Patent Application: US-201515528080-A

Abstract:
an optical coherence tomography image composed of a plurality of a - scans of a structure is analysed by defining , for each a - scan , a set of neighbouring a - scans surrounding the a - slices scan . following an optional de - noising step , the neighbouring a - scans are aligned in the imaging direction , then a matrix x is formed from the aligned a - scans , and matrix completion is performed to obtain a reduced speckle noise image .

Description:
referring to fig1 , a method according to the invention is illustrated . the input to the method is an oct volume , of the kind which can be produced by a conventional oct method . the oct volume is made up of n b - scans ( also referred to in the art as “ frames ” or “ slices ”), b i for i = 1 , 2 , . . . n , as illustrated in fig2 . each b - scan b i consists of ma - scans , a i , j = 1 , 2 , . . . , m , which are each one - dimensional scans formed by imaging the object with a one - dimensional pencil of light extending in the direction which is vertical in fig1 . in other words , the oct volume consists of a set of a - scan lines a i , j , i = 1 , 2 , . . . , n , j = 1 , 2 , . . . , m , where n is the number of b - scans in the volume and m is the number of a - scans in each b - scan . a basic concept underlying the method of fig1 is to formulate a i , j as a sum of its underlying clean image l i , j , and noise g i , j , i . e ., the objective is to reconstruct l i , j from a i , j . it is impossible to solve this problem without some assumptions about l i , j and n i , j , but the embodiment is motivated by the assumption that l i , j is very similar within a small neighborhood . based on this assumption , we model the neighboring a - scans using similar model . where ( p , q ) εω and ω denotes a “ neighborhood ” ( or “ neighbor region ”), that is a set of a - scans which are neighbors of , and surround , the a - scan . thus , the set of a - scans form a two - dimensional array as viewed in the imaging direction . there are many ways to define the neighbor region . a first possible definition is as the rectangular region {( p , q )|− n ≦ p ≦ n ,− m ≦ q ≦ m } as illustrated in fig3 ( a ) . an alternative possible definition is as the elliptical region as illustrated in fig3 ( b ) . if n = m then the neighborhoods are respectively square and circular . in the experiments reported below , the neighborhoods were defined as the rectangular neighborhoods of fig3 ( a ) , using n = 1 and m = 2 . one way to implement this concept would be to define x as the matrix formed by stacking all the a - scans from ω as columns , i . e ., x =[ a i − n , j − m , . . . , a i + n , j + m ], l =[ l i − n , j − m , . . . , l i + n , j + m ], g =[ g i − n , j − m , . . . , g i + n , j + m ]. each column in l may be assumed to be very similar , so the rank of l is expected to be low , and accordingly the method can use low rank matrix completion to solve l from given x . unfortunately , applying the above technique directly to raw oct volume may lead to some blur of the a - scans due to content changes among neighboring a - scans . in addition , the inevitable eye movement also leads to some misalignment . for this reason , fig1 includes a step 2 of aligning the a - scans , before the a - scan reconstruction by matrix completion is performed in step 3 . furthermore , the original oct a - scans are affected by large speckle noise , which make it challenging job to align these a - scans in step 2 . therefore , a pre - processing step 1 is used to reduce the noise before step 2 is carried out . many algorithms [ 1 ]-[ 7 ] can be used for the noise - reduction step 1 . we use the srad algorithm [ 5 ]. srad is applied on every scan b i . specifically , given an intensity image i 0 ( x , y ), the output image i ( x , y ; t ) is evolved according to the pde : in the experimental results presented below , the iteration was performed 50 times . in the a - scan alignment step 2 , neighboring a - scans a i + p , j + q , ( p , q ) εω are aligned to a i , j by a vertical translation a p , q ( i . e ., moving up or down ) such that the difference in between is minimized , where q denotes the locations of neighboring a - scans . from our experience , computing the difference from an a - scan alone may lead to a result dominated by local speckle noise . therefore , we compute the difference between a i , j and a i + p , j + q using their neighboring a - scans as well . in step 2 , for each p and q we define a group (“ window ”) of a - scans centered at a i + p , j + q and a i , j , i . e ., g i + p , j + q =[ a i + p , j + q − w , a i + p , j + q − w + 1 , . . . , a i + p , j + q + w ] and g i , j =[ a i , j − w , a i , j − w + 1 , . . . , a i , j + w ] where w determines the window size , is used to compute the alignment . we find vertical translation δ p , q on g i + p , j + q such that the difference between the translated g i + p , j + q and g i , j is minimized many block matching algorithms can be used to find the alignment . in our numerical investigation of the embodiments , we use the diamond search strategy [ 8 ] to find the vertical translation because of its efficiency and easy implementation . we now present two methods by which step 3 can be carried out , i . e . two versions of step 3 . a first sub - step of both methods is to combine the aligned a - scans as the columns of the matrix x . that is , x =[ a i − n , j − m , . . . , a i + n , j + m ], where the content of the bracket is understood to be the aligned a - scans . method 1 : first , the embodiment decomposes x as a sum of low rank part and noise part , i . e ., where l is the low rank part with rank ( l )≦ r , and g is the noise . in the experiments reported below , we set r = 2 . the notation ∥ c ∥ f of any matrix x denotes the frobenius norm of the matrix ( i . e . the euclidean norm of a vector formed by stacking the columns of the matrix ). the optimization problem above is solved by the bilateral random projections [ 9 ] algorithm . the algorithm is summarized as follows : generate a random matrix a 1 a 1 εr d × r ; where d is the number of pixels in an a - scan compute { tilde over ( l )}=( xx t ) q x ; ( we use q = 2 ) y 1 ={ tilde over ( l )} a 1 , a 2 = y 1 y 2 ={ tilde over ( l )} t y 1 , y 1 ={ tilde over ( l )} y 2 using standard methods , calculate qr decomposition y 1 = q 1 r 1 , y 2 = q 2 r 2 , where q 1 and q 2 are orthogonal matrices and r 1 and r 2 are upper triangular matrices ; l = q 1 [ r 1 ( a 2 t y 1 ) − 1 r 2 t ] 1 /( 2q + 1 ) q 2 t ; method 2 : in the second method , the embodiment decomposes the x as a sum of low rank part , sparse part and noise part , i . e ., where l is the low rank part with rank ( l )≦ r , s is the sparse part with card ( s )≦ k and g is the noise . in the experiments reported below , r was equal to 2 , and k was set as 30 % of the total elements of the matrix s . the optimization problem above is solved by alternatively solving the following two sub - problems until convergence . while ∥ x − l t − s t ∥ f 2 /∥ x ∥ f 2 & gt ; ε , do { tilde over ( l )}=[( x − s t − 1 )( x − s t − 1 ) t ] q ( x − s t − 1 ); generate a random matrix a 1 εr d × r ; here d is the number of pixels in an a - scan . if rank ( a 2 t y 1 )& lt ; r then r = rank ( a 2 t y 1 ), go to the first step ; end if ; l t = q 1 [ r 1 ( a 2 t y 1 ) − 1 r 2 t ] 1 /( 2q + 1 ) q 2 t ; s 1 = δ ω ( x − l t ), ω is the nonzero subset of the first k largest entries of | x − l t |; δ ω is the projection of a matrix to ω . note that the term “ column ” is used here with a meaning which includes also a row of the matrix ; in other words , in principle , x could be formed by stacking the aligned a - scans as the rows of x , but then the transpose of x would be applied before the equations are solved in methods 1 and 2 . it can be see that the first method is a special case of the second method with s = 0 . the main difference is that the second model separates the difference due to content change from the noise . although fig1 shows no further processing steps , optionally various filters can be applied on the reconstructed a - scan volumes . suitable filters include enhanced lee , adaptive wiener filters , etc . for example , an adaptive wiener filter may be used . in addition , a threshold may be applied to assist the de - noising . mathematically , we apply the following process : where t low and t high are two adaptively determined thresholds . we first present results of the use of the embodiment for the method 1 ( i . e . the first variant of step 3 ). for convenience , we examine the b - scan formed from the reconstructed a - scans . fig5 shows an example of the image recovery including : ( i ) a b - scan of the original data ( labelled the “ raw image ”), ( ii ) the recovered image ( labelled the “ clean part ”). each column has been obtained from a respective performance of method 1 . that is , for a given column of the raw image , a corresponding matrix x is formed . from each x , corresponding matrices l and g are formed by method 1 . for each column of the raw image , the corresponding column of the “ clean part ” image is the column of the corresponding matrix l which has the same position in the corresponding matrix l which the raw image column has in the corresponding matrix x . ( iii ) a “ noise part ” image . for each column of the raw image , the corresponding column of the “ noise part ” image is the column of the corresponding matrix g which has the same position in the corresponding matrix g which the raw image column has in the corresponding matrix x . fig6 shows the result when step 3 is performed using the second variant for step 2 ( i . e . method 2 ), modelling x as x = l + s + g . ( i ) a b - scan of the original data ( labelled the “ raw image ”), ( ii ) the recovered image ( labelled the “ clean part ”). each column has been obtained from a respective performance of method 1 . that is , for a given column of the raw image , a corresponding matrix x is formed . from each x , corresponding matrices l , s and g are formed by method 2 . for each column of the raw image , the corresponding column of the “ clean part ” image is the column of the corresponding matrix l which has the same position in the corresponding matrix l which the raw image column has in the corresponding matrix x . ( iii ) a “ spare part ” image . for each column of the raw image , the corresponding column of the “ spare part ” image is the column of the corresponding matrix s which has the same position in the corresponding matrix s which the raw image column has in the corresponding matrix x . ( iv ) a “ noise part ” image . for each column of the raw image , the corresponding column of the “ noise part ” image is the column of the corresponding matrix g which has the same position in the corresponding matrix g which the raw image column has in the corresponding matrix x . in both cases , the image l is much sharper than the original image x . visually , the two results from the two variants of step 3 are very close without much visible difference . to evaluate the image quality , the contrast to noise ratio ( cnr ) metric [ 6 ] is used . it measures the contrast between a set of regions of interest and a background region . where μ r and σ r are the mean and variance of all the region of interest , μ b and σ b are the mean and variance of the background region . ten regions of interest from different retinal layers and one background region from each b - scan image were used to compute cnr . two typical oct volumes with 256 b - scan 992 × 512 images are used for testing . table 1 shows the comparison between ( i ) the raw volume data , ( ii ) a conventional method using a moving algorithm , and ( iii ) the embodiment using method 2 . as we can observe , the embodiment has a significantly higher cnr . fig7 uses box plot to show the variation of cnrs from different frames . fig8 shows visual difference between the proposed and baseline methods using two examples of raw data ( fig8 ( a ) and 8 ( d ) ). the images produced by the moving average method are shown in fig8 ( b ) and 8 ( e ) , while the images produced by an embodiment of the present invention using method 2 are shown in fig8 ( c ) and 8 ( d ) . compared to the raw frames and their moving average , the embodiment provides much better volume quality for structure examination . many more details of the retinal layers and structures such as lamina cribrosa can be examined more comfortably . furthermore , the case of performing step 3 by low rank recovery using bilateral random projection is about 20 times faster than traditional algorithms such as robust pca [ 8 ]. the computational process may be implemented using a computer system having a processor and a data storage device which stores program instructions for implementation by a processor , to cause the processor to carry out the method above substantially automatically ( that is , without human involvement , except optionally for initiation of the method ). the computer system may further comprise a display device having a screen for displaying the result of the method , and / or a printing device for generating a printed form of the result of the method , and / or an interface for transmitting the result of the method electronically . the computer system may be a general purpose computer , which receives the raw images from an interface . alternatively , it may be part of an oct imaging device which first captures the images and then processes them using the embodiment . the resulting images may be used by medical personnel as one tool to perform a diagnosis that a patient is suffering from a condition , and / or to select a medical treatment , such as a surgical procedure , to be carried out on the subject . the disclosure of the following references is incorporated herein by reference : j . s . lee , “ speckle analysis and smoothing of synthetic aperture radar images ,” computer graphics image processing , vol . 17 , pp . 24 - 32 , 1981 . 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