exemplary embodiments of the invention as described herein generally include systems and methods for adaptive spatial compounding in ultrasound images . accordingly , while the invention is susceptible to various modifications and alternative forms , specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail . it should be understood , however , that there is no intent to limit the invention to the particular forms disclosed , but on the contrary , the invention is to cover all modifications , equivalents , and alternatives falling within the spirit and scope of the invention . as used herein , the term “ image ” refers to multidimensional data composed of discrete image elements ( e . g .. pixels for 2 - d images and voxels for 3 - d images ). the image may be , for example , a medical image of a subject collected by computer tomography , magnetic resonance imaging , ultrasound , or any other medical imaging system known to one of skill in the art . the image may also be provided from non - medical contexts , such as , for example , remote sensing systems , electron microscopy , etc . although an image can be thought of as a function from r 3 to r , the methods of the inventions are not limited to such images , and can be applied to images of any dimension , e . g . a 2 - d picture or a 3 - d volume . for a 2 - or 3 - dimensional image , the domain of the image is typically a 2 - or 3 - dimensional rectangular array , wherein each pixel or voxel can be addressed with reference to a set of 2 or 3 mutually orthogonal axes . the terms “ digital ” and “ digitized ” as used herein will refer to images or volumes , as appropriate , in a digital or digitized format acquired via a digital acquisition system or via conversion from an analog image . in spatial compounding , several images i i of the same underlying structures are generated at different positions so that the speckle noise n i in those images is independent . in traditional compounding techniques , the multiple images are assumed to be generated by the same transducer , and hence have the same gain , and are averaged to reduce the speckle noise . in addition , some post processing on the averaged image can be applied later to further reduce the noise based on spatial dependencies . but such schemes do not fully utilize the information provided in the multiple images and are of limited usefulness in designing a good post - processing filter when the imaging device is used in different applications and a prior model of the signal and noise is hard to obtain . if multiple transducers are used in spatial compounding , the gain g i of each transducer will be different . the speckle noise n i in the images is independent and has the same variance when the translation of the apertures of different transducers is large . but the underlying signal s is the same . then , the following image formation model can be obtained : where the resulting image i i , the underlying signal and the noise all have spatial dependencies . it can be easily seen that an averaging of all images is not optimal when the gains of the transducers are different . an iterative process can be used to obtain the optimal estimation of the signal and the gain of each transducer . an exemplary iterative process for estimating the signal and gain for a single transducer and image according to an embodiment of the invention is presented in fig3 . referring now to the figure , the gain of each transducer is initialized at step 31 as ĝ i ( k ) = 1 , where k is an iteration counter initialized to 0 . the signal sub - space can then be estimated at step 32 by summing over the images : s _ = 1 m ⁢ ∑ i = 1 m ⁢ i i g ^ i ( k ) , where m is the number of transducers / images . assuming the speckle noise is independent of the signal , the gain ĝ , can then be estimated at step 33 by projecting the images into the signal sub - space : g ^ i ( k + 1 ) = 〈 i i , s _ 〉 〈 s _ , s _ 〉 , if , at step 34 , the absolute difference of the iterates is ∥∥ ĝ i ( k + 1 ) - ĝ i ( k ) ∥∥& lt ; ε , the iterative process terminates , otherwise , at step 35 , the next iterate of the gain is updated as ĝ i ( k ) = ĝ i ( k + 1 ) , and the counter is updated by k = k + 1 . the process loops to step 32 and repeats . this iterative procedure yields the gain g i of each input images , and the resulting averaged image s has minimal speckle noise . if the assumption that the speckle noise in the images is independent is invalid , weighting factors w i can be estimated to further adjust the weighing of each image for better noise removal : s _ = 1 m ⁢ ∑ i = 1 m ⁢ w i ⁢ i i g ^ i ( k ) . an advantage of compounding is the utilization of multiple images of the same structure with independent noise . but these advantages are not fully utilized in traditional compounding techniques . apart from reducing the noise by weighted averaging , the multiple images can also help estimate the properties of both the underlying structure and the noise so that one can better utilize the spatial dependencies in the images . many filtering techniques have been developed to reduce noise based on the spatial correlations of the noise and signal , such as the wiener filter . but one of the challenges is obtaining an accurate estimation of the power spectrum of the noise and signals , especially when the signal is a spatially varying signal . with multiple images , it should be possible to obtain a more accurate estimation of the signal and noise properties than from a single averaged image . the use of multiple images can be demonstrated with a wiener filter , which is optimal given the power spectrum of the signal and the noise . the wiener filter assumes that a signal and additive noise are stationary linear stochastic processes with known spectral characteristics or known autocorrelation and cross - correlation . the wiener filter is modeled by the convolution where s ( t ) is the original signal to be estimated , n ( t ) is the noise , x ( t ) is the estimated signal which hopefully equals s ( t ), and g ( τ ) is the wiener filter . an optimal g ( τ ) can be is obtained by minimizing the expectation value of the square error , e ⁡ ( ⅇ 2 ) = r s ⁡ ( 0 ) - 2 ⁢ ∫ - ∞ ∞ ⁢ g ⁡ ( τ ) ⁢ r xs ⁡ ( τ ) ⁢ ⅆ τ + ∫ - ∞ ∞ ⁢ ∫ - ∞ ∞ ⁢ g ⁡ ( τ ) ⁢ g ⁡ [ θ ] ⁢ r x ⁡ ( τ - θ ) ⁢ ⅆ τ ⁢ ⅆ θ , where r s is the autocorrelation function of s ( t ), r x is the autocorrelation function of x ( t ), and r xs is the cross - correlation function of x ( t ) and s ( t ). if the signal s ( t ) and the noise n ( t ) are uncorrelated , the cross - correlation is zero . using multiple images , one can estimate the power spectra of a non - stationary case , where the signal and noise spectra are constantly changing , on the fly instead of relying on some pretrained models . referring now to fig1 , one can estimate the power spectra of the signal and noise at each location in an image based on a small neighborhood , such as the small square region i1 indicated in the image . referring again to fig3 , the power spectrum p i ( d ) around location d can be estimated at step 36 in the neighborhood of d on each image as well as the weighted averaged image , p s ( d ). if the noise is zero - mean gaussian distributed and independent to the signal , one obtains : p i ⁡ ( d ) = p s ⁡ ( d ) + p n ⁡ ( d ) = 1 m ⁢ ∑ i ∈ [ 1 , m ] ⁢ p i i ⁡ ( d ) ⁢ ⁢ i = 1 , … ⁢ , m p s _ ⁡ ( d ) = p s ⁡ ( d ) + p n i ⁡ ( d ) / m where p s ( d ) and p n ( d ) are the power spectra of the signal and noise respectively . the power spectra of both the signal and noise can be obtained for designing the optimal wiener filter h o ( d ). p s ( d ) is the power spectrum of the averaged image , which is directly estimated from the averaged image . it is the sum of the true signal power spectrum p s ( d ) and reduced noise power spectrum p n ( d )/ sqrt ( m ), where the noise spectrum is reduced due to the averaging operation . thus , p i ( d ) and p s ( d ) can both be estimated from the images . but one needs to estimate p s ( d ) and p n ( d ) to design the wiener filter , based on the understanding that p i ( d )= p s ( d )+ p n ( d ) and p s ( d )= p s ( d )+ p n ( d ) 1 √{ square root over ( m )}, one can estimate p n ( d ) and p s ( d ) from p i ( d ) and p s ( d ) and hence design the optimal wiener filter at step 37 as follows : h o ⁡ ( d ) = p s ⁡ ( d ) p s ⁡ ( d ) + p n ⁡ ( d ) = m · p s _ ⁡ ( d ) - p i ⁡ ( d ) ( m - 1 ) · p i ⁡ ( d ) , where this wiener filter is a function of location d . the wiener filter can be applied at step 38 to the averaged image as h 0 × s to further reduce the speckle noise . an adaptive spatial filtering algorithm according to an embodiment of the invention was applied to compound real ultrasound images . in this experiment , 3 images were used ( i . e . m = 3 ). the weighted average will only reduce the noise level by √{ square root over ( m )}. simple averaging produces noisy results such as those shown in fig2 ( a ). one can see from fig2 ( a ) that the noise appears more independent between the neighboring pixels than with respect to the signal . by averaging the neighborhood in the image , one should be able to reduce the noise level . but the challenge is to prevent oversmoothing across signal boundaries . however , because the power spectrum of the noise and signal can be estimated to design an optimal wiener filter for each location , an improved filter can be used to remove the speckle noise while keeping the signal boundary sharp . the results of applying an optimal wiener filer of an embodiment of the invention is shown in fig2 ( b ), where the reduction of noise is apparent . based on different imaging characteristics , alternative implementations can achieve improved compounding . according to another embodiment of the invention , if the noise is not gaussian distributed but rather includes a heavy tail distribution , such as salt and pepper noise , higher order statistical filters , such as a weighted median filter , can be used between multiple images instead of weighted averaging . according to another embodiment of the invention , prior knowledge can be exploited in the adaptive wiener filtering . for example , since the structures of interest are usually tissue boundaries , the signal can be modeled by a quadratic signal for improved power spectrum estimation . it is to be understood that embodiments of the present invention can be implemented in various forms of hardware , software , firmware , special purpose processes , or a combination thereof . in one embodiment , the present invention can be implemented in software as an application program tangible embodied on a computer readable program storage device , the application program can be uploaded to , and executed by , a machine comprising any suitable architecture . fig4 is a block diagram of an exemplary computer system for implementing a adaptive spatial filter according to an embodiment of the invention . referring now to fig4 , a computer system 41 for implementing the present invention can comprise , inter alia , a central processing unit ( cpu ) 42 , a memory 43 and an input / output ( i / o ) interface 44 . the computer system 41 is generally coupled through the i / o interface 44 to a display 45 and various input devices 46 such as a mouse and a keyboard . the support circuits can include circuits such as cache , power supplies , clock circuits , and a communication bus . the memory 43 can include random access memory ( ram ), read only memory ( rom ), disk drive , tape drive , etc ., or a combinations thereof . the present invention can be implemented as a routine 47 that is stored in memory 43 and executed by the cpu 42 to process the signal from the signal source 48 . as such , the computer system 41 is a general purpose computer system that becomes a specific purpose computer system when executing the routine 47 of the present invention . the computer system 41 also includes an operating system and micro instruction code . the various processes and functions described herein can either he part of the micro instruction code or part of the application program ( or combination thereof which is executed via the operating system . in addition , various other peripheral devices can be connected to the computer platform such as an additional data storage device and a printing device . it is to be further understood that , because some of the constituent system components and method steps depicted in the accompanying figures can be implemented in software , the actual connections between the systems components ( or the process steps ) may differ depending upon the manner in which the present invention is programmed . given the teachings of the present invention provided herein , one of ordinary skill in the related art will be able to contemplate these and similar implementations or configurations of the present invention . while the present invention has been described in detail with reference to a preferred embodiment , those skilled in the art will appreciate that various modifications and substitutions can be made thereto without departing from the spirit and scope of the invention as set forth in the appended claims .
a method for removing speckle noise from ultrasound images includes providing a plurality of digitized ultrasound images , each image comprising a plurality of intensities corresponding to a domain of points on a 2 - dimensional grid , initializing an initial gain associated with each of said plurality of us images , estimating a signal sub - space by averaging over each us image divided by its associated gain , and estimating an updated gain by projecting its associated image into said signal sub - space . if an absolute difference of said updated gain and said initial gain is less than a pre - determined quantity , obtaining an averaged image from said signal sub - space , estimating an optimal wiener filter from said plurality of us images and said averaged image , and filtering said averaged image with said wiener filter , wherein said speckle noise is substantially minimized .