Recovery of polarimetric Stokes images by spatial mixture models

A Bayesian approach for joint restoration and segmentation of polarization encoded images is presented with emphasis on both physical admissibility and smoothness of the solution. In this probabilistic framework, two distinct models for the sought polarized radiances are used. In the first model, the polarized light at each site of the image is described by its Stokes vector which directly follows a mixture of truncated Gaussians explicitly assigning zero probability to inadmissible configurations. In the second one, the polarization at each site is represented by the coherency matrix whose positive semidefiniteness provides a convenient way to ensure the physical admissibility of the solution. This matrix is parameterized by a set of variables assumed to be generated by a spatially varying mixture of Gaussians. Inference for both models is obtained by the Expectation-Maximization (EM) algorithm. The restored Stokes images are always physically admissible which is not the case for the näıve pseudo-inverse approach. Numerical experiments on real and synthetic images using the proposed methods assess the pertinence of the approach. Experiments on noise-degraded images confirm the robustness to noise, both in terms of visual quality as well as SNR improvement