Directionlet-based method using the Gaussian mixture prior to SAR image despeckling

In this article, a new denoising algorithm is proposed based on the directionlet transform and the maximum a posteriori (MAP) estimation. The detailed directionlet coefficients of the logarithmically transformed noise-free image are considered to be Gaussian mixture probability density functions (PDFs) with zero means, and the speckle noise in the directionlet domain is modelled as additive noise with a Gaussian distribution. Then, we develop a Bayesian MAP estimator using these assumed prior distributions. Because the estimator that is the solution of the MAP equation is a function of the parameters of the assumed mixture PDF models, the expectation-maximization (EM) algorithm is also utilized to estimate the parameters, including weight factors and variances. Finally, the noise-free SAR image is restored from the estimated coefficients yielded by the MAP estimator. Experimental results show that the directionlet-based MAP method can be successfully applied to images and real synthetic aperture radar images to denoise speckle.