Wavelet-based Ultrasound Image Denoising Using an Alpha-stable Prior Probability Model

Ultrasonic images are generally affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. Speckle filtering is thus a critical pre-processing step in medical ultrasound imagery, provided that the features of interest for diagnosis are not lost. We present a novel speckle removal algorithm within the framework of wavelet analysis. First, we show that the subband decompositions of logarithmically transformed ultrasound images are best described by alpha-stable distributions, a family of heavy-tailed densities. Consequently, we design a Bayesian estimator that exploits this a priori information. Using the alpha-stable model we develop a noise-removal processor that performs a non-linear operation on the data. Finally, we compare our proposed technique to current state-of-the-art speckle reduction methods. Our algorithm effectively reduces speckle, it preserves step edges, and it enhances fine signal details, better than existing methods.