Patent Application: US-201313748550-A

Abstract:
a system and a method for improving the quality of ultrasound images . the system comprises a processor being configured to subdivide the ultrasound image , determine a deconvolution factor for the ultrasound image and apply the deconvolution factor to the subdivided ultrasound image , resulting in a restored image .

Description:
generally stated , the non - limitative illustrative embodiment of the present disclosure provides a system and a method for improving the quality of images obtained from an imaging system , such as an ultrasound imaging system , through the application of an image restoration process in order to recover clinically important image details , which are often masked due to resolution limitations . in common ultrasound imaging systems , the spatial resolution is severely limited due to the effects of both the finite aperture and overall bandwidth of ultrasound transducers and the non - negligible width of the transmitted ultrasound beams . this low spatial resolution remains the major limiting factor in the clinical usefulness of medical ultrasound images . to this end , an estimation of the point spread function ( psf ) of the imaging system is required . the image restoration process is a novel , original , reliable , and fast maximum likelihood ( ml ) approach for recovering the psf of an ultrasound imaging system . this new psf estimation method is based on an additional constraint , namely that the psf to be estimated is of known parametric form . under this constraint , the parameter values of its associated modulation transfer function ( mtf ) are then efficiently estimated using a homomorphic filter , a denoising step , and an expectation - maximization ( em ) based clustering algorithm . consequently , this amounts to estimating , in the low - pass - filtered cepstral domain , a mixture of two identical gaussian distributions whose parameters are automatically estimated , in a maximum likelihood sense , by an iterative expectation - maximization ( em ) [ 11 ] based clustering algorithm . given this psf estimate , a deconvolution algorithm can then be efficiently used , in a subsequent stage , in order to improve the spatial resolution of ultrasound images , to obtain an estimate of the true tissue reflectivity function , which is then independent of the properties of the imaging system . referring to fig1 , the image restoration system 10 includes a processor 12 with an associated memory 14 having stored therein processor executable instructions 16 for configuring the processor 12 to perform various processes , namely image restoration process , which process will be further described below . the image restoration system 10 further includes an input / output ( i / o ) interface 18 for communication with an imaging system 20 and a display 30 . the image restoration system 10 obtains images , for example ultrasound images , from the imaging system 20 and executes the image restoration process 16 on the acquired images . the resulting restored images are then displayed on the display 30 and may be saved to the memory 14 , to other data storage devices or medium 40 , or provided to a further system via the i / o interface 18 . referring to fig2 , the image restoration system 10 may be remotely connected to one or more imaging systems 20 and / or remotely operated through a remote station 62 via a wide area network ( wan ) such as , for example , ethernet ( broadband , high - speed ), wireless wifi , cable internet , satellite connection , cellular or satellite network , etc . the remote station 62 may also have associated data storage devices or medium 64 for locally storing restored images provided by the image restoration system 10 . referring now to fig3 , there is shown a flow diagram of an illustrative example of the image restoration process 100 executed by the processor 12 ( see fig1 ). steps of the process 100 are indicated by blocks 102 to 110 . the process 100 starts at block 102 where an image , for example an ultrasound image , is obtained from the imaging system 20 and , at block 104 , subdivided . then , at block 106 , a deconvolution factor is determined for the image and , at block 108 , the deconvolution factor is applied to the subdivided image resulting in a restored image . finally , at block 110 , the restored image is provided , for example through the display 30 and / or stored in a data storage device or medium 40 . the various steps of process 100 will be further detailed below . in ultrasound imaging , the psf happens to exhibit spatial dependency due , among other things , to the non - uniformity of focusing , the dispersive attenuation and the heterogeneity of the different interrogated tissues . nevertheless , a relatively low spatial variability of these phenomena makes it possible to divide the obtained acoustic image into a predefined number of small enough ( possibly overlapping ) images , for which the data within each such smaller image can be considered to be quasi - stationary , with a different psf . it is then assumed that , the entire image can be easily recovered by combining all the local results obtained in this manner . assuming space invariance and linearity , the resolution capabilities of an ultrasound imaging system can be expressed in terms of the psf , h ( x , y ), i . e . the image of a point reflector , by the following classical linear model : g ( x , y )= f ( x ,)* h ( x , y )+ n * x , y ) equation 1 where f ( x , y ) is the spatial reflectance distribution of internal organs of the human body to be imaged , g ( x , y ) is the degraded ultrasound image of the object f ( x , y ), h ( x , y ) is the psf function of the imaging system 20 , which counts for the finite aperture and bandwidth of the transducer , n ( x , y ) describes the additive quantization and electronic noise and finally * designates the 2d discrete linear convolution operator . assuming that the noise term n ( x , y ) is temporarily ignored for the sake of simplicity , equation 1 is more easily described in frequency domain as a simple product and sum where the capital letters indicate the fourier transforms of the corresponding spatial functions : an homomorphic transformation is simply the complex logarithmic transformation of both side of equation 2 . the real ( re ) and the imaginary ( im ) parts of the resultant relation are given correspondingly by : re : log | g ( u , v )|≅ log | f ( u , v )|+ log | h ( u , v )| equation 3 im : g ( u , v )≅ f ( u , v )+ h ( u , v ) equation 4 where the symbols |.| and denote , respectively , the amplitude and the phase of the complex functions . the basic idea for cepstrum - based methods of estimating the psf spectrum h ( u , v ) relies on the fact that log | h ( u , v )| is typically a much smoother function than log | f ( u , v )| and the same holds for the functions h ( u , v ) and f ( u , v ). consequently , in this context , the log - spectrum of the degraded ultrasound image ( amplitude and phase ) is considered to be a noisy version of the complex log - spectrum of the psf to be estimated and in this setting , in which log | f ( u , v )| and f ( u , v ) are considered to be sources of noise to be rejected , the problem of recovering log | h ( u , v )| and h ( u , v ) is thus essentially a denoising problem in the cepstral domain . in order to ensure both an automatic procedure and also a reliable denoising step allowing a good estimate of the psf spectrum , h ( u , v ), without ( ringing or blocking ) artifacts , a two - stage denoising scheme is proposed ; namely a discrete cosine transform ( dct )- based denoising step using a hard thresholding rule followed by a em - based regression model . in addition , since the psf model relies on an even function in x and y , the phase spectrum is assumed to be null . algorithmically [ 12 ], the dct - based denoising procedure consists in applying iteratively , until a maximal number of iterations is reached or until convergence is achieved , frequential filtering based on the dct transform of each 8 × 8 sub - image extracted from the current version of the image to be denoised ( initially , this current image estimate is the noisy image itself ). for the filtering operation in the dct domain , the easily - implemented hard thresholding rule [ 13 ] is used , also classically used in wavelet based denoising approaches , where ε is a threshold level and ω is one of the coefficients obtained by the dct transform of the block ( of size 8 × 8 pixels ) extracted from the current image to be denoised . in order to reduce blocky artifacts across block boundaries , a standard approach is adopted where this transform is made translation - invariant , by using the dct of all ( circularly ) translated version of each channel of the image ( herein assumed to be toroidal ) [ 14 ] ( this implies computing a set of 8 horizontal shifts and 8 vertical shifts transformed images ) which is then averaged at each step of this iterative denoising procedure . in order to speed up the procedure , an overlap of three pixels is used for the sliding 8 × 8 window . this iterative denoising procedure , illustrated in procedure 1 , is applied on the noisy version of log h ( u , v ), i . e ., log g ( u , v ) ( amplitude and phase ) and allows us to obtain a first rough estimate of log h ^( u , v ) which will be refined in the next step . let i [ n ] be the input image to be denoised at iteration n î [ n ] be the denoised estimated image at iteration n ε be the threshold for all ( 8 horizontal and 8 vertical ) shifts of i [ n ] do for all 8 x 8 blocks extracted from i [ n ] do 1 . dct transform 2 . threshold the obtained dct coefficients with the hard thresholding rule hard ε = o if | | ≦ ε , otherwise 3 . inverse dct of these threshold coefficients unshift the filtered image and store it î [ n ] ← averaging of these 64 denoised images in order to refine the estimation given by the above - mentioned denoising step , the estimation method now relies on an additional constraint , namely that the psf to be estimated has the following parametric form : which is the psf model used in [ 15 ], i . e . asymmetric ( across the x - axis and y - axis ) cosine modulated by a gaussian envelope whose the fourier spectrum , i . e . its mtf ( in fact a band - pass filter ), namely h ( u , v ) can be written in the fourier domain : h ( u , v )= πσ x σ y exp (− 2π 2 σ x 2 u 2 ){ exp (− 2π 2 σ y 2 ( v − f o ) 2 )+ exp (− 2π 2 σ y 2 ( v + f o ) 2 )} equation 6 under this constraint , the regression model that gives , for the set of amplitude values of | h ( u , v )|, the best fit , in the least square sense , of two equally weighted gaussian distributions ( with the constraints that these two distributions are centered at u = 0 and symmetric with respect to v ) can now be considered . in that respect , this latter regression model can be efficiently addressed by considering the parameter statistical estimation problem of a ( noisy ) gaussian distribution mixture of two ( equally weighted ) gaussian component in r 2 by considering nf 2 - dimensional vectors v =( u , v ) t , v ={ vi , 1 ≦ i ≦ nf }, taking their values in r 2 and whose cardinality of each v is given by the amplitude value h ( u , v ). finally , it is assumed that v = v1 , . . . , vn f is a realization in , ir 2 , of v whose density takes the form of the following 2 - component mixture : in which , the 2 components pv / ci ( v / ck , ψk ) are , in the present application ( see equation 5 ) assumed to be two equally weighted ( p1 = p2 = 0 . 5 ) bi - variate gaussian distributions with mean vector μk and identical covariance matrix σ ( ψk =( μk , σ )), i . e . : in this setting , the identification of the parameters of the psf spectrum modulus h ( uv ) amounts to estimate the parameters ( ψ1 and ψ2 with the constraints that these two distributions are centered at u = 0 ( μ1 =( u = 0 , v1 ) t and μ2 =( u = 0 , v2 )) and v1 and v2 symmetric with respect to v = 0 , i . e . of opposite signs . this 2 - component gaussian mixture model is estimated thanks to a em - based clustering algorithm [ 11 ]. the initial parameters of this iterative procedure are given by the ml estimation on the partition given by a simple k - means clustering procedure . the constraint of identical covariance matrix and mean vector centered at u = 0 are taken into account at the end of the procedure by simply considering the average value of the two covariance matrices and the average absolute value of v1 and v2 . in order to improve the spatial resolution of the ultrasound images and to obtain an estimate of the true tissue reflectivity function , the ultrasound system &# 39 ; s point - spread function can now be deconvolved out . in the present application , an unsupervised bayesian deconvolution approach [ 16 ] is being used ( or a penalized likelihood framework ) exploiting a non - parametric adaptive prior distribution derived from the recent image model proposed by buades [ 17 ]. this prior distribution expresses that acceptable deconvolved solutions are the images exhibiting a high degree of redundancy . in this setting , the deconvolution of ultrasound images leads to the following cost function to be optimized : where the first term expresses the fidelity to the available data g and the second encodes the expected property of the true undegraded image and y [ g ]( f ) designates the non - local means filter in [ 17 ] applied on f . ρ , the regularization parameter controlling the contribution of the two terms ( which is crucial in the determination of the overall quality of the final estimate ), is estimated with the method proposed in [ 16 ]. the psf estimation approach and deconvolution were texted on ultrasound images of several bones acquired using a portable b - mode ultrasound imaging system ( titan ™, sonosite inc ., bothell , wash ., usa ). the echographic appearance of the various tissues ranges from dark ( low - echoic ) to bright ( high - echoic ), depending on their acoustic impedance . fig4 a and 4b show the original ultrasound images of the distal femur , more specifically the medial side , coronal plane ( fig4 a ) and the medial posterior condyle , axial plane ( fig4 b ) fig5 a and 5b show the modulus of h ^( u , v ) after application of the dct - based denoising step to the images of fig4 a and fig4 b , respectively . it can be seen that two different pass - band filters , related to two different psfs are visible on these images . it can also be seen that there is no aliasing error and this first denoising step allowing the obtainment of the expected shape of a band - pass filter ( see equation 5 ) on which the learning step of the gaussian mixture , exploiting the em procedure , will be achieved . the gaussian mixture , estimated from these two spectrum data by the em algorithm ( without the additional constraint of symmetry ) is shown in fig6 a and 6b . two examples of psf estimation with the present approach are presented in fig7 a to 7d . finally , fig8 a and 8b show examples of deconvolution ultrasound images using the deconvolution scheme presented herein . more specifically , fig6 a and 6b are surface plots of the point - spread function ( psf ) defining a two - component mixture of bivariate gaussian distributions for fig5 a with μ =[ 54 . 18 134 . 21 ; 51 . 82 94 . 88 ] and σ =([ 358 . 66 4 . 18 ; 4 . 18 151 . 00 ], [ 358 . 84 4 . 10 ; 4 . 10 149 . 45 ]), and fig5 a with μ =[ 53 . 05 131 . 53 ; 52 . 94 97 . 40 ] and σ =([ 368 . 94 − 5 . 48 ; − 5 . 48 97 . 40 ], [ 368 . 95 − 5 . 47 ; − 5 . 47 96 . 45 ]); fig7 a to 7d are estimated spectrums of the point - spread function ( psf ) corresponding to fig4 a ( fig7 a and 7c ) and fig4 b ( fig7 b and 7d ), and fig8 a and 8b are deconvolved images corresponding to fig4 a and fig4 b , respectively . using the above - describe image restoration system and method , greater resolution improvement of the deconvolved ultrasound images can be observed with substantially improved definition of the outer contour of biological structures and can easily be used for commercial ultrasound applications due to its spatial resolution improvement or as a prerequisite stage for the segmentation and 3d reconstruction of ultrasound images . it should be noted that although reference has been made to ultrasound images and ultrasound imaging systems throughout the present disclosure , it is to be understood that the image restoration system and method may be applied and / or adapted to other types of images and imaging systems such as , for example , radioscopic , radiographic and echographic images from radioscopic , radiographic and echographic imaging systems , or any other such images and imaging systems . although the present disclosure has been described with a certain degree of particularity and by way of an illustrative embodiments and examples thereof , it is to be understood that the present disclosure is not limited to the features of the embodiments described and illustrated herein , but includes all variations and modifications within the scope and spirit of the disclosure as hereinafter claimed . in the present disclosure , references are made to the following reference documents which are herein incorporated by reference . mignotte , m ., meunier , j ., soucy , j .- p ., and janicki ., c ., “ comparison of deconvolution techniques using a distribution mixture parameter estimation : application in spect imagery ,” journal of electronic imaging 1 , 11 - 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