A fast method for despeckling in wavelet domain using Laplacian prior and Rayleigh noise

In this paper we introduce a new speckle noise reduction algorithm using new probability density functions (pdfs) for log-transformed data in wavelet domain, i.e., Laplacian pdf for clean data and Rayleigh pdf for noise. The maximum a posteriori (MAP) estimator is employed to obtain the clean data from noisy observation. The Laplacian pdf is able to model the heavy-tailed nature of wavelet coefficients and since our new despeckling algorithm is implemented locally, we can model the most important dependency between wavelet coefficients. We examine our fast algorithm for both real and artificial speckle noise and achieve satisfactory performance both visually and qualitatively.