Patent Application: US-201313772765-A

Abstract:
the invention relates to the field of digital image processing and can find use in suppression of noise in digital images , formed by high - energy radiation , including x - ray radiation . specifically , the invention relates to a method for suppression of noise in digital x - ray images . the objective of the invention is to provide a method for noise suppression in digital x - ray images that has extended functionality , specifically , a method that makes it possible to reduce residual noise level and amount of artifacts in the form of discontinuities , directed along local orientation of object borders in textured image areas , to reduce residual lf noise level , and to eliminate over - smoothing of fine details . the technical innovation achieved is the improvement of digital image processing quality .

Description:
x - ray images can be produced , for example , by a device shown in fig1 . it includes x - ray tube 1 , emitting x - ray beam 2 . x - ray beam 2 enters detector 3 . detector 3 includes scintillation screen ( not shown ) and matrix array camera ( not shown ). scintillation screen is optically connected to the active area surface of the matrix array camera . x - ray beam 2 hits detector 3 , and scintillation screen converts it into visible light , which is further converted by detector sensors into a digital image . a filter , proposed by the present invention , is used to perform 4 - stage noise suppression . each of these stages is examined in detail below . estimation of noise variance , dependent on signal intensity . at this stage , original image is first estimated by applying linear low - frequency image filtering [ hensel et . al ., robust and fast estimation of signal - dependent noise in medical x - ray image sequences , springer , 2006 ]. to meet strict filtering speed requirements , it is reasonable to use simple linear filtering ( e . g . by applying binomial filter ). the resulting smoothed image is used to obtain a noise image , which essentially represents the difference between the original and the filtered images . image estimation by applying simple image filters is not perfect , as image edges tend to become over - smoothed . as a result , using difference between the original image and the smoothed image leads to forming a noise image , which includes , in addition to noise pixels in smoothed areas , a certain amount of pixels , associated with abrupt changes ( i . e . borders of anatomical structures ; such pixels are hereafter referred to as non - noise pixels ). such pixels can considerably distort the estimated variance value and should be excluded from calculations . this can be accomplished by various methods [ foi et . al ., practical poissonian - gaussian noise modeling and fitting for single - image raw - data . image processing , ieee transactions on 17 , 1737 - 1754 ( october 2008 ), salmeri et . al ., signal - dependent noise characterization for mammographic images denoising . imeko tc4 symposium ( imekotc4 &# 39 ; 08 ), firenze , italy , september 2008 ], which essentially boil down to thresholding of smoothed derivatives of the original image , where threshold value is determined by local estimation of signal / noise relationship . in image areas with large number of details such estimation usually proves to be inadequate . therefore , as far as rejection of borders is concerned , this invention proposes a simpler approach to border enhancement that does not require calculation of derived and local estimates of standard deviation . such morphological approach to non - noise pixels rejection can be summarized as follows : the noise image is divided into two components — binary images of positive and negative changes ; to enhance areas , associated with borders , resulting images are subjected to morphological operations of erosion , followed by dilatation ; processed images are combined to receive a single binary image , i . e . a map of original image borders . to better preserve fine structures , morphological erosion and dilatation are performed by small size masks ( 2 × 2 window ). calculation of interval estimations of noise variance involves identifying minimum and maximum intensity of estimation image ( intensity range edges ), followed by selection of partitioning interval , e . g ., equal to 32 gray gradations . after that , for each image pixel it is necessary to identify an interval that pixel &# 39 ; s value pertains to , and to use the relevant noise image pixel value to calculate noise variance estimation within that interval ( this involves eliminating pixels that are associated with borders ). in calculating interval estimation of noise variance , various formulas may be applied , such as standard unbiased estimator or robust estimation , based on median absolute deviation formula [ hensel et . al ., robust and fast estimation of signal - dependent noise in medical x - ray image sequences , springer , 2006 ; foi et . al ., practical poissonian - gaussian noise modeling and fitting for single - image raw - data , image processing , ieee transactions on 17 , 1737 - 1754 , 2008 ]. this procedure results in a tabulated function that defines noise variance dependence on signal intensity . inaccuracies in generation of borders map may cause serious errors in calculation of variance interval estimations . therefore such estimations are refined by applying iterative outlier removal technique [ hensel et . al ., robust and fast estimation of signal - dependent noise in medical x - ray image sequences , springer , 2006 ]: specifically , this involves iterative elimination in each interval of noise pixels values that exceed in absolute magnitude a threshold , equal to three standard noise deviations , followed by recalculation of noise variance estimation in that interval . once calculation of noise variance interval estimations is completed , estimation of noise variance dependence on signal intensity is performed . using a parametric estimator , it is basically possible to develop a noise model parameters estimation ( 1 ), using some of available methods ( e . g . least - squares method , likelyhood function minimization or directed optimization ). it is also possible to account for sensor nonlinearities [ foi et . al ., practical poissonian - gaussian noise modeling and fitting for single - image raw - data , image processing , ieee transactions on 17 , 1737 - 1754 , 2008 ]. however , as was noted in [ hensel et . al ., robust and fast estimation of signal - dependent noise in medical x - ray image sequences , springer , 2006 ], for a number of reasons , development of parametric model , able to adequately define noise variance dependence on signal intensity , can pose serious difficulties . such reasons might include sensor operational nonlinearities , or nonlinear original image preprocessing techniques ( such as logarithmation ). therefore , from the point of view of implementation convenience and application versatility , the optimum approach is the one that involves development of non - parametric noise - signal dependency estimation based on estimations of interval variance . the present invention uses non - parametric approach to determination of required relationship , which involves development of interpolating tabulated function based on identified interval estimations of noise variance . such tabulated function is formed based on robust local linear approximation of interval estimations of noise variance . application of robust methods allows additional reduction of outlier effects ( gross errors in interval variance estimations ), while locality of approximation ensures iteration of complex run of a curve , describing dependence of noise on signal intensity . therefore the resultant tabulated function of each original image intensity associates with noise variance estimation . the function of table entry points can be performed by , e . g ., intensities of the estimation image . for a diagram of such single tabulated function ( solid line ) 5 , plotted for the image shown in fig2 , alongside with interval estimations of rms noise deviation 6 ( circles ), see fig3 . in practice , parametric noise estimation may include an approach that involves a conversion process , stabilizing noise variance in the original image [ starck et . al ., image processing and data analysis : the multiscale approach . cambridge university press , 1998 , yane , digital image processing , moscow , technosphera , 2007 ]. in this case , the problem of filtering noise , dependent on signal intensity , is reduced to the challenge of suppression of additive signal - independent noise with preset variance properties . the present invention uses non - parametric noise estimation , therefore it is suggested that the following approach is used in noise map development : building , based on estimation image and interpolating table , a noise map , i . e . an image where each pixel estimates root - mean - square deviation of noise in associated pixel of the original image . the noise map provides pixel - by - pixel noise estimation at precision level , sufficient for practical applications . for a noise map , developed based on image in fig2 , see fig4 . this example illustrates performance of noise estimation algorithm in overexposure ( i . e . sensor saturation / clutter ) conditions that can be easily observed around the head ( light halo , pos . 4 ) on fig2 . when standard filtering process ( 3 ) is used , as the block size increases , filtering quality , measured in peak values of signal / noise relationship , improves . in addition to quality improvement , in case of application of vectorized non - local mean ( 4 ), filter execution speed increases along with pixel block enlargement . however , in highly textured image areas and along abrupt intensity variations ( borders ), block enlargement leads to relatively high level of residual noise and specific artifacts in the form of discontinuities , directed along local orientation of object borders . presence of residual noise and artifacts in textured areas can be attributed to decrease of noise suppression rate , which is caused by reduction of the quantity of such blocks . high level of residual noise can also be observed in smooth areas of processed image . the present invention relates to development of combined noise filtering method , based on combination of bilateral filter and non - local means filter , that should improve downsides of the standard method . such method is hereafter referred to as combined filtering algorithm , or simply combined filter . combined bilateral non - local filtering is based on the following principle . in the course of averaging , weight of each pixel is calculated based on its proximity to the current pixel , using two metrics : bilateral ( brightness ) and non - local ( structural ). if the current pixel and the comparison pixel are close from the point of view of non - local means filter , i . e . their blocks are structurally similar , domination of structural weight should be observed . otherwise , if blocks are not similar , yet current pixel and comparison pixel brightness levels are close , this leads to enhancement of the effect of brightness weight . to reduce residual noise , averaging weights should be calculated based on smoothed ( estimation ) image , which can be produced by applying a simple linear low - frequency filter to the original image . mathematically , this principle leads to the following modification of standard filtering process ( 3 ): here , w ( p , q )= v ( b ( p , q ), n ( p , q )) represents a function that defines averaging weight of combined filter , selected in such a way as to satisfy the combined filtering principle ; b ( p , q )= g ( q − p , a )· f (( ū ( p )− ū ( q )), σ ( ū ( p )), k b , h b ) represents the weight of bilateral filter , and g ( s , a )= exp (− s · s t / a 2 ) represents gaussian function ; n ( p , q )= f (∥ ū ( p , f )− ū ( q , f )∥ 2 , σ ( ū ( p )), k n , h n ) represents the weight of non - local means filter ; ū ( p ), ū ( p , f ) represents the respective values of pixel and pixel block in estimation image ; and σ ( ū ( p )) represents the value of rms error of estimation image noise , dependent on signal intensity . to determine similarity of pixels brightness - and structure - wise , a continuous transition threshold function f ( r , σ , k , h )= exp (− max ( r 2 − k · σ 2 , 0 )/ h 2 ) is used , where k and h represent parameters . here , w ( p m , q , f )= v ( b ( p m , q , f ), n ( p m , q )) represents block of values of weight function of combined filter ; and b ( p m , q , f ) represents block of values of weight function of the bilateral filter , b ( p m , q , f )={ b ( p m + s , q + s ), sεs ( 0 , f )}, and both such values are calculated as b ( p m + s , q + s )= g ( s , a )· f (( ū ( p m + s )− ū ( q + s )), σ ( ū ( p m + s )), k b , h b ), where g ( s , a ) represents a gaussian function ; n ( p m , q )= f (∥ ū ( p m , f )− ū ( q , f )∥ 2 , σ ( ū ( p m )), k n , h n ) represents weight of non - local means filter , which is the same for all pixels of the comparison block ; σ ( u ( p m )) and σ ( ū ( p m , f )) represent the value and the rms error block of estimation image pixel noise , dependent on signal intensity ; • represents an operator for bit - by - bit multiplication / division of blocks ; and û ( p m , f ) represents the result estimation of intensities of pixels within the current partition block . in the combined filtering process , described here ( 5 ), ( 6 ), it is of importance to properly select weight function v that can be determined by various methods . in terms of execution speed - effective combined filtering algorithm , simple yet quite qualitatively effective version of combined filter can be created by framing weight function as a preset proportion of brightness and structural weights : v ( b , n )=( 1 − λ )· b ( p m , q , f )+ λ · n ( p m , q ). ( 8 ) the selected value of λ should be close to maximum possible non - local means filter weight value , e . g . λ ≈ 0 . 8 . selection of ( 7 ) or ( 8 ) weight function allows separating bilateral filter and non - local filter . if filter separation is used , combined filtration comprises sequential bilateral and non - local filtering and further combining obtained results . separation of filters allows selecting more speed - effective values of filter parameters ( e . g . reducing bilateral filter averaging area ), as well as eliminating unnecessary bilateral filtering of pixels , associated with regions where partition blocks overlap . by the example of vectorized combined filter ( 6 ), when using weight function ( 8 ), separable combined filtering can be written down as follows : { circumflex over ( u )}( p m , f )==( λ · û n ( p m , f )+( 1 − λ )· û b ( p m , f ))/( λ · c ( p m )+( 1 − λ )· c ( p m , f )) ( 9 ) represents the result of filtering by vectorized non - local means filter ( without normalizing with respect to total weight ); û b ( p m , f ) represents an image pixel block , processed by bilateral filter ( without normalizing with respect to total weight ), therefore represents total weight and total weight block of non - local means filter and bilateral filter , respectively . when separable bilateral filter is used , separable form of combined filtering ( 9 ) also allows increasing filtering speed , making it considerably closer to execution speed of vectorized version of non - local means filter . effectiveness of combined filtering method ( 6 ) with type ( 8 ) weight is demonstrated in fig5 ( a , b , c , d , e ), where : 5 a is a fragment of radiological test pattern ; 5 b is an image that has been processed by vectorized version ( 4 ) of standard non - local means filter ; 5 c is an image that has been processed by combined filter ; 5 d is a difference between 5 a and 5 b ; and 5 e is a difference between 5 a and 5 c . artifacts , typical of standard non - local means filtering method , well visible along object borders ( figure strips )), turn out to be considerably reduced as a result of application of combined filter . in smooth region of an image ( i . e . areas of the same brightness with homoscedasticity manifesting itself as noise ), bilateral filter , as well as non - local means filter , shows characteristics of an elementary linear neighborhood averaging filter ( i . e . it operates as moving average ). due to using finite averaging region , part of spectral noise components , associated with low frequencies , will not be suppressed and will become well visible in smooth areas of an image . the present invention uses image pyramid with bilateral linear regression filtering for residual lf noise suppression [ burt et . al ., the laplacian pyramid as a compact image code , ieee trans . commun ., vol . com - 31 , pp . 532 - 540 , april 1983 ; tomasi et . al ., bilateral filtering for gray and color images , in proc . 6 th int . conf computer vision , new delhi , india , 1998 , pp . 839 - 846 ]. image pyramid is constructed based on the following formulae : here , i ( p ) represents an original image ; a k ( p ), h k ( p ) represents low - frequency ( approximating ) and high - frequency ( detailing ) images of level k of the image pyramid ; reduce represents an operator for filtering and double reduction of image sampling rate ( decimation ), i . e . reduce ( a )=( a * l r )↓ 2 , where l r represents linear lf filter , and ↓ 2 represents decimation ; expand represents an operator for image downsampling and filtering , i . e . expand ( a )=( a ↑ 2 )* l e , where ↑ 2 represents downsampling , and l e represents linear low - frequency filter . noise variance distribution is estimated based on low - frequency components of the pyramid ( 10 ). to achieve that , white gaussian noise ( awgn ) with standard deviation σ is supplied to the combined filter input . based on the above - mentioned equivalence of combined filter and neighborhood averaging filter in smooth image areas , dependence of lf images rms error value on pyramid level number is calculated : where σ 0 represents rms error level of noise in an image , subjected to combined filtering ; σ k represents rms error level of image noise a k ( p ) in pyramid ( 10 ); and q ( k , l r ) represents reduction rate of rms error of noise in images a k ( p ). to suppress residual lf noise , images a k ( p ) of pyramid ( 10 ) are processed by bilateral filtering . to reduce staircasing artifacts [ buades et . al ., the staircasing effect in neighborhood filters and its solution , ieee transactions on image processing , vol . 15 ( 6 ), pp . 1499 - 1505 , 2006 ], bilateral linear regression filter is applied : s ( i , j , t ) represents an area of radius t , centered at the current pixel a k ( i , j ) of the image with number k of pyramid ( 10 ); w ( x , y )= g ( x − i , y − j , a )· f (( a k ( i , j )− a k ( x , y )), σ k ( i , j )) represents averaging weight , where spatial proximity of pixels is defined by gaussian function g ( x − i , y − j , a )= exp (−(( x − i ) 2 +( y − j ) 2 )/ a 2 ), and brightness proximity of pixels is estimated by function f (( a k ( i , j )− a k ( x , y ), σ k ( i , j ))= exp (−( a k ( i , j )− a k ( x , y )) 2 / σ k 2 ( i , j )); σ k ( i , j ) represents signal - dependent rms error of approximating pyramid image , defined by noise map and dependence of type ( 11 ); and â k ( i , j ) represents the result estimation of intensity of the current image pixel . to speed up filtering process , separable filter version ( 12 ) is used . filtered approximating components of the pyramid are used to restore the image with reduced level of residual low - frequency noise { circumflex over ( a )} k - 1 ( p )={ circumflex over ( h )} k - 1 ( p )+ expand ({ circumflex over ( a )} k ( p )), k = n , 1 . ( 13 ) here , symbols â , ĥ refer to the fact , that construction of pyramid ( 10 ) involved filtering of lf images by filter ( 12 ). in the present invention , over - smoothing of useful high - frequency information is corrected by blending filtered image and its original version together . blending weights are calculated based on pixel and structural similarities of filtered image and original image . to determine structural similarity , euclidean distance between pixel blocks of the images is calculated ; to determine pixel similarity ( intensity similarity ), the distance between brightness levels of pixels of the relevant images is calculated . let û ( p ) and u ( p ) represent intensity values of filtered and original image in pixel p , respectively . in this case , pixel similarity of frames is calculated based on the following threshold function : w i ( p )= exp (− max (({ circumflex over ( u )}( p )− u ( p )) 2 − k i · σ 2 ( u ( p )), 0 )/ h i 2 ), ( 14 ) where k i , h i represent parameters that define characteristic shape of distribution ; and σ 2 ( u ( p )) represents noise variance value in pixel p . in turn , structural similarity of filtered image and original image is determined based on the following formula : w s ( p )= exp ( max (−(∥{ circumflex over ( u )}( p )− u ( p )∥ 2 2 − k s · σ 2 ( u ( p )), 0 )/ h s 2 , ( 15 ) where k s , t s represent parameters , defining shape of threshold function ; and ∥ û ( p )− u ( p )∥ 2 2 represents squared euclidian distance between pixel blocks of the respective images . calculated pixel and structural similarities of the images are combined to determine the final measure of pixel - structural similarity in the following way : w ( p )= w i ( p )· w i ( p )+( 1 − w i ( p ))· w s ( p ). ( 16 ) in this case , over - smoothing correction involves combining filtered image and original noisy image based on the following rule : û c ( p )= w ( p )·{ circumflex over ( u )}( p )+( 1 − w ( p ))· u ( p ). ( 17 ) setting similarity measure as ( 16 ), along with correction based on formula ( 17 ), allows filtering individual abrupt image changes ( i . e . outliers ). to estimate image noise variance , firstly , estimation image and noise image are obtained by applying to original image i ( x , y ) the following 3 × 3 low - frequency linear binomial filter h 1 =[ 1 , 2 , 1 ]/ 4 , h = h 1 t · h . it allows creating smoothed image i e ( p )= i * h , where * represents convolution . after that , noise image n e ( p )= i ( p )− i e ( p ) is calculated . by removing borders from variance calculations based on noise image n e ( p ), images of positive and negative changes are formed : to separate large areas , associated with borders , these binary images are subjected to step - by - step morphological erosion and dilatation , using masks of 2 × 2 size : b e − 1 ( p )= dilate [ 2 × 2 ] ( erode [ 2 × 2 ]( n e − ( p ))), b e + ( p )= dilate [ 2 × 2 ]( erode [ 2 × 2 ]( n e + ( p ))). then these images are combined to create a map of the original image borders e ( p )= b e − ( p )∩ b e + ( p ). to calculate interval estimations of noise variance , minimum i min and maximum i max of image intensity i e ( p ) are determined , increment h m is selected , and intensity range is partitioned into intervals m i in increments of h m ( e . g . h m = 32 ). for each image pixel i e ( p ), an interval such pixel &# 39 ; s value pertains to is identified , and the relevant pixel value of the image n e ( p ) is used to calculate noise variance estimation σ 2 ( i ) within that interval m i , which involves eliminating pixels with border map value e ( p )= 1 . in calculating interval estimation of noise variance , unbiased variance estimator is used : where n e i ( j ) represents the value of pixel of noise image n e ( p ) from interval m i , n i represents total amount of accumulated values of noise image pixels within interval m i , and n i e represents average value of noise pixels within interval m i . the obtained interval estimations of variance σ 2 ( i ) are refined in such a way as to iteratively eliminate in each interval m i the values of noise pixels that exceed in absolute magnitude a threshold , equal to three standard noise deviations , which is followed by conversion of noise variance estimation in that interval : n e i [ k + 1 ]={ n e ( p )|( n e ( p ) ε n e i [ k ])∩( n e ( p )≦ 3σ ( i ))}, where n e i [ k + 1 ] represents a set of values of noise pixels within interval m i with iteration k . further calculations use only intervals , which have accumulated sufficient number of values of noise pixels ( e . g . at least 500 ). besides , excluded from consideration are intervals with average value n i e significantly different from zero ( deviating from zero by more than a half of interval grid increment h m ), as such intervals are most probably dominated by residual values of non - noise pixels . to estimate relationship of noise variance and intensity , interpolating tabulated function is created based on noise variance estimations obtained . such tabulated function is formed based on robust local linear approximation of interval estimations of noise variance . for that , on interval grid m i , increment h i and approximation radius r l are selected ( they can be made dependent on the number of points n i within intervals m i ). values of variance - intensity tabulated function , developed at the previous stage , are approximated based on the following rule : { circumflex over ( σ )} 2 ( k · h i )= a · m k + b , where k represents the number of approximation node ; m k represents the centre of interval m i ( k · h i ); and parameters a , b are calculated based on sum of absolute deviations [ press et . al ., numerical recipes in c : the art of scientific computing , second edition . new york : cambridge university press , 1999 ] the resultant list of values { m i ( k · h i ),{ circumflex over ( σ )} 2 ( k · h i )} is interpolated over the entire range of intensities [ i min , i msc ], thus forming interpolating table of the desired dependence of noise variance on signal intensity . further on , based on the estimation image and the interpolating table , a noise map is developed , i . e . an image where each pixel estimates noise variance in associated pixel of the original image . to ensure proper balance between filtering quality and filtering speed , combined bilateral non - local filtering is performed using formula ( 9 ), where λ = 0 . 85 , averaging region radius t = 5 , pixel block radius f = 4 , and blocks are assumed to overlap by 1 pixel . to determine similarity of pixels from the point of view of brightness and structure , a continuous transition threshold function f ( r , σ , k , h )= exp (− max ( r 2 − k · σ 2 , 0 )/ h 2 ) is used , where k and h represent parameters . parameter value for brightness similarity is assumed as k b = 9 , and parameter value for structural similarity is assumed as k n = 2 . 1 . values of parameter h b are selected in such a way as to achieve the pre - set rate of decreasing of function f , which is achieved by setting function value f ( r , σ , k , h ), e . g . as f = 0 . 1 , at preset threshold value level kσ 2 , e . g . as kσ 2 = 10 · σ 2 , which results in parameter value h b = 9 . in calculation of weight function , geometric distance is not taken in consideration . in similar way , parameter h n value for non - local means filter weight function is identified : at level kσ 2 = 3 · σ 2 , function value is assumed as f = 0 . 5 , which results in parameter value h n = 1 . estimation image , used as a basis for calculation of averaging weights , is determined by filtering the original image with the following lf linear binomial filter of h 1 =[ 1 , 2 , 1 ]/ 4 , h = h 1 t ˜ h size . the value of parameter σ is taken from the noise map , developed at noise estimation stage . at residual lf noise filtering stage , image pyramid ( 10 ) with number of levels n = 4 is used , wherein low frequency filter within the reduce operator is assumed as l r =[ 1 , 1 ] 2 , l r = l r t · l r . with this kind of filter , noise rms error level with low - frequency components of the image pyramid decreases by law of q ( k , l r )= 2 − k , k = 1 , n . in the course of construction of the pyramid hf components after downsampling , lf filter l e =[ 1 , 4 , 6 , 4 , 1 ]/ 16 . l e = l e t · l e is used in expand operator . for lf filtering , bilateral filter is used , where geometric distance is not taken into account ; 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