Statistical approach for Despeckling of Medical Ultrasound Images Using Non Sub-Sampled Shearlet Transform

Speckle (Multiplicative noise) removal has become one of the essential steps in ultrasonic imaging. Speckle reduction in ultrasound images causes minimizing the risk of either the miss-interpretation or wrong diagnosis for the patients. Interpreting the ultrasonic images leads to having a better understanding of tumors or other types of diseases, and it can be employed as a complementary tool for helping the doctor to diagnosis the illness as well.Many speckle removal filters have been proposed in the spatial domain such as, median filtering method [1]. Nevertheless, the usage of advanced methods by employing well-known transformations, such as Wavelet transform, has been widely developed in recent years [2,3]. The main reason for employing such transforms is their simplified representation in the transformed domain, which can be effectively modeled by known statistical or optimization tools. In the statistical viewpoint, these methods are followed by two pre-processing steps; first, the log transform should be applied to contaminated image to be able to take the linear transformation from the additive form, second, taking the intended transform and estimating the parameters of the prior distribution and noise distribution. The critical point in these methods is designing a suitable processor to remove the effect of contaminating noise, which in the literature is considered as MMSE of MAP processors [4,5]. Choosing the prior distribution for noise-free coefficients and log-transformed noise has important role in designing such processors. Many prior distributions have been proposed for wavelet coefficients such as, 2D-Garch [6] and Alpha-stable [5], and Normal Inverse Gaussian(NIG) for Contourlet transform [7]. But, wavelet transform and its extensions have some drawbacks in singularity modeling of high-dimensional functions. To overcome the weaknesses of the wavelet transform, shearlet transform has been proposed [8]. The statistical modeling of shearlet coefficients for SAR image denoising contaminated by the same noise (speckle) was studied [9]. An optimization approach in SAR image denoising to recover sparsity of shearlet coefficients was proposed in [10]. In this work, we propose a novel MMSE processor for speckle removal of ultrasound images.This paper is organized as follows; firstly, we model the multiplicative noise problem for ultrasound images. Next, we estimate parameters of the prior distribution (NIG) and unknown noise variance, and then the remainder of the section is devoted to designing the MMSE processor. In the next section, we discuss the experimental results as well as introducing the comparing criteria. Finally, the conclusion would be given.