Patent Publication Number: US-8532422-B2

Title: Image restoring device and image restoring method

Description:
This is a National Phase Application filed under 35 USC 371 of International Application No. PCT/JP2009/003780, filed on Aug. 6, 2009, an application claiming foreign priority benefits under 35 USC 119 of Japanese Application No. 2008-206316, filed on Aug. 8, 2008, the content of each of which is hereby incorporated by reference in its entirety. 
     TECHNICAL FIELD 
     The present invention relates to an image restoring apparatus and image restoring method. 
     BACKGROUND ART 
     In recent years, much research and development has been carried out in the field of image engineering into a technology for restoring an original image from a degraded image. That is to say, removing unnecessary information (blurring and noise) from a degraded image (received information) in which unnecessary information (blurring and noise) is mixed in with an original image (desired information, clear image), and extracting only the original image (desired information), is an essential technology in the field of image engineering, and has been the subject of much research and development in recent years. For example, an image captured by means of a digital camera (a generic term for a digital still camera and digital video camera), a mobile phone, or the like, inevitably shows image degradation in comparison with an original object due to the influence of “blurring” caused by camera shake, inaccurate focusing, or the like, and Gaussian or impulse “noise” caused by a dark current, thermal noise, or the like. “Image restoration” is the restoration of an image that is as close as possible to an original image from such a degraded image. 
     The majority of popular image restoration technologies currently on the market are preventive technologies that reduce the influence of blurring and noise in advance using, for example, camera shake correction, face recognition, color correction, various filters, and the like. As a result, in the field of digital cameras in particular, it has recently become possible to obtain vivid images easily through improved digital camera functionality and performance. 
     However, although there is no problem with such preventive technologies in circumstances in which images are recaptured numerous times, restoration for images that do not permit recapturing, as in the case of an already degraded image of an old document or the like, or images that change instantaneously in such fields as sport and medicine, remains a difficult problem. Here, images that change instantaneously in the fields of sport and medicine include, for example, an instantaneous action of a player, and instantaneous states of organs such as the heart and lungs. Therefore, image restoration in circumstances that do not permit recapturing has now become particularly important. 
     One widely known conventional image restoration technology for circumstances that do not permit recapturing is an image restoring method that uses a Wiener Filter (Non-Patent Literature 1, Non-Patent Literature 2). This method uses a filter that minimizes a mean squared error between a restored image obtained via a filter and an original image, and this filter is also called a least-squares filter. This method is an image restoring method in which processing is performed in the frequency domain, and therefore presupposes stationarity of a stochastic process and an image size of semi-infinite length. 
     Another known image restoration technology is an image restoring method that uses a projection filter (Non-Patent Literature 3, Non-Patent Literature 4). A projection filter evaluates closeness between an original image and a restored image, and minimizes a mean squared error of a restored image noise component among items for which an image component of noise of an original image has best approximation to individual original images—that is orthogonal projections of individual original images. From this property, a projection filter is a method of restoring a best-approximation image irrespective of frequency of appearance. 
     Yet another known image restoration technology is an image restoring method that uses a Kalman Filter (Non-Patent Literature 5, Non-Patent Literature 6). In this method, first, in step 1, an AR (Auto Regressive) system parameter (hereinafter referred to as “AR coefficient”) is estimated, and then, in step 2, a state space model (comprising a state equation and observation equation) is configured using the AR coefficient estimated in step 1, and high-performance image restoration is implemented by applying this Kalman filter theory (Kalman filter algorithm). 
     CITATION LIST 
     Non-Patent Literature 
     NPL 1 
     
         
         NISHIMIYA Ryohei et al., (Image Restoration by Using Multiple Wiener Filters), Technical Report of IEICE, A, Vol. J83-A, No. 7, pp. 892-902, July 2000
 
NPL 2
 
         YAMANE Nobumoto et al., (An Optimal Noise Removal Using Adaptive Wiener Filter Based on Locally Stationary Gaussian Mixture Distribution Model for Images), Technical Report of IEICE, A, Vol. J85-A, No. 9, pp. 993-1004, September, 2002
 
NPL 3
 
         OGAWA Hidemitsu et al., (Properties of Partial Projection Filter), Technical Report of IEICE, A, Vol. J71-A, No. 2, pp. 527-534, February, 1988
 
NPL 4
 
         KOIDE Yuji et al., (A Unified Theory of the Family of Projection Filters for Signal and Image Estimation), Technical Report of IEICE, D-II, Vol. J77-D-II, No. 7, pp. 1293-1301, July, 1994
 
NPL 5
 
         TAKASHI Jo et al., (Image Modeling and Parameter Identification for Image Restoration Using a Kalman Filter), Technical Report of IEICE, D-II, Vol. J80-D-II, No. 11, pp. 2912-2919, November, 1997
 
NPL 6
 
         MATSUMURA Atsushi et al., (A Kalman Filter Using Adaptive Image Modeling for Noise Reduction), Technical Report of IEICE, D-II, Vol. J86-D-II, No. 2, pp. 212-222, February, 2003 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     However, an image restoring method that uses a Wiener filter, while offering the advantage of restoration being possible irrespective of the state of degradation of an image, also has a deficiency in that restoration precision is low for a natural image (an unprocessed image that is as captured) for which non-stationarity (variation of image variance) is high. 
     That is to say, as stated above, an image restoring method that uses a Wiener filter performs processing in the frequency domain, and therefore presupposes stationarity of a stochastic process and an image size of semi-infinite length, but in actuality, it is difficult to achieve this presupposition in a real environment, and therefore there are cases in which appropriate restoration is not performed (a natural image non-stationarity problem). Also, since this method comprises batch processing in which a minimum mean squared error is taken as an evaluation amount, there is a possibility of blurring remaining in a restored image (an evaluation amount problem). 
     Specifically, a problem with an image restoring method that uses a Wiener filter is that, if the frequency of appearance of an image is low, restoration precision decreases—that is, restoration of an edge part with a low frequency of appearance in an image is affected. In other words, there is a problem of not being able to perform optimum restoration of an edge part of an image captured with a camera because edge parts mostly have low non-stationarity. However, good restoration precision can normally be obtained for a monotone background part or the like in which gradation and color do not vary—that is, image variance does not vary—since stationarity is high in such a part. 
     An image restoring method that uses a Kalman filter is a method for solving the problems with an image restoring method that uses a Wiener filter (the natural image non-stationarity problem and evaluation amount problem), and while this method offers the advantage of enabling the problems with an image restoring method that uses a Wiener filter to be solved, there is a problem of restoration precision being low if there is degradation due to blurring in an image subject to processing (observed image, degraded image). 
     That is to say, with an image restoring method that uses a Kalman filter, in step 1, to consider the correlation between a pixel of interest and its surrounding pixels, and an AR coefficient is estimated for the pixel of interest and its surrounding pixels as preprocessing, and then, in step 2, a state space model (comprising a state equation and observation equation) is configured using the AR coefficient estimated in step 1—specifically, an image is restored using Kalman filter theory (a Kalman filter algorithm) by configuring a state equation from an AR coefficient estimated in step 1 and the original image, and configuring an observation equation from the original image, a degradation function, and noise. Therefore, an image restoring method that uses a Kalman filter is processing in the time domain only that does not presuppose stationarity, and is sequential processing that takes estimation error variance as an evaluation amount, and can therefore solve the problems of an image restoring method that uses a Wiener filter. 
     On the other hand, however, since a step 2 Kalman filter algorithm is executed using an AR coefficient estimated in step 1, there is a problem in that the restoration precision of a degraded image greatly depends on the precision of AR coefficient estimation in step 1 (an AR system problem). For example, in the case of a digital camera, if an image subject to processing includes degradation due to blurring (inaccurate focusing or the like), an AR order decision and AR coefficient estimation in step 1 become difficult, and therefore the precision of image restoration by means of a Kalman filter in step 2 is affected. 
     In this respect, accurate AR coefficient estimation is generally difficult. With image restoration, accurate AR coefficient estimation depends, for example, on a clear image (original image). This means that an original image must be known in advance, and therefore real-time processing is difficult. Also, even if it is possible to estimate an AR coefficient accurately in real time by some means or other, processing increases, and a problem of the amount of computation is unavoidable. Moreover, AR coefficient estimation is, in the first place, performed after an AR coefficient order has been decided, but deciding the order of an AR coefficient is extremely difficult, and it therefore follows that accurate AR coefficient estimation is difficult. 
     Therefore, there is now a demand for a simple and practical high-performance image restoring method that is capable of solving both the problems of an image restoring method that uses a Wiener filter and the problems of an image restoring method that uses a Kalman filter—that is, an image restoring method that has a simple configuration and can be used in a real environment, and furthermore provides high degraded image restoration performance (that is, image restoration capability). 
     It is an object of the present invention to provide a simple and practical image restoring apparatus and image restoring method capable of improving image restoration performance. 
     Solution to Problem 
     An image restoring apparatus of the present invention estimates original image information from only degraded image information in which unnecessary information is mixed in with the original image information, and employs a configuration having: a correlation computation section that calculates a correlation value of estimation error when a system state quantity at time n+1 that includes the original image information is estimated based on information until time n or time n+1 for degraded image information of only time n; a weighting factor calculation section that calculates a weighting factor for specifying a relationship of an optimum estimate of the state quantity at time n+1 based on information until time n+1, an optimum estimate of the state quantity at time n+1 based on information until time n, and estimation error of an observed quantity including the degraded image information, using a correlation value calculated by the correlation computation section, for degraded image information of only time n; and an optimum estimate calculation section that calculates an optimum estimate of the state quantity at time n+1 based on information until time n or time n+1, using a weighting factor calculated by the weighting factor calculation section, for degraded image information of only time n. 
     An image restoring apparatus of the present invention preferably estimates original image information from only degraded image information in which unnecessary information is mixed in with the original image information, and employs a configuration having: a first correlation computation section that calculates an estimation error correlation value matrix when a system state quantity at time n+1 that includes the original image information is estimated based on information until time n for degraded image information of only time n; a weighting factor calculation section that calculates a weighting factor matrix for specifying a relationship of an optimum estimate of the state quantity at time n+1 based on information until time n+1, an optimum estimate of the state quantity at time n+1 based on information until time n, and estimation error of an observed quantity including the degraded image information, using an estimation error correlation value matrix calculated by the first correlation computation section, for degraded image information of only time n; a first optimum estimate calculation section that calculates an optimum estimate vector of the state quantity at time n+1 based on information until time n for degraded image information of only time n; a second optimum estimate calculation section that calculates an optimum estimate vector of the state quantity at time n+1 based on information until time n+1, using a weighting factor matrix calculated by the weighting factor calculation section, for degraded image information of only time n; and a second correlation computation section that calculates an estimation error correlation value matrix when the state quantity at time n+1 is estimated based on information until time n+1 for degraded image information of only time n. 
     An image restoring method of the present invention estimates original image information from only degraded image information in which unnecessary information is mixed in with the original image information, and has: a correlation computation step of calculating a correlation value of estimation error when a system state quantity at time n+1 that includes the original image information is estimated based on information until time n or time n+1 for degraded image information of only time n; a weighting factor calculation step of calculating a weighting factor for specifying a relationship of an optimum estimate of the state quantity at time n+1 based on information until time n+1, an optimum estimate of the state quantity at time n+1 based on information until time n, and estimation error of an observed quantity including the degraded image information, using a correlation value calculated by the correlation computation step, for degraded image information of only time n; and an optimum estimate calculation step of calculating an optimum estimate of the state quantity at time n+1 based on information until time n or time n+1, using a weighting factor calculated by the weighting factor calculation step, for degraded image information of only time n. 
     An image restoring method of the present invention preferably estimates original image information from only degraded image information in which unnecessary information is mixed in with the original image information, and has: a first correlation computation step of calculating an estimation error correlation value matrix when a system state quantity at time n+1 that includes the original image information is estimated based on information until time n for degraded image information of only time n; a weighting factor calculation step of calculating a weighting factor matrix for specifying a relationship of an optimum estimate of the state quantity at time n+1 based on information until time n+1, an optimum estimate of the state quantity at time n+1 based on information until time n, and estimation error of an observed quantity including the degraded image information, using an estimation error correlation value matrix calculated by the first correlation computation step, for degraded image information of only time n; a first optimum estimate calculation step of calculating an optimum estimate vector of the state quantity at time n+1 based on information until time n for degraded image information of only time n; a second optimum estimate calculation step of calculating an optimum estimate vector of the state quantity at time n+1 based on information until time n+1, using a weighting factor matrix calculated by the weighting factor calculation step, for degraded image information of only time n; and a second correlation computation step of calculating an estimation error correlation value matrix when the state quantity at time n+1 is estimated based on information until time n+1 for degraded image information of only time n. 
     Advantageous Effects of Invention 
     The present invention enables a simple and practical image restoring apparatus and image restoring method to be obtained that are capable of improving image restoration performance. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram showing the configuration of an image restoring apparatus according to an embodiment of the present invention; 
         FIG. 2A  is a block diagram showing the configuration of the image restoration processing section in  FIG. 1 , and  FIG. 2B  is a block diagram showing the configuration of the first restoration processing section in  FIG. 2A ; 
         FIG. 3  is a drawing for explaining an image degradation process; 
         FIG. 4  is a block diagram representing a system configuration of a state space model of an invention method; 
         FIG. 5  is a drawing for explaining an actual example of formulation of a state equation of an invention method, wherein more particularly,  FIG. 5A  is a drawing showing a state process of a state space model,  FIG. 5B  is a drawing showing an example of a processing-object block and time variation thereof, and  FIG. 5C  is a drawing showing an actual example of a state equation; 
         FIG. 6  is a drawing for explaining a configuration of a state equation of an invention method; 
         FIG. 7  is a drawing for explaining an actual example of formulation of an observation equation of an invention method, wherein more particularly,  FIG. 7A  is a drawing showing an observation process of a state space model, and  FIG. 7B  is a drawing showing an actual example of an observation equation; 
         FIG. 8  is a drawing for explaining a configuration (general example) of a conventional general observation equation, wherein more particularly,  FIG. 8A  is a drawing showing a definition of a conventional observation process, and  FIG. 8B  is a drawing showing visually a range of state quantities that influence an observation quantity; 
         FIG. 9  is a drawing for explaining a configuration of an observation equation of an invention method, wherein more particularly,  FIG. 9A  is a drawing showing a definition of an observation process of an invention method, and  FIG. 9B  is a drawing showing visually a range of state quantities that influence an observation quantity; 
         FIG. 10  is a drawing for explaining an assignment method of factors that configure an observation transition matrix; 
         FIG. 11  is a drawing showing a range of state quantities that influence observation quantities, based on the observation transition matrix shown in  FIG. 9A , together with assigned factors; 
         FIG. 12  is a drawing showing an example of an algorithm of an invention method; 
         FIG. 13  is a flowchart showing a processing procedure that executes the algorithm in  FIG. 12 ; 
         FIG. 14  is an explanatory drawing that visually summarizes an invention method; 
         FIG. 15  is a drawing for explaining simulation conditions; 
         FIG. 16  is a drawing for explaining original image “Cameraman”; 
         FIG. 17  is a drawing showing simulation results (visual evaluation) for original image “Cameraman”; 
         FIG. 18  is a drawing in which the area circled with a dotted line in  FIG. 17  has been enlarged; 
         FIG. 19  is a drawing showing simulation results (visual evaluation) for original image “Cameraman”; 
         FIG. 20  is a drawing in which the area circled with a dotted line in  FIG. 19  has been enlarged; 
         FIG. 21  is a drawing showing simulation results (visual evaluation) for original image “Lenna”; 
         FIG. 22  is a drawing in which the area circled with a dotted line in  FIG. 21  has been enlarged; 
         FIG. 23  is a drawing showing simulation results (objective evaluation) for original images; 
         FIG. 24  is a drawing showing simulation results (subjective evaluation) for original images; 
         FIG. 25  is a flowchart showing an example of the operation of the image restoring apparatus in  FIG. 1 ; 
         FIG. 26  is a drawing for explaining an example of a detection method of step S 2300  in  FIG. 25 ; 
         FIG. 27  is a drawing for explaining an example of restoration mode implementation; and 
         FIG. 28  is a drawing for explaining another example of restoration mode implementation. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Now, an embodiment of the present invention will be described in detail with reference to the accompanying drawings. 
       FIG. 1  is a block diagram showing the configuration of an image restoring apparatus according to an embodiment of the present invention. Here, a preferred image restoring apparatus to which an image restoring method of the present invention is applied will be described taking a general-purpose image restoring apparatus suitable for a variety of uses as a particular example. 
     Image restoring apparatus  100  shown in  FIG. 1  is configured by means of a computer, and broadly comprises image input apparatus  110 , input interface section  120 , operating section  130 , internal interface section  140 , storage section  150 , image restoration processing section  160 , output interface section  170 , and image output apparatus  180 . 
     Image input apparatus  110  is an input apparatus for inputting image data (a degraded image) that is a restoration processing object to a camera as digital data. An input image may be a still image or a moving image. Camera  112 , scanner  114 , recording medium  116 , modem  118 , or the like, can be used as image input apparatus  110 . Camera  112  means any apparatus that has a photographic function, and, in addition to a digital camera (digital still camera or digital video camera), can include a mobile phone with a built-in camera function, a crime-prevention camera (surveillance camera), or a medical device for performing diagnostic imaging (such as an endoscope, X-ray machine, CT scanner, or MRI scanner), for example. Scanner  114  is a representative image input apparatus, and includes a film scanner that performs dedicated reading from a negative or positive file, or the like. Recording medium  116  refers to recording media capable of recording image data in general, and includes, for example, a magnetic disk (HDD, FD, or the like), an optical disk (CD, DVD, BD, or the like), magneto-optical disk (MO), flash memory (such as a memory card or USB memory), and so forth. Modem  118  is an apparatus for connecting to an external communication network (such as a telephone line or LAN, or the Internet, for example). The type of image input apparatus  110  can be selected as appropriate according to the use of image restoring apparatus  100 . 
     Input interface section  120  performs input processing such as converting image data provided from image input apparatus  110  to a data format that can be processed by a computer. Although not shown in the drawing, input interface section  120  is provided separately and independently according to the type of image input apparatus  110 . For example, input interface section  120  of recording medium  116  is called a drive, and various kinds of drive can be used according to the type of recording medium  116 . A drive is an apparatus that reads a recording medium, and for a recording medium only, input interface section  120  and output interface section  170  are normally integrated. Also, since modem  118  can function both as image input apparatus  110  and image output apparatus  180 , modem  118  is also normally integrated with input interface section  120  and output interface section  170 . Input interface section  120  may be an internal card (board) accommodated inside the computer body, or may be an external device connected via internal interface section  140 . 
     If image input apparatus  110  outputs image information as analog data, corresponding input interface section  120  has a sampling section and A/D conversion section (neither of which is shown). The sampling section performs sampling processing of an input analog signal at a predetermined sampling frequency, and outputs the result to the A/D conversion section. The sampling frequency can be changed according to the type of restoration processing object (information source). The A/D conversion section performs A/D conversion processing of an amplitude value of a sampled signal at a predetermined resolution. 
     Operating section  130  is typically a keyboard, mouse, touch panel, or the like, but a speech recognition apparatus may also be used. A user can use operating section  130  and operate the computer while confirming the operation on display  182  described later herein, for example. Operating section  130  has parameter setting section  132 , area specification section  134 , and restoration mode specification section  136 , described later herein. Parameter setting section  132  sets the values of various parameters necessary for image restoration processing according to this embodiment, described in detail later herein, by means of a user input operation. Area specification section  134  specifies an area (a specific range of an image) that is to be an object of image restoration processing for an input image by means of a user input operation. Restoration mode specification section  136  specifies a restoration mode described later herein by means of a user input operation. 
     Internal interface section  140  is inside the computer body, and has a function of mutually connecting input interface section  120 , operating section  130 , storage section  150 , image restoration processing section  160 , and output interface section  170 . The exchange of various signals inside the computer is performed via internal interface section  140 . 
     Storage section  150  has main storage apparatus  152  and auxiliary storage apparatus  154 . Main storage apparatus  152  is one component element of the computer body, and mainly stores programs and data. Auxiliary storage apparatus  154  is a storage apparatus that supplements insufficient main storage apparatus  152  capacity. Auxiliary storage apparatus  154  is typically a hard disk (HD), but may also be volatile storage such as a CD-ROM, DVD, SSD (Solid State Drive), flash memory, or the like, or a combination of these. A program (image restoration algorithm) that executes image restoration processing in this embodiment may be stored in storage section  150  (main storage apparatus  152  or auxiliary storage apparatus  154 ) beforehand, or may be installed in storage section  150  from recording medium  116  via both interface sections  120  and  140 , or downloaded to storage section  150  from outside via modem  118  and both interface sections  120  and  140 . 
     In order to execute a series of processing operations comprising fetching image data from image input apparatus  110 , performing image restoration processing on fetched image data, and fetching image data that has undergone restoration processing from image output apparatus  180 , a storage area required temporarily during data processing (also called a work area or work memory) and a storage area that stores image data to be output are necessary. These storage areas can be located in main storage apparatus  152  or auxiliary storage apparatus  154 , but here, for convenience of explanation, a case in which image data that has undergone restoration processing is output to display  182  described later herein is assumed, and display memory  156  is shown separately in the drawing. 
     Image restoration processing section  160  is a characteristic configuration element of the present invention that executes a built-in image restoration algorithm described later herein. With a conventional image restoring method that uses a Kalman filter, image restoration is implemented by means of two-step processing—that is, first deciding an AR order and estimating an AR coefficient, and then configuring a state space model (comprising a state equation and observation equation) using this estimated AR coefficient and executing Kalman filtering—whereas with an image restoring method of the present invention (hereinafter referred to as “invention method”), image restoration is implemented by means of a new prediction method comprising a state equation and an observation equation. Specifically, with the invention method, image restoration is implemented by configuring a new state space model (comprising a state equation and observation equation) that does not require the concept of an AR system, and, more specifically, by using a new state space model in which a state equation is configured using only clear image information (original image information), and an observation equation is configured using degraded image information, clear image information (original image information), blurring information, and noise. An image that is to be an object of image restoration may be a still image or a moving image. Details of an image restoring method of the present invention will be given later herein. 
     Image output apparatus  180  is an output apparatus for outputting image data that has undergone restoration processing by the computer (image restoration processing section  160 ) (a restored image) in a predetermined output form. For example, display  182 , printer  184 , recording medium  186 , modem  188 , or the like, can be used as image output apparatus  180 . Recording medium  186  and modem  188  may also be shared as image input apparatus  110  recording medium  116  and modem  118 . The type of image input apparatus  110  can be selected as appropriate according to the use of image restoring apparatus  100 . 
     Output interface section  170  performs output processing such as converting data that has undergone restoration processing by the computer (image restoration processing section  160 ) to a data format that can be output to image output apparatus  180 . Although not shown in the drawing, output interface section  170  is provided separately and independently according to the type of image output apparatus  180 . As described above, a recording medium and modem are normally integrated with input interface section  120  and output interface section  170 . Like input interface section  120 , output interface section  170  may be an internal card (board) accommodated inside the computer body, or may be an external device connected via internal interface section  140 . 
       FIG. 2A  is a block diagram showing the configuration of image restoration processing section  160  in  FIG. 1 , and  FIG. 2B  is a block diagram showing the configuration of first restoration processing section  160   a  in  FIG. 2A . 
     As shown in  FIG. 2A , in this embodiment image restoration processing section  160  has first restoration processing section  160   a  and second restoration processing section  160   b . First restoration processing section  160   a  implements an image restoring method of the present invention. Second restoration processing section  160   b  implements an image restoring method other than an image restoring method of the present invention—for example, a conventional image restoring method such as an image restoring method that uses a Wiener filter or an image restoring method that uses a Kalman filter. By this means, image restoration processing that uses first restoration processing section  160   a  and second restoration processing section  160   b  is possible. Below, an image restoring method that uses a Wiener filter (hereinafter referred to as “conventional method”) is taken as an example of a conventional image restoring method implemented by second restoration processing section  160   b.    
     As shown in  FIG. 2B , first restoration processing section  160   a  has initialization section  162 , correlation computation section  164 , weighting factor calculation section  166 , and optimum estimate calculation section  168 . First restoration processing section  160   a  restores a clear image (original image) from only captured data (a degraded image) by executing a built-in image restoration algorithm (invention method) through the collaboration of sections  162  through  168 . At this time, initialization section  162  performs initialization of the image restoration algorithm of the invention method, correlation computation section  164  performs estimation error correlation computation for an original image (desired information, clear image), weighting factor calculation section  166  performs calculation of a weighting factor necessary for calculation of an original image (desired information) optimum estimate, and optimum estimate calculation section  168  performs calculation of an original image (desired information) optimum estimate. The details of processing in sections  162  to  168  will be described later. 
     Below, image restoration processing operations performed by first restoration processing section  160   a  will be described in detail, but first, a degraded image model constituting an image restoration theory will be described. 
     A degraded image is generally obtained by means of a model in which noise is added to a convolution of an original image and a blurring Point Spread Function (PSF). That is to say, if an object is represented by f(n,m), a blurring point spread function by h(x,y), and noise by n(x,y), then degraded image g(x,y) obtained by means of an imaging system (an apparatus that photographs an object, a system that generates an image, and so forth) is represented by equation 1 below. Blurring point spread function h(x,y) represents imaging system characteristics including imaging conditions and the like. 
     
       
         
           
             
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       FIG. 3  is a drawing for explaining an image degradation process. 
     For example, when blurring occurs in the original image shown on the left side of  FIG. 3 , the image shown in the center of  FIG. 3  results, and when noise is added to this image, the degraded image shown on the right side of  FIG. 3  results. Blurring is caused by a certain pixel affecting surrounding pixels, but noise occurs without relation to pixels. As explained above, when an image is captured with a camera or the like, blurring occurs due to camera shake, inaccurate focusing, or the like, while noise occurs unavoidably due to a dark current, thermal noise, or the like. As shown in  FIG. 3 , the original image of a degraded image is simply the degraded image with blurring and noise removed. 
     As explained above, in the invention method, a new state space model (comprising a state equation and observation equation) is configured so as not to use the concept of an AR system. That is to say, a state equation is configured using only clear image information (original image information), and an observation equation is configured using degraded image information, clear image information (original image information), blurring information, and noise. 
     Specifically, in the invention method, a new state space model (comprising a state equation and observation equation) is configured, and this new state space model is represented by equations 2 below. In a state equation, vector x p1 (n) is a state vector (original image information), matrix Φ p1  is a state transition matrix, and vector δ p1 (n) is a drive source. In an observation equation, vector y p1 (n) is an observation vector (observed image information, degraded image information), matrix M p1  is an observation transition matrix, and vector ε p1 (n) is observed noise. Also, “n” is apparatus time n. Time n represents an order (“nth”) of processing of a processing-object block comprising a plurality of surrounding pixels including a pixel of interest. Here, one actual method (hereinafter referred to as “invention method 1”) is presented as an invention method. In the following description, subscript “p1” indicates an item relating to invention method 1.
 
[2]
 
[STATE EQUATION]:  x   p1 ( n+ 1)=Φ p1   x   p1 ( n )+δ p1 ( n+ 1)
 
[OBSERVATION EQUATION]:  y   p1 ( n )= M   p1   x   p1 ( n )+ε p1 ( n )  (Equations 2)
 
       FIG. 4  represents a system configuration according to this state space model by means of a block diagram. 
     As shown in  FIG. 4 , this state space model is configured by means of a state process and an observation process. The state process is described by means of a state equation, and the observation process is described by means of an observation equation. In  FIG. 4 , “ 201 ” is state vector x p1 (n) at time n, “ 202 ” is state vector x p1 (n+1) at time n+1, “ 203 ” is observation vector y p1 (n) at time n, “ 204 ” is observed noise vector ε p1 (n) at time n, “ 205 ” is drive source vector δ p1 (n+1) at time n+1, “ 206 ” is state transition matrix Φ p1 , and “ 207 ” is observation transition vector M p1 . A state equation in equations 2 describes an observation object system as a state space model, and represents a generation process for a time of an internal state—that is, state variables (here, state vectors x p1 (n) and x p1 (n+1)). Also, the observation equation in equations 2 describes a process observed via an observation apparatus of some kind, and shows how an observation result (here, observation vector y p1 (n)) is generated depending on an observed quantity—that is, input (here, state vector x p1 (n)). 
       FIG. 5  is a drawing for explaining an actual example of formulation of a state equation of the invention method, wherein more particularly,  FIG. 5A  is a drawing showing a state process of a state space model,  FIG. 5B  is a drawing showing an example of a processing-object block and time variation thereof, and  FIG. 5C  is a drawing showing an actual example of a state equation. 
     In this embodiment, in degraded image restoration processing, processing is performed that does not use only a processing-object pixel, but also includes surrounding pixels. That is to say, a surrounding K×K (where J&gt;K) area (hereinafter referred to as “area of interest”) centered on a certain processing-object pixel of a J×J-size image is taken as a processing-object block, and image restoration processing is performed using pixel information of the center of this processing-object block. Thus, “area of interest” means a range in which processing is performed using K×K pixels in image restoration. 
     For example, as shown in  FIG. 5 , if J=256 and K=3, a surrounding 3×3 area of interest centered on a certain processing-object pixel of a 256×256-size image becomes a processing-object block. In the drawing, a processing-object block is shaded. Image restoration processing is performed using pixel information of the center of this 3×3 area of interest. If, simply for convenience of explanation, numbers 1 to 36 are assigned to some pixels of a 256×256-size image as shown in  FIG. 5B , a processing-object block corresponding to state vector x p1 (n) at time n has 3×3=9 pixels numbered 1, 2, 3, 7, 8, 9, 13, 14, 15 as component pixels, and a processing-object block corresponding to state vector x p1 (n+1) at next time n+1 has 3×3=9 pixels numbered 7, 8, 9, 13, 14, 15, 19, 20, 21 as component pixels. 
     At this time, a state equation in equations 2 is defined by equation 3 below, which is also shown in  FIG. 5C . Here, state vector x p1 (n) is a 9×1 vector with nine items of pixel information x 1 (n), x 2 (n)), x 3 (n), x 4 (n), x 5 (n), x 6 (n), x 7 (n), x 8 (n), x 9 (n) included in a 3×3 processing-object block as a state quantity including original image information as elements. Also, state transition matrix Φ p1  is a 9×9 matrix defined by equation 3, and drive source vector δ p1 (n) is a 9×1 vector also defined by equation 3. 
     
       
         
           
             
               
                 
                   
                       
                   
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       FIG. 6  is a drawing for explaining the configuration of the state equation represented by equation 3. 
     Characteristics of the state equation represented by equation 3 are that some pixels of state transition matrix Φ p1  are set to “1” and the remaining pixels are all set to “0”, and that some pixels of drive source vector δ p1 (n) are represented by state quantity x i (n) (i=7, 8, 9) that is a colored signal. This is in order to mutually associate present state quantities (original image pixel information)) x 1 (n+1), x 2 (n+1), x 3 (n+1), x 4 (n+1), x 5 (n+1), x 6 (n+1), and past state quantities (original image pixel information) x 4 (n), x 5 (n), x 6 (n), x 7 (n), x 8 (n), x 9 (n) As a result, a state equation representing the relationship between x p1 (n) and x p1 (n+1) is composed of x p1 (n) from a clear image, Φ p1  comprising 0s and 1s, and drive source vector δ p1 (n) comprising a clear image that is a colored signal, and therefore is configured by means of only desired state quantities (original image pixel information)—that is, clear image information (original image information). 
       FIG. 7  is a drawing for explaining an actual example of formulation of an observation equation of the invention method, wherein more particularly,  FIG. 7A  is a drawing showing an observation process of a state space model, and  FIG. 7B  is a drawing showing an actual example of an observation equation. 
     Corresponding to the examples in  FIG. 5  and  FIG. 6 , an observation equation in equations 2 is defined by equation 4 below, which is also shown in  FIG. 7B . Here, observation vector y p1 (n) is a 9×1 vector with nine items of pixel information y 1 (n), y 2 (n), y 3 (n), y 4 (n), y 5 (n), y 6 (n), y 7 (n), y 8 (n), y 9 (n) included in a 3×3 processing-object block as observation quantities including degraded image information as elements. Also, observation transition matrix M p1  is a 9×9 matrix defined by equation 4, and corresponds to a blurring point spread function (PSF) in an image degradation model. Elements h r,s  (where r, s are h coordinates, and r, s=−1, 0, 1) configuring observation transition matrix M p1  are known, and are defined appropriately by conversion to data beforehand. Observed noise vector ε p1 (n) is a 9×9 vector having observed noise ε 1 (n), ε 2 (n), ε 3 (n), ε 4 (n), ε 5 (n), ε 6 (n), ε 7 (n), ε 8 (n), ε 9 (n) corresponding to nine pixels included in a 3×3 processing-object block as elements. 
     
       
         
           
             
               
                 
                   
                       
                   
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       FIG. 8  is a drawing for explaining a configuration (general example) of a conventional general observation equation, and  FIG. 9  is a drawing for explaining a configuration of an observation equation represented by equation 4. More particularly,  FIG. 8A  is a drawing showing a definition of a conventional observation process and  FIG. 8B  is a drawing showing visually a range of state quantities that influence an observation quantity, while  FIG. 9A  is a drawing showing a definition of an observation process of the invention method, and  FIG. 9B  is a drawing showing visually a range of state quantities that influence an observation quantity. For convenience, observed noise vector ε p1 (n) will be omitted in the descriptions of  FIG. 8  and  FIG. 9 . 
     As explained above, in degradation due to blurring in an image, a certain pixel degrades due to the influence of surrounding pixels. Thus, hitherto, an observation equation has generally been defined as shown in  FIG. 8A . In this case, blurring occurs due to the influence of all surrounding pixels. That is to say, each pixel in a processing-object block is influenced by all the pixels in the processing-object block. In other words, each observation quantity y i  (where i=1, 2, . . . , 9) is established under the influence of all state quantities x, (where i=1, 2, . . . , 9). This can be represented visually as shown in  FIG. 8B , for example. That is to say, as shown in  FIG. 8B , both when an observation quantity is y 1  and when an observation quantity is y 2 , for example, the observation quantity is influenced by all 3×3 (=9) state quantities x 1  through x 9 . 
     In this regard, a characteristic of an observation equation represented by equation 4 is that some pixels of observation transition matrix M p1  are set in a regular manner using 3×3 (=9) factors h r,s  (where r, s=−1, 0, 1), and the remaining elements are all set to “0.”. For example,  FIG. 9A  shows some equations (y 1 (n) and y 2 (n)) obtained by expanding an observation equation. The method of assigning factors h r,s  to observation transition matrix M p1  is as follows. Namely, nine factors h r,s  (where r, s=−1, 0, 1) are arranged in the form of a matrix (hereinafter referred to as a “factor matrix”) as shown in  FIG. 10 , and when the position in the center of the factor matrix (that is, factor h 0,0 ) is aligned with the position of pixel of interest i of observation quantity y i  (where i=1, 2, . . . , 9), factors h r,s  (where r, s=−1, 0, 1) are assigned to some pixels of transition matrix M p1  in accordance with that factor matrix. This can be represented visually as shown in  FIG. 9B , for example. That is to say, as shown in  FIG. 9B , for example, when an observation quantity is y1, the observation quantity is influenced by five (x 1  through x 5 ) of the 3×3 (=9) state quantities x 1  through x 9 , and when an observation quantity is y 2 , the observation quantity is influenced by six (x 1  through x 6 ) of state quantities x 1  through x 9 . 
       FIG. 11  is a drawing showing a range of state quantities x i  that influence observation quantities y i , based on observation transition matrix M p1  shown in  FIG. 9A , together with assigned factors h r,s  (where r, s=−1, 0, 1). For convenience of explanation, in  FIG. 11A  through  FIG. 11I , only observation quantity y i  of interest is shown in the left-hand processing-object block, and only h r,s  that is multiplied by state quantity x i  is shown in the location of each influenced state quantity x i  in the right-hand processing-object block. 
     With an observation equation represented by equation 4, observation quantity y 1  is influenced by five state quantities x 1  through x 5  as shown in  FIG. 11A , observation quantity y 2  is influenced by six state quantities x 1  through x 6  as shown in  FIG. 11B , observation quantity y 3  is influenced by seven state quantities x 1  through x 7  as shown in  FIG. 11C , 
     observation quantity y 4  is influenced by eight state quantities x 1  through x 8  as shown in  FIG. 11D , observation quantity y 5  is influenced by nine state quantities x 1  through x 9  as shown in  FIG. 11E , observation quantity y 6  is influenced by eight state quantities x 2  through x 9  as shown in  FIG. 11F , observation quantity y 7  is influenced by seven state quantities x 3  through x 9  as shown in  FIG. 11G , observation quantity y 8  is influenced by six state quantities x 4  through x 9  as shown in  FIG. 11H , and observation quantity y 9  is influenced by five state quantities x 5  through x 9  as shown in  FIG. 11I . 
       FIG. 12  is a drawing showing an example of an algorithm of the invention method. This algorithm does not depend on the type of image, and can be applied to a moving image as well as a still image. 
     As shown in  FIG. 12 , an algorithm of invention method 1 is broadly divided into an initialization process and an iteration process, and the iteration process is configured based on a new state space model (comprising a state equation and observation equation). In the iteration process, procedures 1 through 6 are repeated sequentially. 
       FIG. 13  is a flowchart showing a processing procedure that executes the algorithm in  FIG. 12 . 
     First, initialization section  162  performs initialization (S 1000 ). Specifically, in initialization section  162 , initial value x p1 (0|0) of the optimum estimate of a state vector—that is, a state quantity desired signal (original image signal) vector (hereinafter referred to as “desired signal optimum estimate vector”), initial value P p1 (0|0) of a correlation matrix of state vector estimation error (hereinafter referred to as “desired signal estimation error vector”), drive source vector covariance R δp1 (n) [i,j], and observed noise vector covariance R εp1 (n)[i,j], are set as shown in equations 5 below. Also, although not shown in  FIG. 12 , state transition matrix Φ p1  and observation transition matrix M p1  are set as shown in equation 3 and equation 4 respectively. Here, the initial value of a time n counter is set to “0.”. When vector and matrix elements are shown, the i&#39;th element of vector a(n) is denoted by a(n)[i], and the row i/column j element of matrix A(n) is denoted by A(n)[i,j]. In  FIG. 12 , desired signal optimum estimate vector x p1  is denoted by ^x p1 . 
     
       
         
           
             
               
                 
                   
                       
                   
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     Vector 0 K  is a K-dimensional zero vector, and matrix I K  is a K-order unitary matrix. When K=3, K 2 −K=6, and “i,j&gt;K 2 −K” corresponds to “i,j=7, 8, 9.”. E[δ p1 (n), δ p1   T (n)] is an autocorrelation matrix of drive source vector δ p1 (n). E[ε p1 (n), ε p1   T (n)][i,j] is an autocorrelation matrix of observed noise vector ε p1 , and is here assumed to be equal to σ 2   ε [i,j], and to be known. “Known” here means found and given by another arbitrary method (algorithm). If observed noise vector ε p1 (n) is white noise and is zero-average, σ 2   ε  is given by the variance of a predetermined number of samples. 
     Next, correlation matrix computation section  164  calculates an n→(n+1) estimation error correlation value (matrix) (hereinafter referred to as “correlation matrix”) (S 1100 ). Specifically, correlation matrix computation section  164  calculates correlation matrix P p1 (n+1|n) of error (a desired signal estimation error vector) when a time n+1 desired signal vector is estimated based on information until time n. This calculation is performed by means of equation 6 below using the values of state transition matrix Φ p1  and drive source vector covariance R δp1 (n+1)[i,j] set in step S 1000 , and desired signal estimation error vector correlation matrix P p1 (n|n) set in step S 1000  (when n=0) or calculated in previous step S 1600  (when n&gt;=1). This step S 1100  corresponds to procedure  1  of the iteration process in  FIG. 12 .
 
 P   p1 ( n+ 1 |n )=Φ p1   P   p1 ( n|n )Φ p1   T   +R   δ     p1   ( n+ 1)  (Equation 6).
 
     Next, weighting factor matrix calculation section  166  performs weighting factor (matrix) calculation (S 1200 ). Specifically, weighting factor matrix calculation section  166  calculates weighting factor matrix K p1 (n+1) such that a result of multiplying estimation error of an observed signal vector that is an observed quantity (hereinafter referred to as “observed signal estimation error vector”) by the weighting factor (matrix) and adding optimum estimate vector x p1 (n+1|n) of a desired signal at time n+1 based on information until time n is optimum estimate vector x p1 (n+1|n+1) of a desired signal at time n+1 based on information until time n+1. This calculation is performed by means of equation 7 below using desired signal estimation error vector correlation matrix P p1 (n+1|n) calculated in step S 1100 , and observation transition matrix M p1  and noise vector covariance R εp1 (n+1)[i,j] values set in step S 1000 . This step S 1200  corresponds to procedure  2  of the iteration process in  FIG. 12 .
 
[7]
 
 K   p1 ( n+ 1)={ P   p1 ( n+ 1 |n ) M   p1   T   }{M   p1   P   p1 ( n+ 1 |n ) M   p1   T   +R   ε     p1   ( n+ 1)} −1   (Equation 7)
 
     Next, optimum estimate vector calculation section  168  calculates an n→(n+1) state quantity (desired signal) optimum estimate (vector) (S 1300 ). Specifically, optimum estimate vector calculation section  168  calculates desired signal optimum estimate vector x p1 (n+1|n) at time n+1 based on information until time n. This calculation is performed by means of equation 8 below using state transition matrix Φ p1  set in step S 1000 , and desired signal optimum estimate vector x p1 (n|n) calculated in previous step S 1400 . This step S 1300  corresponds to procedure  3  of the iteration process in  FIG. 12 .
 
[8]
 
 {circumflex over (x)}   p1 ( n+ 1 |n )=Φ p1   {circumflex over (x)}   p1 ( n|n )  (Equation 8)
 
     Next, optimum estimate vector calculation section  168  calculates an (n+1)→(n+1) state quantity (desired signal) optimum estimate (vector) (S 1400 ). Specifically, optimum estimate vector calculation section  168  calculates desired signal optimum estimate vector x p1 (n+1|n+1) at time n+1 based on information until time n+1. This calculation is performed by means of equation 9 below using desired signal optimum estimate vector x p1 (n+1|n) calculated in step S 1300 , weighting factor matrix K p1 (n+1) calculated in step S 1200 , observation transition matrix M p1  set in step S 1000 , and observed signal vector y p1 (n+1) at time n+1. This step S 1400  corresponds to procedure  4  of the iteration process in  FIG. 12 .
 
[9]
 
 {circumflex over (x)}   p1 ( n+ 1 |n+ 1)= {circumflex over (x)}   p1 ( n+ 1 |n )+ K   p1 ( n+ 1){ y   p1 ( n+ 1)− M   p1   {circumflex over (x)}   p1 ( n+ 1 |n )}  (Equation 9)
 
     Next, it is determined whether or not processing is to be terminated (S 1500 ). This determination is made, for example, by determining whether or not time n has reached predetermined number of samples N. If the result of this determination is that time n has not reached predetermined number of samples N (S 1500 : NO), the processing flow proceeds to step S 1600 , whereas if the result of this determination is that time n has reached predetermined number of samples N (S 1500 : YES), the processing flow proceeds to step S 1800 . The criterion for this determination is not limited to the above example. For example, when processing is performed in real time, provision may be made for processing to be terminated when there are no more samples, even if time n has not reached predetermined number of samples N. 
     In step S 1600 , correlation matrix computation section  164  calculates an (n+1)→(n+1) error covariance matrix—that is, an (n+1)→(n+1) estimation error correlation value (matrix). Specifically, correlation matrix computation section  164  calculates correlation matrix P p1 (n+1|n+1) of error (a desired signal estimation error vector) when a desired signal vector of time n+1 is estimated based on information until time n+1. This calculation is performed by means of equation 10 below using weighting factor matrix K p1 (n+1) calculated in step S 1200 , observation transition matrix M p1  set in step S 1000 , and desired signal estimation error vector correlation matrix P p1 (n+1|n) calculated in step S 1100 . This step S 1600  corresponds to procedure  5  of the iteration process in  FIG. 12 .
 
[10]
 
 P   p1 ( n+ 1 |n+ 1)={ I−K   p1 ( n+ 1) M   p1   }P   p1 ( n+ 1 |n )  (Equation 10)
 
     Next, in step S 1700 , the time n counter is incremented by 1 (n=n+1), and the processing flow returns to step S 1100 . 
     On the other hand, in step S 1800 , a calculation result of this algorithm is temporarily stored as an output value. Specifically, desired signal optimum estimate vector x p1 (n+1|n+1) calculated in step S 1400  is temporarily stored in image restoration processing section  160  as an output value of this algorithm. 
       FIG. 14  is an explanatory drawing that visually summarizes the invention method. Thus, with invention method 1, a new state space model (comprising a state equation and observation equation) is configured, making possible image restoration processing by means of one-step processing. This is one major characteristic of the present invention. 
     Characteristics and effects of the invention method will be now described as contrasted with a conventional image restoring method that uses a Kalman filter. 
     As explained above, with a conventional image restoring method that uses a Kalman filter, image restoration is implemented by means of two-step processing (in which, in step 1, an AR order is decided and an AR coefficient is estimated, and then, in step 2, a state space model (comprising a state equation and observation equation) is configured using this AR coefficient, and Kalman filtering is executed). Therefore, it is only to be expected that image restoration performance by means of a Kalman filter in step 2 is greatly influenced by the precision of the AR order decision and AR coefficient estimation in step 1. In contrast, with the invention method, a new state space model (comprising a state equation and observation equation) is configured that does not require the concept of an AR system, and high-performance image restoration is implemented by means of a new one-step processing prediction method using this. Also, with the invention method, the number of processing steps can be reduced by one, enabling the amount of computation to be reduced, and thus making it possible to achieve a reduction in the circuit scale and memory capacity. 
     Also, with a conventional image restoring method that uses a Kalman filter, deciding the order of an AR coefficient when performing AR coefficient estimation in step 1 is a major problem. Since the order of an AR coefficient generally depends on a state quantity, it is theoretically difficult to decide the order of an AR coefficient accurately unless the state quantity is known. This means that a state quantity must be known, making real-time processing difficult. Also, since this results in an inaccurate AR coefficient order being used, accurate AR coefficient estimation is difficult. Therefore, this is a major cause of degradation of the image restoration performance of a conventional image restoring method that uses a Kalman filter. Also, even if it were possible to estimate an AR order and AR coefficient accurately in real time by means of some technology or other, an increase in the amount of computation would be unavoidable due to the addition of a processing step. In contrast, with the invention method, the concept of an AR system is not necessary, and therefore this kind of problem does not arise. 
     Also, with a conventional image restoring method that uses a Kalman filter, modeling is performed by representing a state quantity using an AR system. This means that a conventional image restoring method that uses a Kalman filter can only be applied to a state quantity capable of being modeled by means of an AR system. That is to say, a conventional image restoring method that uses a Kalman filter cannot be applied to a state quantity for which modeling by means of an AR system is difficult. In contrast, with the invention method, the concept of an AR system is not necessary, and therefore there is no such restriction on an application object. 
     Also, with a conventional image restoring method that uses a Kalman filter, Kalman filter theory is applied on the assumption that a drive source of a state equation is a white signal, and a state quantity and observed noise are uncorrelated. In contrast, with the invention method, an invention method algorithm can be executed by means of a special configuration of a state equation and observation equation even if a drive source is a colored signal (clear image). This means that the invention method can be implemented without considering general Kalman filter theory application conditions. That is to say, the invention method can be said to be more widely applicable than Kalman filter theory. 
     Therefore, the invention method, which renders the concept of an AR system unnecessary, is a technology that can make a contribution in areas that do not permit image recapturing, such as restoration of an instantaneous image of the heart, lungs, or the like in the medical field, restoration of a soiled or otherwise degraded old document, and character and object recognition. 
     The present inventors conducted simulations in order to demonstrate the effects of the present invention (the effectiveness of the invention method). Specifically, (1) visual evaluation, (2) objective evaluation, and (3) subjective evaluation were performed in order to evaluate the image restoration capability of invention method 1. Visual evaluation is an evaluation in which an original image and restored image are compared visually, objective evaluation is a numerical evaluation, and subjective evaluation is a poll. These are described in order below. 
     First, the simulation conditions will be described. 
       FIG. 15  is a drawing for explaining the simulation conditions. 
     In these simulations, the two images shown in FIG.  15 —that is, (a) “Cameraman” and (b) “Lenna”—were used. The two-dimensional Gaussian function shown in  FIG. 15  was used as a point spread function (PSF) model corresponding to blurring applied to an original image, and additive Gaussian white noise was used as noise. The signal to noise ratio (SNR) was assumed to be 30 dB. For comparison, simulations were performed under identical conditions for conventional method 1 (an image restoring method that uses a Wiener filter), conventional method 2 (an image restoring method that uses a projection filter), conventional method 3 (an image restoring method that uses a Kalman filter), and the invention method (invention method 1). As shown in  FIG. 16 , the “Cameraman” image, for example, can be said to have high stationarity since image variance does not vary for the part showing the sky, and high non-stationarity since image variance varies for the part showing the man&#39;s face. 
     (1) Visual evaluation.  FIG. 17  is a drawing showing simulation results (visual evaluation) for original image “Cameraman”, and  FIG. 18  is a drawing in which the area circled with a dotted line in  FIG. 17  has been enlarged. 
     As is clearly shown in  FIG. 18 , with conventional method 1, blurring has scarcely been removed. Also, with conventional method 2, blurring has been removed to a greater extent than with conventional method 1, but blurring still remains as compared with the original image. On the other hand, with conventional method 3, blurring appears to have been removed to give a clear image as compared with conventional methods 1 and 2, but the restored image differs from the original image. More particularly, with conventional method 3, the image is darker overall than the original image, and degradation is greater than in the degraded image in the part showing the sky. 
     In contrast, with the invention method, it can be confirmed that, as is clearly shown in  FIG. 18 , the original image has been more faithfully restored than in the case of conventional methods 1, 2, and 3. That is to say, the effectiveness of the invention method can be confirmed even in the enlarged images in  FIG. 18 . 
       FIG. 19  is a drawing showing simulation results (visual evaluation) for original image “Cameraman”, and  FIG. 20  is a drawing in which the area circled with a dotted line in  FIG. 19  has been enlarged. 
     As is clearly shown in  FIG. 20 , when the part showing the camera tripod is considered, with conventional method 1, blurring has not been removed at all. Also, with conventional method 2, blurring has been removed to a greater extent than with conventional method 1, but not to the extent of restoring the original image. On the other hand, with conventional method 3, blurring appears to have been removed to a greater extent than with conventional methods 1 and 2, but the entire image can be confirmed to have become coarser, and to be far removed from the original image. 
     In contrast, with the invention method, it can be confirmed that, as is clearly shown in  FIG. 20 , the original image has been more faithfully restored than in the case of conventional methods 1, 2, and 3. That is to say, the effectiveness of the invention method can be confirmed even in the enlarged images in  FIG. 20 . 
       FIG. 21  is a drawing showing simulation results (visual evaluation) for original image “Lenna”, and  FIG. 22  is a drawing in which the area circled with a dotted line in  FIG. 21  has been enlarged. 
     As is clearly shown in  FIG. 22 , with conventional method 1, blurring has scarcely been removed, and the restored image is whiter overall than the original image (brightness has been increased). Also, with conventional method 2, blurring has been removed to a greater extent than with conventional method 1, but not to the extent of restoring the original image. On the other hand, with conventional method 3, blurring appears to have been removed to give a clear image as compared with conventional methods 1 and 2, but degradation is greater than in the degraded image, and the image is far removed from the original image. This is particularly noticeable in the part showing skin. 
     In contrast, with the invention method, it can be confirmed that, as is clearly shown in  FIG. 22 , the original image has been more faithfully restored than in the case of conventional methods 1, 2, and 3. That is to say, the effectiveness of the invention method can be confirmed even in the enlarged images in  FIG. 22 . 
     (2) Objective evaluation (numerical evaluation).  FIG. 23  is a drawing showing simulation results (objective evaluation) for the original images. 
     Here, image restoration capability was evaluated using SNR out  [dB] represented by equation 11 below, which is also shown in  FIG. 23 , in order to evaluate the image restoration capability of conventional methods and the invention method. SNR is a ratio of a signal to noise, and the larger the numeric value of SNR, the smaller is the degree of degradation (blurring, noise, or the like), and the better an image can be said to be. 
     
       
         
           
             
               
                 
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     In this case, as shown in  FIG. 23 , it can be confirmed that the numeric value of SNR out  is larger for both the “Cameraman” and “Lenna” images in the case of the invention method than in the case of conventional methods 1, 2, and 3. It can be seen from this that the invention method also has higher image restoration capability than conventional methods 1, 2, and 3 from the standpoint of an objective evaluation.  FIG. 24  is a drawing showing simulation results (subjective evaluation) for the original images. 
     Here, subjective evaluation was performed by means of a poll in order to evaluate the image restoration capability of conventional methods and the invention method. Image restoration performance evaluation was performed by means of a poll using a 5-level MOS (Mean Opinion Score) based on ACR (Absolute Category Rating). MOS evaluation standard is as shown in  FIG. 24 . Fifty pollees evaluated images obtained by image restoration (see  FIG. 17  through  FIG. 22 ). Each pollee gave an evaluation value (score) of from 1 to 5 points, 5 points being the highest evaluation. 
     As shown in  FIG. 24 , it can be confirmed that in the MOS evaluation a higher evaluation was obtained for both the “Cameraman” and “Lenna” images in the case of the invention method than in the case of conventional methods 1, 2, and 3. It can be seen from this that the invention method also has higher image restoration capability than conventional methods 1, 2, and 3 from the standpoint of a subjective evaluation. 
     From the above simulation results, it can be seen that an image restoring method of the present invention (invention method 1) demonstrates higher image restoration capability than conventional methods. More particularly, as is clear from the visual evaluations of  FIG. 17  through  FIG. 22 , it can be seen that an image restoring method of the present invention achieves significantly higher restoration precision than conventional methods in edge parts and the like where non-stationarity is high. 
     The operation of image restoring apparatus  100  having the above configuration will now be described using the flowchart shown in  FIG. 25 . The flowchart shown in  FIG. 25  is stored in storage section  150  (main storage apparatus  152  or auxiliary storage apparatus  154 ) as a computer program, and is executed by a CPU (not shown). 
     First, in step S 2000 , image data that is a restoration processing object (a degraded image) is fetched from image input apparatus  110 , and is stored in a predetermined storage area of storage section  150  (main storage apparatus  152  or auxiliary storage apparatus  154 ). 
     Then, in step S 2050 , the image data fetched in step S 2000  is written to display memory  156  and displayed on display  182 . 
     Then, in step S 2100 , area specification processing is performed by area specification section  134  of operating section  130 . Specifically, when an area (a specific range of an image) that is to be an object of image restoration processing is specified within an image displayed on display  182  in step S 2050  by means of a user input operation, data of that specified area is generated. Area specification is performed on the screen by means of a pointer or the like, for example. If area specification is not performed by the user, the entire displayed image is treated as having been specified. 
     Then, in step S 2150 , it is determined whether or not enlargement processing is to be performed. This determination can be performed based on the specified area data generated in step S 2100 . Specifically, if the specified area is smaller than the entire image displayed, it is determined that enlargement processing is to be performed. If enlargement processing is to be performed as a result of this determination (S 2150 : YES), the processing flow proceeds to step S 2200 , whereas if enlargement processing is not to be performed (S 2150 : NO), the processing flow proceeds directly to step S 2250 . 
     In step S 2200 , enlargement processing is performed on the area specified in step S 2100 . Specifically, for example, enlargement processing is performed so that the specified area becomes of a size corresponding to the entire image displayed. The result of the enlargement processing is written to storage section  150  (main storage apparatus  152  or auxiliary storage apparatus  154 ) work memory. That image data is written to work memory even if enlargement processing is not performed. 
     Then, in step S 2250 , a time n processing-object block (for example, of 3×3 size) is selected. 
     Then, in step S 2300 , it is determined whether or not an abruptly varying area of the image has been detected for the processing-object block selected in step S 2250 . An abruptly varying area of the image corresponds to an edge part of the image or the like, for example. Specifically, for example, whether or not there is an abrupt pixel data variation point is determined for the image data written to work memory (irrespective of whether or not enlargement processing is performed) by sequentially scanning pixel data in the (3×3-size) processing-object block selected in step S 2250 . If the result of this determination is that an abruptly varying area of the image has been detected (S 2300 : YES), the processing flow proceeds to step S 2350 , whereas if the result is that an abruptly varying area of the image has not been detected (S 2300 : NO), the processing flow proceeds to step S 2400 . The absolute value of the difference between average value y′(n−1) of a certain quantity of past observation quantities and current observation quantity y(n)—that is, the value of |y′(n−1)−y(n)|—is compared with threshold value α. Then, if that value is greater than or equal to threshold value α—that is, |y′(n−1)−y(n)|&gt;=α—it is determined that there is an abrupt pixel data variation point, whereas if that value is less than threshold value α—that is, |y′(n−1)−y(n)|&lt;α—it is determined that there is no abrupt pixel data variation point. For example, in  FIG. 26 , average value y′(n−1) of a certain quantity of observation quantities of predetermined part  302  in processing-object block  301  of time n−1 is compared with observation quantity y(n) of pixel-of-interest part  304  in processing-object block  303  of time n. 
     In step S 2350 , image restoration processing according to the invention method is performed on the processing-object block selected in step S 2250 . As described above, with image restoration processing according to the invention method, high-precision restoration processing is possible even if there is an abrupt pixel data variation point—that is, even if an edge part or the like is included. An example of the detailed procedure of image restoration processing according to the invention method is as described using the flowchart in  FIG. 13 . 
     On the other hand, in step S 2400 , image restoration processing according to an image restoring method other than that of the invention method is performed on the processing-object block selected in step S 2250 . Any image restoring method, including an image restoring method that uses a Wiener filter, an image restoring method that uses a projection filter, or an image restoring method that uses a Kalman filter, can be used as this other image restoring method. The reason for this is that high-precision restoration processing can also be performed by means of another image restoring method if there is no abrupt pixel data variation point—that is, if an edge part or the like is not included. 
     Then, in step S 2450 , step S 2350  image restoration processing results or step S 2400  image restoration processing results are stored sequentially in storage section  150  (main storage apparatus  152  or auxiliary storage apparatus  154 ) work memory. 
     Then, in step S 2500 , the time n counter value is incremented by 1. 
     Then, in step S 2550 , it is determined whether or not one page worth of image restoration processing has ended. This determination is performed based on the time n counter value. If the result of this determination is that one page worth of image restoration processing has ended (S 2550 : YES), the processing flow proceeds to step S 2600 , whereas if the result is that one page worth of image restoration processing has not ended (S 2550 : NO), the processing flow returns to step S 2250 . 
     In step S 2600 , since one page worth of image restoration processing has ended, display memory  156  update processing is performed. That is to say, the configuration here provides for display memory  156  to be updated at a point in time at which one page worth of image restoration processing ends. 
     Then, in step S 2650 , it is determined whether or not image restoration processing has ended for all pages of image data fetched in step S 2000 . If the result of this determination is that image restoration processing has not ended for all pages (S 2650 : NO), the processing flow returns to step S 2250 , whereas if the result is that image restoration processing has ended for all pages (S 2650 : YES), the above series of processing steps is terminated. 
     An actual example of the setting and implementation of observation transition matrix M p1  corresponding to a point spread function (PSF) comprising blurring information will now be described using  FIG. 27  and  FIG. 28 . 
       FIG. 27  is a drawing for explaining an example of restoration mode implementation. 
     As explained above, observation transition matrix M p1  is a 9×9 matrix that is defined by equation 4 and corresponds to a blurring point spread function (PSF) in an image degradation model, and elements h r,s  (where r, s are h coordinates, and r, s=−1, 0, 1) configuring observation transition matrix M p1  are known and are defined appropriately by conversion to data beforehand. That is to say, in this embodiment, since the nature of blurring varies according to the image, the configuration provides for a number of sets of values of elements h r,s  of observation transition matrix M p1  constituting blurring information, so to speak, to be set beforehand as restoration modes, and for a user to specify such a restoration mode arbitrarily via restoration mode specification section  136  of operating section  130 . For example, in the example shown in  FIG. 27 , an appropriate observation transition matrix M p1  is set beforehand for each shooting mode, such as a nightscape mode, sports mode, and so forth, often set for digital cameras and the like. Therefore, a user can use an optimum restoration mode by switching the shooting mode. It is also possible for the restoration mode itself (the values of elements h r,s  of observation transition matrix M p1 ) to be readjusted automatically or manually. 
       FIG. 28  is a drawing for explaining another example of restoration mode implementation. 
     In the example shown in  FIG. 28 , since the nature of blurring varies according to the image, a processing-object degraded image is first selected on display  182  as shown in  FIG. 28(A) , and then a number of restored images for which observation transition matrix M p1  has been changed (values of elements h r,s  have been changed) are displayed on display  182  as shown in  FIG. 28(B) . At this time, a restored image is decided, for example, when the user selects an optimum restored image from among the plurality of restored images displayed on display  182  via operating section  130  (a touch panel or the like). Storing a user selection history as data makes it possible for a restoration mode (values of elements h r,s  of observation transition matrix M p1 ) in line with the user&#39;s preferences to be selected automatically. 
     Thus, according to this embodiment, a new state space model (comprising a state equation and observation equation) is configured that does not require the concept of an AR system, and image restoration is implemented by means of a new one-step processing prediction method, enabling simple and practical high-performance image restoration to be implemented. That is to say, this embodiment uses a simple configuration that does not require an AR order decision and AR coefficient estimation step, has practicality that enables restoration processing to be performed effectively even for a natural image with high non-stationarity, and also enables image restoration capability to be improved compared with conventional methods. 
     Also, as explained above, since this embodiment does not require the concept of an AR system, it can be widely applied to areas that do not permit image recapturing. Here, too, of course, as stated above, the type of image is not restricted, and may be a still image or a moving image. 
     For example, by regarding scratching, soiling, and so forth of an old document as noise, removing these using the invention method, and using character and object recognition technology, this embodiment can be expected to demonstrate its effectiveness in the deciphering, restoration, and conversion to a digital database of old documents. 
     In the field of crime prevention, also, the installation of crime-prevention cameras (surveillance cameras) and the like is becoming increasingly widespread, and in many case criminals are photographed by a crime-prevention camera or the like and the images help in the search for those criminals. However, the quality of such images is generally poor, and it is common for blurring to occur in images of moving objects. Moreover, such images usually show still greater degradation when enlarged. Thus, quicker identification of criminals can be expected by applying the invention method to such degraded images, including enlarged images, to remove blurring and noise from a degraded image and provide a clear image. Applying the invention method to degraded images, including enlarged images, to remove blurring and noise from a degraded image and provide a clear image in this way is not limited to the field of crime prevention, and can also be applied to cases in which determination of the cause of an accident, diagnosis of an equipment failure, or the like, is performed based on an image captured by a surveillance camera or the like. 
     Also, with the rapid spread of camera-equipped mobile phones, digital cameras, and so forth, in recent years, we have entered an age in which virtually everyone has such a device. However, image restoration technology provided in such products is face recognition, filtering, or suchlike technology for preventing blurring and noise, and does not make provision for situations that do not permit image recapturing. Therefore, applying the invention method to these products will make instantaneous image restoration possible in situations that do not permit image recapturing. 
     Meanwhile, in the medical field, one of the most effective means of checking a patient&#39;s health is diagnostic imaging using an endoscope, X-ray machine, CT scanner, MRI scanner, or the like. For example, in diagnostic imaging of the heart or lungs, a medical diagnosis is performed based on information that includes blurring and noise due to the action of the heart or lungs. Removing blurring and noise by applying the invention method to such diagnostic imaging makes it possible to provide a specialist with a clear image without delay, and can be expected to be of help in the early discovery of an illness. 
     In addition, with the growing popularity of car navigation systems in recent years, an increasing number of vehicles are being equipped with front and rear cameras. The invention method is also effective in the case of such vehicle front and rear cameras that require image restoration processing in real time. 
     The disclosure of Japanese Patent Application No. 2008-206316, filed on Aug. 8, 2008, including the specification, drawings and abstract, is incorporated herein by reference in its entirety. 
     INDUSTRIAL APPLICABILITY 
     An image restoring apparatus and image restoring method according to the present invention are suitable for use as a simple and practical image restoring apparatus and image restoring method capable of improving image restoration performance. 
     REFERENCE SIGNS LIST 
     
         
           100  Image restoring apparatus 
           110  Image input apparatus 
           112  Camera 
           114  Scanner 
           116 ,  186  Recording medium 
           118 ,  188  Modem 
           120  Input interface section 
           130  Operating section 
           132  Parameter setting section 
           134  Area specification section 
           136  Restoration mode specification section 
           140  Internal interface section 
           150  Storage section 
           152  Main storage apparatus 
           154  Auxiliary storage apparatus 
           156  Display memory 
           160  Image restoration processing section 
           160   a  First restoration processing section 
           160   b  Second restoration processing section 
           162  Initialization section 
           164  Correlation computation section 
           166  Weighting factor calculation section 
           168  Optimum estimate calculation section 
           170  Output interface section 
           180  Image output apparatus 
           182  Display 
           184  Printer