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Home Page Technology Electronics Computer Curvelet-based Bayesian Estimator for Speckle Suppression Essay Example
Curvelet-based Bayesian Estimator for Speckle Suppression Essay Example
Curvelet-based Bayesian Estimator for Speckle Suppression Essay Example

Curvelet-based Bayesian Estimator for Speckle Suppression Essay Example

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Curvelet-based bayesian estimator for speckle suppression in ultrasound imaging

Ultrasound images are inherently affected by speckle noise, and thus reducing this noise is crucial for successful interpretation. Bayesian estimation is a powerful technique used to remove speckle noise in images.

This paper presents a new despeckling scheme for ultrasound images using a Bayesian-based approach. The main focus is on selecting appropriate statistical models and developing a shrinkage function for estimating the noise-free signal. The proposed scheme involves using curvelet coefficients to decompose the noisy ultrasound image into noise-free and signal-dependent noise components. The noise-free component is modeled using a Cauchy distribution, while the signal-dependent noise component is modeled using a two-sided exponential distribution. The Bayesian estimator is implemented in a low-complexity manner. Experimental results confirm the effectiveness of the despeckling scheme in significantly reducing speckle noise while preserving image detail

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Keywords: Ultrasound imaging, curvelet transform, speckle noise, Bayesian estimation, statistical modeling.

Introduction

The use of ultrasound imaging is essential in medical diagnosis and offers cost-effectiveness, portability, acceptability, and safety advantages. However, the quality of ultrasound images is often compromised by speckle noise contamination. This type of noise significantly decreases image quality and hinders diagnostic tasks. As a result, it is important to reduce speckle noise while preserving anatomical information in order to accurately identify regions of interest in ultrasound images. Several spatial-based techniques that employ single-scale or multi-scale filtering have been developed in previous research to suppress speckle noise in ultrasound images.

Early single-scale spatial filtering methods had limited effectiveness in reducing speckle noise. However, more recent techniques such as bilateral filtering and nonlocal filtering have shown promise. This research was partially supported by the Natura

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Sciences and Engineering Research Council (NSERC) of Canada and the Regroupement Strategique en Microelectronique du Quebec (ReSMiQ). These techniques rely on the size of the filter window, which means that significant speckle suppression requires a long computational time.

Alternatively, the literature has explored multi-scale spatial techniques that utilize partial differential equations. These techniques are iterative and produce smooth images while preserving edges. Unfortunately, important structural details are degraded during the iteration process. To address this drawback, various despeckling techniques based on different transform domains, such as wavelet, contourlet, and curvelet, have been proposed. Wavelet transform is known for its noise reduction capabilities but is limited by poor directionality in many applications. However, the use of contourlet transform offers improved noise reduction performance due to its flexible directional decomposability.

The contourlet transform is less effective than the curvelet transform in capturing curve-like details and directional sensitivity. Thresholding is commonly used to create linear estimators for noise-free signal coefficients when developing despeckling techniques using transform domains, but determining an appropriate threshold value is a significant challenge. To address this issue, non-linear estimators based on Bayesian estimation principles have been developed. The selection of the correct probability distribution to model coefficients in the transform domain is crucial for an efficient Bayesian-based despeckling scheme. It is also important to consider the complexity of the Bayesian estimation process when choosing suitable statistical models.

When utilizing a specific probabilistic model in a Bayesian framework, it is crucial to take into account the implementation challenge of the Bayesian estimator. In this study, a novel Bayesian approach is introduced that makes use of curvelets for efficiently eliminating speckles from ultrasound images with reduced computational requirements. The

ultrasound image being observed follows a multiplicative degradation model and it is divided into an additive model which includes noise-free and signal-dependent noise components. The prior statistical model for the curvelet coefficients of the signal-dependent noise relies on a two-sided exponential distribution.

The low-complexity Bayesian estimator incorporates the model and Cauchy distribution. The performance of the Bayesian despeckling scheme is assessed on both synthetic speckled and real ultrasound images and compared to other existing despeckling schemes. In the spatial domain, the degradation model for a speckle-corrupted ultrasound image g(i, j) is given by g(i, j) = v(i, j) s(i, j)(1), where v(i, j) represents the noise-free image and s(i, j) represents the speckle noise. The model for the noisy observation of v can be decomposed into a noise-free signal component and a signal-dependent noise: g=v+(s' 1)v=v+u(2), where (s' 1)v denotes the signal-dependent noise. Equation (3) refers to the curvelet transform of equation (2) at level l. This equation states that y[l,d], representing the curvelet coefficient at position (i,j), equals x[l,d], representing the curvelet coefficient of the noise-free image, plus n[l,d], which represents additive signal-dependent noise at direction d = 1, 2, 3, A· , or D. To simplify notation, superscripts l and d as well as index i and j will be omitted from now on.

We propose using the statistical characteristics of the curvelet coefficients to reduce noise in ultrasound images. To do this, we establish a prior probabilistic model for the curvelet coefficients of and n. The distribution of curvelet coefficients in noise-free images can be modeled using the Cauchy distribution. The zero-mean Cauchy distribution is expressed as p(x) = (I?/I?)(x2 + I?2).

Here, I? represents the dispersion parameter. We estimate the parameter I? of the Cauchy distribution by minimizing the function An I†emap>E†ytp>a?’I†emap>t. In this equation, I†emap>E†y(t) represents the empirical characteristic function corresponding to the curvelet coefficients y of the noisy observation. Specifically, it is defined as I†cropx(t) = e|t| and I†Edocument(t) = exp(a?'I?'). The deviation obtained from estimating I?E is equivalent to MAD(y(i,j)) 0 .6745 (6).The equation (6) shows how to calculate the median absolute deviation using the MAD operation.

A prior statistical assumption is necessary to derive the Bayesian estimator for signal-dependent noise in curvelet coefficients. Experimental observation has determined that the tail portion of the empirical distribution of decay has a low rate. Therefore, this research proposes using a two-sided exponential (TSE) distribution represented as 1pn(n) = ea?’|n|I?2I?, where I? is the scale parameter and a positive real constant. The method used to estimate this parameter (I?E.) is log-cumulants (MoLC), resulting in an estimated value denoted as I?E = exp(1/N1N2j(log(y(i,j))) + I?). Here, N1 and N2 determine the size of the considered curvelet subband. Both Cauchy and TSE distributions have only one parameter, reducing the complexity of the Bayesian estimator for this scenario. However, there is no formula available to obtain Bayes estimates under the quadratic loss function for noise-free curvelet coefficientsx'?x?/x? ?x'>?x?/x? ? x".tThe values are determined by the shrinkage function: xE†(y) = p(x|y) ?xdx <u>y'?<x> <p>(<x>) ?'(y'?x)'(x)(9)'/sup>.

The process of obtaining the Bayesian estimates for the noise-free curvelet coefficients involves performing numerical calculations on each coefficient by integrating (9) twice. This computational-intensive procedure is necessary for acquiring accurate results.Bayesian estimates are obtained by substituting the integrals in (9) with infinite series, as proposed in

a previous study. The Bayesian shrinkage function can be expressed as ea?y/I?[f(y)I¶]+ey/I?[f(y)+I¶]xE†(y)= (10)e·ay/I? +ey/I?[f(y)+I¶] e·ay/I?[/f21(y)]+I¶2+ey/I?a?f22(y)+[I¶2], where f11(y)=f12(a?y)=sin(I?/I?)Im E(a?y+jI?).aSi(I?/I?) + I?1.I?a.y+jI?.cos(I?/I?)A ReA E1(I+a.Si(I?/I?) ,(11)f(y)=a?f1a?(y+j(sUb)a?i).sin(I?/I?)Re E()+Ci( I ? / I ? )2122.cos( I ? / I ? A ImA E1( I ?, a?.Si( I ? / I ? )+2,(12)In the equations above, j=a?s.a?'1, Im {A·} and Re {A·} are the imaginary and real parts, respectively, of a complex argument, and E1(A·), Si(A·) and Ci(A·) are, respectively, the exponential, sine and cosine integral functions obtained as in. The Experimental results demonstrate that our despeckling scheme has undergone comprehensive testing to assess its performance.The performance of various despeckling schemes, including enhanced Lee filtering, adaptive-wavelet shrinkage, and contourlet thresholding, is compared to the outcomes achieved. The evaluation is conducted on both synthetically-speckled and real ultrasound images.

The implementation of the proposed speckling scheme involves using a 5-level decomposition of the curvelet transform. However, it has been found that increasing the level of decomposition does not improve the despeckling performance. Since the curvelet transform is shift-variant, cycle spinning is performed on the observed noisy image to prevent pseudo-Gibbs artifacts near discontinuities. In this despeckling scheme, only the detail curvelet coefficients are despeckled using the Bayesian shrinkage function in equation (10). The peak signal-to-noise ratio (PSNR) is used to quantitatively evaluate the despeckling performance of different schemes when applied to synthetically-speckled images.

The PSNR values obtained when applying various schemes on two synthetically-speckled images of size 512, namely Lena and Boat, are given in Table I. It is evident from this table that the proposed despeckling scheme consistently provides higher PSNR values compared to the other schemes. To

gain a better understanding of the despeckling performance, the results in Table 1 are visualized in Figure 1. From this figure, it is clear that the superiority of the proposed scheme over the others becomes more apparent when a higher level of speckle-noise is introduced to the test images.

Two ultrasound images from Figure 2 are used to study the performance of various despeckling schemes. Due to the unavailability of noise-free images, subjective evaluation is the only way to assess scheme performance. Figure 2 shows that schemes in [2] and [6] produce despeckled images with noticeable speckle noise. Conversely, scheme [7] excessively smooths noisy images, causing the loss of texture details in despeckled images. However, the proposed despeckling scheme effectively reduces speckle noise and preserves the original image textures. In conclusion, this paper introduces a new curvelet-based scheme that applies Bayesian estimation to suppress speckle noise in ultrasound images.

The first step in the despeckling process is to break down the observed ultrasound image into two components: noise-free and signal-dependant noise. To model these components, the Cauchy distribution is used for the noise-free curvelet coefficients, while the two-sided exponential distribution is used for the signal-dependant noise curvelet coefficients. These probabilistic models are then used to create a Bayesian shrinkage function, which allows us to estimate the noise-free curvelet coefficients. A simplified version of this shrinkage function is implemented to reduce computational complexity. To evaluate the effectiveness of this despeckling scheme, experiments are conducted on both synthetic and real ultrasound images.

The proposed despeckling scheme has been compared to other existing schemes and has shown superior results, providing higher PSNR values and well-despeckled images with better diagnostic details.

References

  1. Dhawan, A.P.: Medical image analysis.Volume 31.John Wiley &Sons (2011) Loupas, T., McDicken, W., Allan, P.: A An adaptive weighted median filter for speckle suppression in medical ultrasonic images.IEEE transactions on Circuits and Systems 36 (1) (1989) 129-135
  2. Coupe, P., Hellier, P., Kervrann, C., Barillot, C.: Nonlocal means-based speckle filtering for ultrasound images.IEEE transactions on image processing 18 (10) (2009) 2221-2229
  3. Sridhar, B., Reddy, K., Prasad, A.: An unsupervisory qualitative image enhancement using adaptive morphological bilateral filter for medical images.International Journal of Computer Applications 10 (2i) (2014) 1
  4. Abd-Elmoniem, K.Z., Youssef, A.B., Kadah, Y.M.: Real-time speckle reduction and coherence enhancement in ultrasound imaging via nonlinear anisotropic diffusion.IEEE Transactions on Biomedical Engineering 49 (9) (2002) 997-1014
  5. Swamy, M., Bhuiyan, M., Ahmad, M.: Spatially adaptive thresholding in wavelet domain for despeckling of ultrasound images.The article "Speckle reducing contourlet transform for medical ultrasound images" was published in IET Image Process 3 (3) (2009), pages 147-162.

    Int J Compt Inf Engg 4 (4) (2010) 284-291

  6. Jian, Z., Yu, Z., Yu, L., Rao, B., Chen, Z., Tromberg, B.J.: Speckle attenuation in optical coherence tomography by curvelet shrinkage. Optics letters 34 (10) (2009) 1516-1518
  7. Deng, C., Wang, S., Sun, H., Cao, H.: Multiplicative spread spectrum watermarks detection performance analysis in curvelet domain. In: 2009 International Conference on E-Business and Information System Security. (2009)
  8. Damseh, R.R., Ahmad, M.O.: A low-complexity mmse bayesian estimator for suppression of speckle in sar images.

    9. In: Circuits and Systems (ISCAS), 2016 IEEE International Symposium on, IEEE (2016) 1002-1005

  9. Temizel, A., Vlachos, T., Visioprime, W.: Wavelet domain image resolution enhancement using cycle-spinning. Electronics Letters 41 (3) (2005) 119-121
  10. Siemens A Healthineers:A https://www.healthcare.siemens.com/ultrasound. Accessed: A 2017-01-06.
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