Speckle noise modeling in the dual-tree complex wavelet domain

Medical ultrasound images are inherently corrupted with speckle noise in a multiplicative manner. The most popular approach of despeckling is homomorphic filtering, in which the multiplicative speckle noise converted to an additive one by log-transformation. The knowledge of the statistics of the log-transformed speckle is necessary for developing effective methods for speckle reduction. The Bessel K-Form (BKF) probability density function (pdf) is proposed to model the logarithmically transformed speckle noise in the dual-tree complex wavelet transform (DT-CWT) domain. A maximum likelihood based method is developed for estimating the parameters of the BKF pdf. The suitability of the BKF pdf in modeling the speckle is studied for different noise levels in the 2D DT-CWT domain. It is shown that the BKF can capture the statistics of the DT-CWT coefficients corresponding to log-transformed speckle better than the Gaussian and normal inverse Gaussian pdfs.