Speckle noise modeling in the contourlet transform domain

Speckle noise is an inherent phenomenon in medical ultrasound (US) images. Since it degrades an ultrasound image quality and reduces its diagnostic value, reduction of speckle noise is a very important pre-processing step in ultrasound image processing. For this purpose, the knowledge of the statistics of speckle noise is necessary; especially in the multi-resolution transform domain due to their sparse and efficient representation of images. In this paper a Bessel K-Form (BKF) probability density function (pdf) is proposed as a highly suitable prior for modeling the log-transformed speckle noise in the well-known contourlet transform domain. A maximum likelihood based method is presented for estimating the parameters of the BKF pdf. The appropriateness of the BKF pdf in modeling the speckle is studied for different noise levels in the contourlet transform domain, in addition the suitability of BKF model is investigated for the case of real US images. It is shown that, in general the BKF can model the statistics of the contourlet transform coefficients corresponding to log-transformed speckle better than the traditional Gaussian and normal inverse Gaussian pdfs.