Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Ultrasound images obtained with a simple linear or sector scan show a granular appearance, called "speckle." This speckle is analyzed. The reduction in speckle that can be obtained with a compound scan with maximum amplitude writing is computed. The reduction in speckle is almost as large as can be obtained with averaging. It depends on the number of independent amplitude values that are measured. The condition for the independence of two amplitude values is derived, and thus a limit is given for the possible reduction in speckle. <s> BIB001 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> the of the magnitude, i.e., intensity, of the field.) It is shown that Rayleigh statistics govern the fist-order behavior of the magnitude; and the autocorrelation of the resulting image speckle is obtained by the methodof Middleton. The corresponding power spectrum follows immediately by Fourier transformation. Theoretical and experimentally determined autocorrelation functions and power spectra derived from B-scans of a scattering phantom containing many scatterers per resolution cell are presented. These functions lead naturally to the definition of the average speckle spot or cell sue, and this inturn is comparable to the resolution cell. Each independent speckle servesas a degreeof freedom that determines the number of samples of tissue available over a target.As the speckle cell size decreases this number increases in a manner predictable from the physical parameters of the cell size. However, it is found that the speckle cellis broadened, the degrees of freedom diminished, when the object structureis correlated. This yields the possibilityof deducing information about the object structure from the second-order statistics of the speckle texture, in addition to that obtainable from the fiistorder statistics. <s> BIB002 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Tissue signatures are obtained from the first and second order statistics of ultrasonic B-scan texture. Laboratory measurements and early clinical results show that the image may be segmented to discriminate between different normal tissues and to detect abnormal conditions based on a three-dimensional feature space. These features describe the intrinsic backscatter properties of the tissues imaged and may be used as the basis of an automatic tissue characterization algorithm. <s> BIB003 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> A model for the scattering of ultrasound from breast tissue is proposed. The model is based on the use of non-Rayleigh statistics, specifically the K distribution to describe the backscattered echo from the tissue. A multiparameter test based on this model has been designed to characterize the tissue. The data from the B-scan images of the breasts of 6 different patients were analyzed using this model. The results indicate that the non-Rayleigh statistics seem to be useful in characterizing and identifying malignant, benign, and normal tissue regions. > <s> BIB004 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Abstract Historically, it has been assumed that the first-order envelope statistics of ultrasonic backscatter from myocardium are best described by the Rayleigh probability distribution function (PDF); however, few studies have tested this assumption. This study compares the ability of five PDFs, including the Rayleigh, to describe high-frequency (5–15 MHz) ultrasonic backscatter from in vivo canine myocardium and in vitro human myocardium. The PDFs used have all been previously proposed as descriptions of backscatter from parenchymal tissue or other random media. In this study goodness-of-fit testing of backscatter recorded at several frequencies and insonification angles shows that only in a minority of cases is the envelope Rayleigh-distributed. In most cases, the K distribution provides the best fit. In addition, computer simulation shows that sparse Poisson scattering can produce K -distributed backscatter. Scattering of this type may contribute to the observed non-Rayleigh character of myocardial backscatter. We conclude that the Rayleigh distribution is not an adequate description of backscatter from myocardium. Non-Rayleigh distributions may offer an additional approach to myocardial tissue characterization. <s> BIB005 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The statistics of ultrasound echo envelope signals can be used to characterize scattering media. The Rayleigh distribution and its generalized forms, the K and Rice distributions, have been previously used to model the echo signal. A more generalized statistical model, the homodyned K distribution, combines the K and Rice distribution features to better account for the statistics of the echo signal. We show that this model can give two parameters that are useful for media characterization: k, the ratio of coherent to diffuse signals, and, β, which characterizes the clustering of scatterers in the medium. <s> BIB006 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The SNR (signal-to-noise ratio) of the echo envelope image is a monotonically-increasing function of scatterer number density. Various SNRs, like amplitude SNR and intensity SNR, can be used to quantify the scatterer density. The problem of using a SNR based on higher order moments like the intensity SNR is that they require large sample sizes to obtain estimates with high confidence (the variance of the estimate becomes large for higher moments). In this paper, we consider SNRs based on fractional order moments (moments of order less than 1), and obtain mathematical analyses of their properties using the K distribution, which has been shown to be a good model for the density function of backscatter echo envelope signal. Statistics of SNRs based on fractional moment are derived and appear to be more robust and useful than the amplitude and intensity SNRs previously studied. The SNRs based on fractional order moments have greater dynamic range and the sample size requirements are smaller than those for integral order moment SNRs, like amplitude SNR or intensity SNR. Thus, SNRs based on fractional order moments could be used to better quantify the variations in scatterer density which can be used for tissue classification problems. <s> BIB007 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> An adaptive smoothing technique for speckle suppression in medical B-scan ultrasonic imaging is presented. The technique is based on filtering with appropriately shaped and sized local kernels. For each image pixel, a filtering kernel, which fits to the local homogeneous region containing the processed pixel, is obtained through a local statistics based region growing technique. The performance of the proposed filter has been tested on the phantom and tissue images. The results show that the filter effectively reduces the speckle while preserving the resolvable details. The simulation results are presented in a comparative way with two existing speckle suppression methods. > <s> BIB008 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Log compression of A lines to produce B-scan images in clinical ultrasound imaging systems is a standard procedure to control the dynamic range of the images. The statistics of such compressed images in terms of underlying scatterer statistics have not been derived. The statistics are analyzed for partially formed speckle using a general K distribution model of envelope statistics to derive the density function for the log-compressed envelope. This density function is used to elucidate the relation between the moments of the compressed envelope, the compression parameters, and the statistics of the scatterers. The analysis shows that the mean of the log-compressed envelope is an increasing function of both the backscattered energy and the effective scatterer density. The variance of the log-compressed envelope is a decreasing function of the effective scatterer density and is independent of the backscattered energy. <s> BIB009 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> A good statistical model of speckle formation is useful for designing a good adaptive filter for speckle reduction In ultrasound B-scan images. Previously, statistical models have been used, but they failed to account for the log compression of the echo envelope employed by clinical ultrasound systems. Log-compression helps in reducing the dynamic range of the B-scan Images for display on a monitor as well as enhancing weak backscatters. In this article, statistics of log-compressed echo images, using the K-distribution statistical model for the echo envelope, are used to derive a parameter that can be used to quantify the extent of speckle formation. This speckle quantification can be used with an unsharp masking filter to adaptively reduce speckle. The effectiveness of the filter is demonstrated on images of contrast detail phantoms and on in-vivo abdominal images obtained by a clinical ultrasound system with log-compression. <s> BIB010 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> In this article, a model for the amplitude statistics of the backscattered ultrasonic signal is presented. We propose to view a tissue as being composed of a large number of small units, each having slightly different characteristics. This variability within the tissue is expressed by fluctuations in the parameters of the local probability distribution function (PDF). Based on analogous expressions derived for radio propagation and optical scintillations, the local PDF is modulated by a lognormal distribution of the local standard deviation. Integrating the local contributions yields the amplitude PDF for the entire tissue. We show that the local entropy is a normal variable, since for four different local PDFs it is linearly related to the logarithm of the local standard deviation. When the local entropy histogram exhibits distinct and multiple peaks, the local entropy distribution can be used for region segmentation. This fact is demonstrated for ultrasonic images of ovarian cysts. <s> BIB011 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Describes a new fully motion-adaptive spatio-temporal filtering technique to reduce the speckle in ultrasound images. The advantages of this approach are demonstrated in echocardiographic boundary detection and in comparison with other techniques. The first stage of many automated echocardiographic image interpretation schemes is filtering to reduce the amount of speckle noise. The authors show how the two-dimensional least mean squares (TDLMS) filter can be configured as a motion-compensated filter for a time sequence of ultrasound images that eliminates the blurring associated with direct averaging. For an image corrupted by multiplicative speckle noise, the mode of the intensity distribution approximates the maximum likelihood estimator. In consequence, the temporal filter's output is biased towards the mode from the mean, using information contained within the speckle itself. A new adaptive algorithm for controlling the filter's convergence is also included. To evaluate performance, application to simulated, phantom, and an in vivo test sequence of the carotid artery are considered in comparison with other techniques. The effect of filtering on edges is of great importance, as these are used by subsequent image interpretation schemes. Quantitative measurements demonstrate the effectiveness of the Biased TDLMS filter, for both noise reduction and edge preservation. Echocardiographic images have a high noise content and suffer from poor contrast. Despite this challenging environment, the Biased TDLMS filter is shown to produce images that are better inputs for subsequent feature extraction. The benefits for echocardiographic images are highlighted by considering the problems of mitral valve analysis and extraction of the left atrium boundary. <s> BIB012 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The K distribution is an efficient model to the nonRayleigh statistics of the envelope of backscattered signals in random media. This modeling leads to estimate a parameter of effective density by means of the calculation of statistical moments of the envelope signal. In this study, we propose a mathematical analysis of an effective density estimator previously used and based on superior order moments. In order to improve the effective density estimate, we propose several estimators based on low and fractional order moments. The performances of these estimators are evaluated both with simulated signals and in an experimental context with synthetic foams. Estimators based on low and fractional moments appear to be more robust than superior moment-based estimator and an improvement of the spatial resolution of the estimate can be obtained. Results also confirm the capability of the effective density parameter to characterize the spatial distribution of scattering structures. <s> BIB013 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> This paper presents an algorithm for speckle reduction and contrast enhancement of echocardiographic images. Within a framework of multiscale wavelet analysis, the authors apply wavelet shrinkage techniques to eliminate noise while preserving the sharpness of salient features. In addition, nonlinear processing of feature energy is carried out to enhance contrast within local structures and along object boundaries. The authors show that the algorithm is capable of not only reducing speckle, but also enhancing features of diagnostic importance, such as myocardial walls in two-dimensional echocardiograms obtained from the parasternal short-axis view. Shrinkage of wavelet coefficients via soft thresholding within finer levels of scale is carried out on coefficients of logarithmically transformed echocardiograms. Enhancement of echocardiographic features is accomplished via nonlinear stretching followed by hard thresholding of wavelet coefficients within selected (midrange) spatial-frequency levels of analysis. The authors formulate the denoising and enhancement problem, introduce a class of dyadic wavelets, and describe their implementation of a dyadic wavelet transform. Their approach for speckle reduction and contrast enhancement was shown to be less affected by pseudo-Gibbs phenomena. The authors show experimentally that this technique produced superior results both qualitatively and quantitatively when compared to results obtained from existing denoising methods alone. A study using a database of clinical echocardiographic images suggests that such denoising and enhancement may improve the overall consistency of expert observers to manually defined borders. <s> BIB014 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> A brief review of the history, properties and applications of K-distributed noise is presented. Statistical relationships and generalizations of the model are summarized, and processing techniques developed to extract signals embedded in this kind of noise are briefly discussed. <s> BIB015 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> This paper describes an approach to boundary detection in ultrasound speckle based on an image enhancement technique. The enhancement algorithm works by filtering the image with "sticks," short line segments which are varied in orientation to achieve the maximum projected value at each point. The statistical properties of this approach have been described in an earlier paper; in this work we present three significant extensions to improve the performance of the basic method. First, we investigate the effect of varying the size and shape of the sticks. We show that these variations affect the performance of the algorithm in very fundamental ways, for example by making it more or less sensitive to thinner or more tightly curving boundaries. Second, we present a means of improving the performance of this technique by estimating the distribution function of the orientation of the line passing through each point. Finally, we show that images can be "stained" for easier visual interpretation by applying to each pixel a false color whose hue is related to the orientation of the most prominent line segment at that point. Examples are given to illustrate the performance of the different settings on a single image. <s> BIB016 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The K-distribution had been introduced as a valid model to represent the statistics of the envelope of the backscattered echo from phantom and tissue. This paper investigates the efficacy of the parameters of this statistical model; namely, the effective number and the effective cross-section, to characterize breast lesions as benign or malignant. Based on the normalized values of the effective number and the effective scattering cross-section, images containing benign and malignant masses were classified for a data set from 52 patients having breast masses/lesions. The receiver operating characteristic (ROC) curves were then obtained to test the classification based on these two parameters. The results indicate that the parameters of the K-distribution may be useful in classification of the breast lesions as benign and malignant. <s> BIB017 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The statistics of the backscattered ultrasonic echo from tissue have been described using Rayleigh, K, and Nakagami distributions. The Nakagami and K distributions, each with two parameters, can model the envelope reasonably well. However, a three-parameter distribution is likely to match the envelope of the backscattered echo much better than these two-parameter distributions. Starting with the Nakagami distribution and including an additional parameter to account for the tails of the density function, a generalized Nakagami distribution has been derived. Computer simulation of A-scans and analysis of data collected from tissue-mimicking phantoms show that the generalized Nakagami distribution fits the statistics of the echo of the envelope better than the Nakagami distribution. The parameters of the generalized Nakagami distribution appear to be far more sensitive to the scattering conditions than the parameters of the Nakagami distribution. <s> BIB018 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The Nakagami distribution was proposed recently for modeling the echo from tissue. In vivo breast data collected from patients with lesions were studied using this Nakagami model. Chi-square tests showed that the Nakagami distribution is a better fit to the envelope than the Rayleigh distribution. Two parameters, m (effective number) and alpha (effective cross section), associated with the Nakagami distribution were used for the classification of breast masses. Data from 52 patients with breast masses/lesions were used in the studies. Receiver operating characteristics (ROC) were calculated for the classification methods based on these two parameters. The results indicate that these parameters of the Nakagami distribution may be useful in classification of the breast abnormalities. The Nakagami distribution may be a reasonable means to characterize the backscattered echo from breast tissues toward a goal of an automated scheme for separating benign and malignant breast masses. <s> BIB019 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> A novel speckle suppression method for medical ultrasound images is presented. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain. We show that the subband decompositions of ultrasound images have significantly non-Gaussian statistics that are best described by families of heavy-tailed distributions such as the alpha-stable. Then, we design a Bayesian estimator that exploits these statistics. We use the alpha-stable model to develop a blind noise-removal processor that performs a nonlinear operation on the data. Finally, we compare our technique with current state-of-the-art soft and hard thresholding methods applied on actual ultrasound medical images and we quantify the achieved performance improvement. <s> BIB020 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The quality of ultrasound images is limited due to granular speckle noise. The presented despeckle algorithm compensates the depth-dependent shape of granular speckles in sector scans by an initial coordinate transform. This yields a horizontally oriented speckle pattern of constant resolution and hence allows the use of constant filter templates. The signal-dependent nature of multiplicative speckle noise is considered by a ratio pyramid containing noise-normalized, subsampled scales corrupted by signal- independent noise. Since speckles can be identified as positive and negative impulses on the subsampled scales, they are removed by selfdual nonlinear multistage filters (NMF). The templates are adapted to the granular appearance of the speckles and the degree of filtering is individually controlled by the local noise power in each scale. We propose a new selfdual morphological pyramid with the common erosion/dilation as analysis operators and the reconstructive dilation/erosion as synthesis operators. The resulting closing-by-reconstruction and opening-by- reconstruction branches consider local intensity amplifications and attenuations, respectively. They are generated separately and combined only for scale-selective restoration by NMFs. Besides morphological decomposition, a ratio Laplacian pyramid is evaluated and its performance is compared with the proposed morphological decomposition, a ratio Laplacian pyramid is evaluated and its performance is compared with the proposed morphological decomposition. Both methods lead to significant noise reduction, where the morphological method introduces less signal degenerations. <s> BIB021 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> The K distribution is an accurate model for ultrasonic backscatter. A neural approach is developed to estimate K distribution parameters. Accuracy and consistency of the estimates from simulated K and envelope data compare favorably with other techniques. Neural networks can potentially be used as a complementary technique for tissue characterization. <s> BIB022 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> This paper presents a novel approach for speckle reduction and coherence enhancement of ultrasound images based on nonlinear coherent diffusion (NCD) model. The proposed NCD model combines three different models. According to speckle extent and image anisotropy, the NCD model changes progressively from isotropic diffusion through anisotropic coherent diffusion to, finally, mean curvature motion. This structure maximally low-pass filters those parts of the image that correspond to fully developed speckle, while substantially preserving information associated with resolved-object structures. The proposed implementation algorithm utilizes an efficient discretization scheme that allows for real-time implementation on commercial systems. The theory and implementation of the new technique are presented and verified using phantom and clinical ultrasound images. In addition, the results from previous techniques are compared with the new method to demonstrate its performance. <s> BIB023 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Classification of breast masses in greyscale ultrasound images is undertaken using a multiparameter approach. Five parameters reflecting the non-Rayleigh nature of the backscattered echo were used. These parameters, based mostly on the Nakagami and K distributions, were extracted from the envelope of the echoes at the site, boundary, spiculated region and shadow of the mass. They were combined to create a linear discriminant. The performance of this discriminant for the classification of breast masses was studied using a data set consisting of 70 benign and 29 malignant cases. The Az value for the discriminant was 0.96 ± 0.02, showing great promise in the classification of masses into benign and malignant ones. The discriminant was combined with the level of suspicion values of the radiologist leading to an Az value of 0.97 ± 0.014. The parameters used here can be calculated with minimal clinical intervention, so the method proposed here may therefore be easily implemented in an automated fashion. These results also support the recent reports suggesting that ultrasound may help as an adjunct to mammography in breast cancer diagnostics to enhance the classification of breast masses. <s> BIB024 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> This paper describes the image formation in medical ultrasound for the case of scattering media. The texture statistics are dominated by speckle formation. The effects of spatial, fixed and adaptive, filtering, as well as, of grey scale encoding on the detection of lesions are analytically described and illustrated with representative images. <s> BIB025 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> In this paper, we define a new adaptive morphological operation, in which the value of a structuring element varies adaptively depending on the local intensity information of the processing image of interest. We prove that the proposed adaptive morphological operation has almost the same mathematical structure and properties as the conventional ones have. There are many useful functions in the method. Among them are the opening and closing, which implement both smoothing of the image and emphasizing of the edges at a time. Conventional opening operation has a smoothing function but not both. Applying our method to relatively unclear images such as ultrasound ones with speckle noise, its usefulness can be found in extracting regions. We also discuss parameter setting, and its enhancement effect together with experimental results is demonstrated. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(3): 33–43, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10196 <s> BIB026 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> Fractional low order moments have been reported as beneficial for sampling computations using the K distribution. However, it has been recently pointed out that this it not the case for the homodyned-K distribution for a tissue discrimination problem. In this paper we show that such an statement is not fully justified. To that end, we follow a standard pattern recognition procedure both to determine class separability measures and to classify data with several classifiers. We conclude that the optimum order of the moments is intimately linked to the specific statistical properties of the tissues to be discriminated. Some ideas on how to choose the optimum order are discussed. <s> BIB027 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> This paper presents a diffusion stick method for speckle suppression in ultrasonic images. An asymmetric stick filter kernel is firstly defined by decomposing the rectangle neighborhood into line segments of variable orientations. Then, the weighted sum of averages along each stick is used to produce the filtered images. Implemented in an iteration scheme, our method works as a pseudo-diffusion process, where the diffusivity is controlled by a normalized variance function. Experiments of synthetic and real images show that the diffusion stick technique performs effectively in suppressing speckle noise, preserving resolvable structures and enhancing linear features. <s> BIB028 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> We present a morphological multi-scale method for image sequence processing, which results in a truly coupled spatio-temporal anisotropic diffusion. The aim of the method is not to smooth the level-sets of single frames but to denoise the whole sequence while retaining geometric features such as spatial edges and highly accelerated motions. This is obtained by an anisotropic spatio-temporal level-set evolution, where the additional artificial time variable serves as the multi-scale parameter. The diffusion tensor of the evolution depends on the morphology of the sequence, given by spatial curvatures of the level-sets and the curvature of trajectories (=acceleration) in sequence-time. We discuss different regularization techniques and describe an operator splitting technique for solving the problem. Finally we compare the new method with existing multi-scale image sequence processing methodologies. <s> BIB029 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> This paper deals with anisotropic diffusion in images affected by speckle. Two existing methods are reviewed. The first is a robust diffusion technique, non adapted to speckle, based on the Tukey function. The second applies an isotropic diffusion to speckle but lacks robustness. The contribution of this paper is to create a robust anisotropic diffusion filter adapted to speckle. The proposed approach is based on the two reviewed methods and introduces an original diffusion tensor Experimentation results are presented and the performance of the three methods compared. The proposed algorithm shows significant enhancement. <s> BIB030 </s> Ultrasound image segmentation: a survey <s> B. Speckle-Noise or a Feature? <s> A novel speckle-reduction method is introduced, based on soft thresholding of the wavelet coefficients of a logarithmically transformed medical ultrasound image. The method is based on the generalised Gaussian distributed(GGD) modelling of sub-band coefficients. The method used was a variant of the recently published BayesShrink method by Chang and Vetterli, derived in the Bayesian framework for denoising natural images. It was scale adaptive, because the parameters required for estimating the threshold depend on scale and sub-band data. The threshold was computed by Kσ 2 /σ x , where σ and σ x were the standard deviation of the noise and the sub-band data of the noise-free image, respectively, and K was a scale parameter. Experimental results showed that the proposed method outperformed the median filter and the homomorphic Wiener filter by 29% in terms of the coefficient of correlation and 4% in terms of the edge preservation parameter. The numerical values of these quantitative parameters indicated the good feature preservation performance of the algorithm, as desired for better diagnosis in medical image processing. <s> BIB031
Speckle gives ultrasound images their characteristic granular appearance. It inherently exists in coherent imaging, including ultrasound imaging. The analysis of this signal-dependent effect has been a major subject of investigation in the medical ultrasound imaging community, as well as the optical (laser) and radar imaging communities. The texture appearance of the observed speckle does not correspond to underlying tissue structure. However, the local brightness of the speckle pattern does reflect the local echogeneity of the underlying scatterers. Speckle can be undesirable and hence is seen as noise to be reduced, or, as signal carrying some information about the observed tissues. Thus, from a segmentation perspective, you may chose to remove it or utilize it for the information it contains. The received echo signals are obtained by a coherent summation of echo signals from many ultrasound scatterers. Speckle has a random and deterministic nature as it is formed from backscattered echoes of randomly or coherently distributed scatterers in the tissue BIB002 , BIB001 . It has been shown that the statistical properties of the received signal, and thus of the echo envelope, depend on the density and the spatial distribution of the scatters BIB002 . Several distribution families have been proposed in the literature. For the special case of a large number of randomly located scatterers, the statistics of the envelope signal shows a Rayleigh distribution (see e.g., BIB002 and BIB001 ). In this condition, the speckle is called fully developed. Deviations from such special scattering conditions have been previously modeled via • the Rice distribution to account for a coherent component due to the presence of a regular structure of scatterers within the tissue BIB002 , BIB003 ; • the -distribution to account for low effective scatter density (partially developed speckle) (see e.g., BIB004 and BIB015 ). Unfortunately, the Rician family fails to account for reduced scatterer densities, and the -distribution model does not take into account the presence of a coherent component. General models have been proposed in the literature namely the generalized -distribution and the homodyned -distribution (see e.g., BIB015 and BIB006 ) and most recently the Rician Inverse of Gaussian distribution  . The three models are general and can account for the different scattering conditions. However, the analytical complexity with these families is significant. Some effort has been put into efficiently estimating the parameters BIB007 BIB013 BIB027 BIB022  and alternative simple models have also been proposed such as the Nakagami family (see e.g.,  ). Note that all these models are for the envelope of the received echo signal. In clinical ultrasound imaging systems, a log-compression is performed to control the dynamic range of the image. An approximate algorithm for the estimation of the log-compression parameter from pixel values of a displayed -scan images was recently proposed  . Statistics of the log-compressed echo envelope have also been proposed BIB009 ,  . A number of tissue characterization algorithms BIB003 , BIB004 ,  ,  , BIB005 BIB017 BIB018 BIB019 BIB024  BIB025 , denoising algorithms  , BIB010 , local entropy statistics BIB011 , and an MRF model  based on the above models have been proposed in the literature. There is also an extensive literature on speckle reduction which has been proposed as a presegmentation step; recent works include wavelets-based methods BIB020 BIB031 BIB014 BIB028 , anisotropic diffusion methods BIB029 ,  , BIB023  BIB030 , and others BIB016 ,  , BIB012 BIB008  BIB021 BIB026 .