Modeling of Log-Transformed Speckle Noise in the Contourlet Transform Domain for Medical Ultrasound Images

Speckle noise in medical ultrasound (US) degrades the image quality and reduces its diagnostic value. Reduction of speckle noise is an important pre-processing step for the analysis and processing of medical ultrasound images. Knowledge of the statistics of the log-transformed speckle especially in the multi-resolution transform domain is important for developing effective homomorphic despeckling techniques, the most popular approach of speckle reduction from ultrasound images. In this paper, the 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 introduced for estimating the parameters of the BKF pdf. The effectiveness of the proposed estimation method is demonstrated using Monte Carlo simulations. The appropriateness of the BKF pdf in modeling the speckle is first studied extensively for simulated noise of different levels in the contourlet transform domain. Next, the suitability of BKF model is investigated for the case of real US images that include neonatal brain and breast tumors. It is shown that, in general the BKF prior can model the statistics of the contourlet transform coefficients corresponding to the log-transformed speckle better than the traditionally used Gaussian, normal inverse Gaussian and generalized Nakagami pdfs.