at this point is a reduced image having a resolution reduced to 4 times of the original image. Further, the wavelet transform unit  401  supplies a LH 1  component, a HL 1  component, and a HH 1  component to a Shrinkage unit  412 . 
     The wavelet transform unit  402  applies the wavelet transform to the LL 1  component of the first layer that was supplied from the wavelet transform unit  401  and supplies thus obtained LL 2  component of the wavelet transform coefficient to a wavelet transform unit  403 . The LL 2  component at this point is a reduced image having a resolution reduced to 16 times of the original image. Further, the wavelet transform unit  402  supplies a LH 2  component, a HL 2  component, and a HH 2  component to a Shrinkage unit  408 . 
     The wavelet transform unit  403  applies the wavelet transform to the LL 2  component of the second layer that was supplied from the wavelet transform unit  402  and supplies thus obtained wavelet transform coefficients LL 3 , LH 3 , HL 3 , and HH 3  to a Shrinkage unit  404 . 
     At this point, the multiresolution wavelet transform is realized for the three-layer structure (step S 19 ). Subsequently, the wavelet transform unit  403  executes the noise removal processing starting from a layer having the lowest resolution (step S 20 ). 
     The Shrinkage unit  404  applies the Shrinkage processing to the wavelet transform coefficients that were supplied from the wavelet transform unit  403  and supplies post-Shrinkage wavelet transform coefficients to an inverse wavelet transform unit  405 . 
     The inverse wavelet transform unit  405  applies the inverse wavelet transform to the wavelet transform coefficients supplied from the Shrinkage unit  404  to generate an initial denoised image U 3, init  having a resolution reduced to 16 times of the original image (step S 21 ). Then, the inverse wavelet transform unit  405  supplies the resulting image to a skeleton component/residual component separation unit  407 . The inverse wavelet transform unit  405  also supplies an initial residual component V 3, init  separated from the input image F to an iteration control unit  406 . 
     The iteration control unit  406  controls the iteration of the T-V method in the skeleton component/residual component separation unit  407  based on the initial residual component V 3, init  supplied from the inverse wavelet transform unit  405 . Steps S 9  and S 10  for the iteration control method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. 
     The skeleton component/residual component separation unit  407  applies the T-V method to the initial denoised image U 3, init  that was supplied from the inverse wavelet transform unit  405  as an initial solution. Then, the skeleton component/residual component separation unit  407  separates the resulting image to a skeleton component U 3, T-V  and a residual component V 3, T-V  composed of a texture and a noise based on the iteration stop condition set by the iteration control unit  406 . Steps S 1 , S 2 , S 3 , S 4 , and S 5  for the separation method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. Since there remains an unprocessed upper layer (step S 22 ), the skeleton component/residual component separation unit  407  supplies thus obtained skeleton component U 3, T-V  to an inverse wavelet transform  409  as a LL′ 2  component of the wavelet transform coefficient. 
     After the completion of the processing at the third layer, processing continuously starts at the second layer (step S 23 ). 
     The Shrinkage unit  408  applies the Shrinkage processing to the LH 2  component, the HL 2  component, and the HH 2  component of the wavelet transform coefficient supplied from the wavelet transform unit  402 . The Shrinkage unit  408  supplies a post-Shrinkage LH′ 2  component, a post-Shrinkage HL′ 2  component, and a post-Shrinkage HH′ 2  component to an inverse wavelet transform unit  409 . 
     The inverse wavelet transform unit  409  applies the inverse wavelet transform to the image using the LH′ 2  component, the HL′ 2  component, and the HH′ 2  component of the wavelet transform coefficient that are supplied from the Shrinkage unit  408  and the LL′ 2  component of the wavelet transform coefficient that is supplied from the skeleton component/residual component separation unit  407  to generate an initial denoised image U 2, init  having a resolution reduced to 4 times of the original image (step S 21 ). Then, the inverse wavelet transform unit  409  supplies the resulting image to a skeleton component/residual component separation unit  411 . Also, the inverse wavelet transform unit  409  supplies an initial residual component V 2, init  that was separated from the input image F to an iteration control unit  410 . 
     The iteration control unit  410  controls the iteration of the T-V method in the skeleton component/residual component separation unit  411  based on the noise component V 2, init  supplied from the inverse wavelet transform unit  409 . Steps S 9  and S 10  for the iteration control method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. 
     The skeleton component/residual component separation unit  411  applies the T-V method to the initial denoised image U 2, init  that was supplied from the inverse wavelet transform unit  409  as an initial solution. Then, the skeleton component/residual component separation unit  411  separates the resulting image to a skeleton component U 2, T-V  and a residual component V 2, T-V  composed of a texture and a noise based on the iteration stop condition set by the iteration control unit  410 . Steps S 1 , S 2 , S 3 , S 4 , and S 5  for the separation method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. Since there remains an unprocessed upper layer (step S 22 ), the skeleton component/residual component separation unit  411  supplies thus obtained skeleton component U 2, T-V  that is considered as a LL′ 1  component of the wavelet transform coefficient to an inverse wavelet transform unit  413 . 
     After the completion of the processing at the second layer, processing continuously starts at the first layer (step S 23 ). 
     The Shrinkage unit  412  applies the Shrinkage processing to the LH 1  component, the HL 1  component, and the HH 1  component of the wavelet transform coefficient that was supplied from the wavelet transform unit  401 . Then, the Shrinkage unit  412  supplies a post-Shrinkage LH′ 1  component, a post-Shrinkage HL′ 1  component, and a post-Shrinkage HH′ 1  component of the wavelet transform coefficient to the inverse wavelet transform unit  413 . 
     The inverse wavelet transform unit  413  uses the LH′ 1  component, the HL′ 1  component, and the HH′ 1  component of the wavelet transform coefficient that were supplied from the Shrinkage unit  412  and the LL′ 1  component of the wavelet transform coefficient supplied from the skeleton component/residual component separation unit  411  to perform the inverse wavelet transform, thereby generating an initial denoised image U 1, init  having a resolution identical to the original image (step S 21 ). Then, the inverse wavelet transform unit  413  supplies thus generated initial denoised image U 1, init  to a skeleton component/residual component separation unit  415 . Also, the inverse wavelet transform unit  413  supplies the initial residual component V 1, init  that was separated from the input image F to an iteration control unit  414 . 
     The iteration control unit  414  controls the iteration of the T-V method in the skeleton component/residual component separation unit  415  based on the initial residual component V 1, init  supplied from the inverse wavelet transform unit  413 . Steps S 9  and S 10  for iteration control method are identical to those of the first embodiment. Therefore, descriptions thereof are omitted here. 
     The skeleton component/residual component separation unit  415  applies the T-V method to an initial denoised image U 1, init  having a resolution identical to the original image, the initial denoised image U 1, init  being supplied from the inverse wavelet transform unit  413  as an initial solution. Accordingly, the skeleton component/residual component separation unit  415  obtains a skeleton component U 1, T-V  and a texture component V 1, T-V . 
     After the completion of the processing at the first layer, the skeleton component/residual component separation unit  415  outputs thus obtained skeleton component U 1, T-V  as the output image Z (step S 6 ). 
     The image processing method of the present invention generates a denoised image based on the above described operations. 
     Next, an image processing device that executes the image processing method according to the fourth embodiment will be described.  FIG. 18  illustrates an exemplary configuration of the image processing device according to the fourth embodiment. 
     An image processing device  1004  applies the image processing to the input image  1  to output it as the output image  2 . 
     The image processing device  1004  includes, similar to the image processing device  1000  of  FIG. 7 , the initial residual component storage memory  4 , the standard deviation calculation unit  5  of the initial residual component, the standard deviation storage memory  6  of the initial residual component, the parameter calculation unit  7  of the subgradient method, the parameter storage memory  8  of the subgradient method, the iteration control unit  9  of the subgradient method, and the skeleton component/residual component separation unit  10 . The processing of each of the above components is identical to each corresponding one of the image processing device  1000 . Therefore, descriptions thereof are omitted here. 
     A multiresolution wavelet transform unit  17  applies the multiresolution wavelet transform to the input image  1  according to a procedure of step S 19 . 
     A high frequency component storage memory  18  stores a high frequency component of the wavelet transform coefficient that is supplied from the multiresolution wavelet transform unit  17 . 
     The initial denoised image generation unit  3  generates an initial denoised image according to a procedure of step S 21  based on a low frequency component of the wavelet transform coefficient of a layer to be processed and a high frequency component of the wavelet transform coefficient of a layer to be processed, the low frequency component being supplied from the multiresolution wavelet transform unit  17  or an output image control unit  19 , and the high frequency component being obtained with reference to the high frequency component storage memory  18 . 
     The output image control unit  19  outputs the skeleton component supplied from the skeleton component/residual component separation unit  10  as the output image  2  when a resolution of the layer to be processed matches the resolution of the input image  1 . When the resolution of the layer to be processed is lower than the resolution of the input image  1 , the output image control unit  19  considers the skeleton component supplied from the skeleton component/residual component separation unit  10  as a low frequency component of the wavelet transform coefficient of a layer having a resolution of a next higher layer and supplies it to the initial denoised image generation unit  3  according to procedures of steps S 22  and S 23 . 
     Meanwhile, a configuration of the image processing device illustrated in  FIG. 18  is a mere example. Any other configuration may be employed so far as the device realizes the equivalent function with the configuration. 
     According to the fourth embodiment, obtainment of the initial denoised image for each layer to use it as the initial solution of the T-V method of each layer ensures reduction of the iteration count of the Chambolle&#39;s projection method required until the solution is converged in the T-V method at each layer. This further ensures smooth removal of the high frequency noise as well as the low frequency noise. 
     Meanwhile, it is possible to easily configure an image processing method by combining the fourth embodiment and the second embodiment or an image processing method by combining the fourth embodiment and the third embodiment. Descriptions of the processing thereof are omitted here. 
     As apparent from the above description, it is possible to configure each unit with hardware. It is also possible to realize each function using a computer program. In this case, a processor operated by a program stored in the program memory realizes functions and operations equivalent to those of the above described embodiments. Alternatively, it is also possible to realize only a portion of the function of the above described embodiment with a computer program. 
     The above embodiments can be described partially or in whole according to the following supplementary notes. However, the present invention should not be limited to the following supplementary notes. 
     (Supplementary note 1) An image processing method including: 
     generating an initial denoised image with a reduced noise while preserving an edge in an input image; 
     controlling an iterative operation performed based on energy defined in advance based on an initial residual component calculated from the input image and the initial denoised image; and 
     separating the initial denoised image to a skeleton component and a residual component by the controlled iterative operation to generate the skeleton component as an output image. 
     (Supplementary note 2) The image processing method according to supplementary note 1, further including: 
     extracting an edge component and a texture component from the residual component; and 
     generating the output image by synthesizing the skeleton component, the edge component, and the texture component. 
     (Supplementary note 3) The image processing method according to supplementary note 1 further including: 
     extracting an edge component and a texture component from the initial residual component and the residual component; and 
     generating the output image by synthesizing the skeleton component, the edge component, and the texture component. 
     (Supplementary note 4) The image processing method according to supplementary note 2 or supplementary note 3, wherein the edge component and the texture component are extracted based on a standard deviation of the initial residual component and a standard deviation of the residual component. 
     (Supplementary note 5) An image processing method including: 
     generating a plurality of images having different resolutions from an input image; 
     wherein, when an output image is generated by applying the image processing method according to any one of supplementary note 1 to supplementary note 4 for each different image, the output image generated based on an image having a low resolution is used for generation of an initial denoised image in an image having a next higher resolution. 
     (Supplementary note 6) An image processing device including: 
     an initial denoised image generation unit generating an initial denoised image by a noise removal method for storing an edge component in an input image; 
     a skeleton component/residual component separation unit separating the initial denoised image to a skeleton component and a residual component by an iterative operation based on energy defined in advance and generating the skeleton component as an output image; and 
     a control unit controlling the iterative operation based on the initial residual component. 
     (Supplementary note 7) The image processing device according to supplementary note 6, 
     wherein the skeleton component/residual component separation unit 
     extracts an edge component and a texture component from the residual component, and 
     synthesizes the skeleton component, the edge component, and the texture component to generate the output image. 
     (Supplementary note 8) The image processing device according to supplementary note 6, 
     wherein the skeleton component/residual component separation unit 
     extracts an edge component and a texture component from the initial residual component and the residual component, and 
     synthesizes the skeleton component, the edge component, and the texture component to generate the output image. 
     (Supplementary note 9) The image processing device according to supplementary note 7 or supplementary note 8, 
     wherein the skeleton component/residual component separation unit 
     extracts the edge component and the texture component based on a standard deviation of the initial residual component and a standard deviation of the residual component. 
     (Supplementary note 10) The image processing device according to any one of supplementary note 6 to supplementary note 9, further including: 
     generation units generating a plurality of images having different resolutions from the input image; 
     wherein the initial denoised image generation unit, the skeleton component/residual component separation unit, and the control unit are provided correspondingly for each of the images having different resolutions; and 
     wherein the initial denoised image generation unit uses the output image that was generated based on an image having a resolution next lower than the corresponding resolution for the generation of the initial denoised image. 
     (Supplementary note 11) A program causing a computer to execute 
     generation processing for generating an initial denoised image with a reduced noise while preserving an edge in an input image: 
     control processing for controlling an iterative operation based on energy defined in advance based on an initial residual component calculated from the input image and the initial denoised image; and 
     generation processing for separating the initial denoised image to a skeleton component and a residual component by the controlled iterative operation to generate the skeleton component as an output image. 
     (Supplementary note 12) The program according to supplementary note 11 causing the computer to execute 
     extraction processing for extracting an edge component and a texture component from the residual component; and 
     generation processing for synthesizing the skeleton component, the edge component, and the texture component to generate the output image. 
     (Supplementary note 13) The program according to supplementary note 11 causing the computer to execute 
     extraction processing for extracting an edge component and a texture component from the initial residual component and the residual component; and 
     generation processing for synthesizing the skeleton component, the edge component, and the texture component to generate the output image. 
     (Supplementary note 14) The program according to supplementary note 12 or supplementary note 13, 
     wherein the edge component and the texture component are extracted based on a standard deviation of the initial residual component and a standard deviation of the residual component. 
     (Supplementary note 15) A program including: 
     generation processing for generating a plurality of images having different resolutions from an input image; 
     wherein, when an output image is generated by applying processing according to any one of supplementary note 11 to supplementary note 14 for each different image, an output image generated based on an image having a low resolution is used to generate an initial denoised image in an image having a next higher resolution. 
     The present invention has been described above with reference to the preferred embodiments and examples. The present invention, however, is not always limited to the above embodiments and examples, but may be modified to be carried out in various forms without departing from the technical concept of the present invention. 
     This application claims the benefit of Japanese Application No. 2012-102019, filed Apr. 27, 2012, the full disclosure of which is hereby incorporated by reference. 
     REFERENCE SIGNS LIST 
     
         
           1  input image 
           2  output image 
           3  initial denoised image generation unit 
           4  initial residual component storage memory 
           5  standard deviation calculation unit 
           6  standard deviation storage memory 
           7  parameter calculation unit 
           8  parameter storage memory 
           9  iteration control unit 
           10  skeleton component/residual component separation unit 
           11  noise suppression unit 
           12  synthesizing unit 
           13  noise suppression unit 
           14  restriction space creation unit 
           15  restriction storage memory 
           16  restriction processing unit 
           19  output image control unit 
           101  skeleton component/residual component separation unit 
           102  noise suppression unit 
           103  initial denoised image generation unit 
           104  iteration control unit 
           201  noise suppression unit 
           301  wavelet transform unit 
           302  Shrinkage unit 
           303  inverse wavelet transform 
           304  restriction space creation unit 
           305  wavelet transform unit 
           306  projection unit 
           307  inverse wavelet transform 
           401  wavelet transform unit 
           402  wavelet transform unit 
           403  wavelet transform unit 
           412  Shrinkage unit 
           404  Shrinkage unit 
           405  inverse wavelet transform 
           406  iteration control unit 
           407  skeleton component/residual component separation unit 
           408  Shrinkage unit 
           409  inverse wavelet transform 
           410  iteration control unit 
           411  skeleton component/residual component separation unit 
           413  inverse wavelet transform 
           414  iteration control unit 
           415  skeleton component/residual component separation unit 
           1000  image processing device