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:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefits of U.S. provisional patent application No. 61/632,340 and Canadian patent application No. 2,765,244, both filed on Jan. 23, 2012, which are herein incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to an image restoration system and method. More specifically, the present disclosure relates to an image restoration system and method for restoring images obtained from an ultrasound imaging system. 
     BACKGROUND 
     Contrary to other medical imaging techniques (e.g., X-rays, magnetic resonance imaging, and computerized tomography), ultrasound imagery is currently considered to be a non-invasive, portable, non-expensive and safe (for the patient and operator) visualization medical tool for investigating biological tissues of a body. However, despite considerable advances in the technology of ultrasound imaging equipment over the last years, the primary limitation of this imaging modality remains its poor image quality (i.e. low signal-to-noise ratio, low resolution and contrast), and also the presence of artifacts due to the speckle noise effect that drastically deteriorates image quality and sometimes makes imperceptible clinically important details within these images (such as contours of anatomical structures). 
     In order to improve the quality of such ultrasound images, an image deconvolution/restoration procedure could be efficiently applied and, to this end, given a Point Spread Function (PSF) estimate, many deconvolution models exist [1]. The only requirement for such deconvolution algorithms consists, as a prerequisite first stage, of an estimation of the PSF of the underlying ultrasound imaging system. This problem of estimating the PSF and restoring is called a blind deconvolution process and an alternative approach to this above-mentioned estimation and deconvolution (disjoint) procedures consists of the simultaneous (generally iterative) estimation of the undegraded original image and the PSF (or its inverse) [2-5]. 
     Amongst the first blind deconvolution strategy for which estimating the PSF estimation and the restoration process are two disjoint procedures, there is the PSF identification procedure based on frequency domain [6] zeros or the homomorphic filtering method which consists in low-pass filtering (also called liftering) in the complex cepstral domain (the cepstrum being defined by the inverse Fourier transform of the log of the spectrum). This low-pass filtering is commonly achieved either with an ideal low-pass filter [7, 8] or by hard or a soft shrinkage rule in the wavelet domain [9]. It is also worth mentioning the estimation approach by means of local polynomial approximation proposed by Adam and Michailovich [10], which can be viewed as a modification of homomorphic estimation by using wavelet bases instead of the Fourier basis. Nevertheless, ideal low-pass filtering in the cepstral domain or by other wavelet-based filtering procedures have several drawbacks. 
     First, they are highly supervised to adequately set the cutoff frequency parameter which is crucial and different for each ultrasound image because of the spatial variability of the PSF (due to the presence of different interrogated tissues between the transducer and the anatomical structure to be imaged). 
     Second, these classical filtering methods are not robust enough to give a good estimate of the PSF spectrum and often tend to produce artifacts in this estimation mainly due to the ringing effect of such ideal low pass filter in the Fourier domain or due to the blocky effect inherent to the wavelet based filtering procedure. 
     Accordingly, there is a need for an image restoration system and method that addresses the above-described shortcomings. 
     SUMMARY 
     The present disclosure provides a system for improving the quality of an imaging system image, comprising:
         an input/output interface configured to receive the imaging system image;   a processor in communication with the input/output interface, the processor being configured to:
           a) subdivide the imaging system image;   b) determine a deconvolution factor for the imaging system image;   c) apply the deconvolution factor to the subdivided image; and   d) provide a restored image based on the deconvoluted subdivided image.   
               

     There is further provided a system for improving the quality of an imaging system image as above wherein step b) includes the sub-steps of:
         i) applying a homomorphic filter to the associated modulation transfer function of the point spread function of the imaging system image;   ii) applying denoising using a hard thresholding rule;   iii) applying an iterative expectation-maximisation regression model;   iv) estimating the point spread function; and   v) setting the deconvolution factor to the estimated point spread function.       

     The present disclosure also provides a corresponding method for improving the quality of an imaging system image as well as a processor executable product stored on a data storage medium, configured to cause the processor to perform operations corresponding to the method for improving the quality of an imaging system image. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Embodiments of the disclosure will be described by way of examples only with reference to the accompanying drawing, in which: 
         FIG. 1  is a schematic representation of an image restoration system in accordance with an illustrative embodiment of the present disclosure; 
         FIG. 2  is a schematic representation of an image restoration system in a remote usage configuration; 
         FIG. 3  is a flow diagram of an image restoration process in accordance with an illustrative embodiment of the present disclosure; 
         FIGS. 4A and 4B  are ultrasound images of a distal femur showing the medial side, coronal plane ( FIG. 4A ) and the medial posterior condyle, axial plane ( FIG. 4B ); 
         FIGS. 5A and 5B  show the modulus of H^(u,v) after application of the discrete cosine transform (DCT)-based denoising step to the images of  FIG. 4A  and  FIG. 4B , respectively; 
         FIGS. 6A and 6B  are surface plots of the point-spread function (PSF) defining a two-component mixture of bivariate Gaussian distributions for  FIG. 5A  with α=[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  FIG. 5A  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]); 
         FIGS. 7A to 7D  are estimated spectrums of the point-spread function (PSF) corresponding to  FIG. 4A  ( FIGS. 7A and 7C ) and  FIG. 4B  ( FIGS. 7B and 7D ); and 
         FIGS. 8A and 8B  are deconvolved images corresponding to  FIG. 4A  and  FIG. 4B , respectively. 
     
    
    
     Similar references used in different Figures denote similar components. 
     DETAILED 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  FIG. 1 , 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  FIG. 2 , 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  FIG. 3 , there is shown a flow diagram of an illustrative example of the image restoration process  100  executed by the processor  12  (see  FIG. 1 ). 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. 
     PSF Estimation by Homomorphic Transformation 
     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:
 
 G ( u,v )= F ( u,v ) H ( u,v )  Equation 2
 
     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.
     Denoising Step 
     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. 
     DCT-Based Denoising Step 
     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. 
     Procedure 1—DCT-Based Denoising 
                                                                                                                         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                        
EM-Based Estimation Step
 
     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: 
     
       
         
           
             
               
                 
                   
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     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: 
     
       
         
           
             
               
                 
                   
                     
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     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. 
     Deconvolution 
     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:
 
 E ( f )=∥ g−h*f∥+ρ∥f−Y   [g] ( f )∥  Equation 9
 
     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]. 
     EXAMPLE 
     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.  FIGS. 4A and 4B  show the original ultrasound images of the distal femur, more specifically the medial side, coronal plane ( FIG. 4A ) and the medial posterior condyle, axial plane ( FIG. 4B ) 
       FIGS. 5A and 5B  show the modulus of H^(u,v) after application of the DCT-based denoising step to the images of  FIG. 4A  and  FIG. 4B , 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  FIGS. 6A and 6B . Two examples of PSF estimation with the present approach are presented in  FIGS. 7A to 7D . Finally,  FIGS. 8A and 8B  show examples of deconvolution ultrasound images using the deconvolution scheme presented herein. 
     More specifically,  FIGS. 6A and 6B  are surface plots of the point-spread function (PSF) defining a two-component mixture of bivariate Gaussian distributions for  FIG. 5A  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  FIG. 5A  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]); 
       FIGS. 7A to 7D  are estimated spectrums of the point-spread function (PSF) corresponding to  FIG. 4A  ( FIGS. 7A and 7C ) and  FIG. 4B  ( FIGS. 7B and 7D ), and  FIGS. 8A and 8B  are deconvolved images corresponding to  FIG. 4A  and  FIG. 4B , 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. 
     REFERENCES 
     In the present disclosure, references are made to the following reference documents which are herein incorporated by reference.
     [1] 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, 11-25 (January 2002).   [2] Ayers, G. and Dainty, J., “Iterative blind deconvolution method and its application,” Optics Letters 13, 547-549 (July 1988).   [3] Katsaggelos, A. and Lay, K., “Maximum likelihood blur identification and image restoration using the expectation-maximization algorithm,” IEEE Trans. on Signal Processing 39, 729-733 (March 1991).   [4] Kundur, D. and Hatzinakos, D., “Blind image restoration via recursive filtering using deterministic constraints,” in [Proc. International Conference on Acoustics, Speech, and Signal Processing], 4, 547-549 (1996).   [5] Benameur, S., Mignotte, M., Soucy, J.-P., and Meunier, J., “Image restoration using functional and anatomical information fusion with application to spect-mri images,” International Journal of Biomedical Imaging 2009, 12 pages (October 2009).   [6] Cannon, M., “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Transactions on Acoustics, Speech and Signal Processing 24, 58-63 (February 1976).   [7] Abeyratne, U., Petropulu, A., and Reid, J., “Higher order spectra based deconvolution of ultrasound images,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 42, 1064-1075 (November 1995),   [8] Taxt, T., “Restoration of medical ultrasound images using two-dimensional homomorphic deconvolution,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 42, 543 554 (July 1995),   [9] Michailovich, O. and Adam, D., “A novel approach to the 2-d blind deconvolution problem in medical ultrasound,” IEEE Trans. on Medical Imaging 24, 86-104 (January 2005).   [10] Adam, D. and Michailovich, O., “Blind deconvolution of ultrasound sequences using nonparametric local polynomial estimates of the pulse,” IEEE Transactions on Biomedical Engineering 49, 118-131 (February 2002).   [11] Dempster, A., Laird, N., and Rubin, D., “Maximum likelihood from incomplete data via the EM algorithm,” Royal Statistical Society 1-38 (1976).   [12] Mignotte, M., “Fusion of regularization terms for image restoration,” Journal of Electronic Imaging 19, 333004—(July-September 2010).   [13] Donoho, D. L. and Johnstone, I. M., “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425-455 (1994).   [14] Coifman, R. and Donohu, D., “Translation in variant denoising,” in [Wavelets and Statistics, Lecture Notes in Statistics], 103, 125-150, A. Antoniadis and G. Oppenheim, Eds. New York: Springer-Verlag (1995).   [15] KaDel, F., Bertrand, M., and Meunier, J., “Speckle motion artifact under tissue rotation,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 41, 105-122 (January 1994).   [16] Mignotte, M., “A non-local regularization strategy for image deconvolution,” Journal Pattern Recognition Letters 29(16), 2206-2212 (2008).   [17] Buades, A., Coll, B., and Morel, J. M., “A review of image denoising algorithms, with a new one,” Multiscale Modeling and Simulation (SIAM Interdisciplinary Journal) 4(2), 490-530 (2005).