Expected Patch Log Likelihood with a Prior of Mixture of Matrix Normal Distributions for Image Denoising

Mixture of Matrix Normal Distributions (MMND) is the two dimensional extension of Gaussian Mixture Model, which has been widely applied for clustering three-way data. It is the key issue to build image prior model for solving image denoising problem. In this paper, the Expected Patch Log Likelihood (EPLL) with a prior of MMND is proposed for image denoising. Expectation Maximization algorithm and flip-flop algorithm are adopted to estimate the parameters in MMND. Regularization parameter of covariance matrix is selected by the criterion of minimization the Kullback Leibler information measure (KLIM) with a heuristic approximation. Under the framework of the EPLL, the approximate MAP estimation for the unknown image x is developed. It is shown by experiments that MMND based patch prior performs well on image denoising problem.