Spatially adaptive Bayesian wavelet thresholding for speckle removal in medical ultrasound images

Abstract

In this paper, a novel spatially adaptive wavelet thresholding method based on Bayesian maximum a posteriori (MAP) criterion is proposed for speckle removal in medical ultrasound (US) images. The method firstly performs logarithmical transform to original speckled ultrasound image, followed by redundant wavelet transform. The proposed method uses the Rayleigh distribution for speckle wavelet coefficients and Laplacian distribution for modeling the statistics of wavelet coefficients due to signal. A Bayesian estimator with analytical formula is derived from MAP estimation, and the resulting formula is proven to be equivalent to soft thresholding in nature which makes the algorithm very simple. In order to exploit the correlation among wavelet coefficients, the parameters of Laplacian model are assumed to be spatially correlated and can be computed from the coefficients in a neighboring window, thus making our method spatially adaptive in wavelet domain. Theoretical analysis and simulation experiment results show that this proposed method can effectively suppress speckle noise in medical US images while preserving as much as possible important signal features and details.