Nonlocaly Multi-Morphological Representation for Image Reconstruction From Compressive Measurements

A novel multi-morphological representation model for solving the nonlocal similarity-based image reconstruction from compressed measurements is introduced in this paper. Under the probabilistic framework, the proposed approach provides the nonlocal similarity clustering for image patches by using the Gaussian mixture models, and endows a multi-morphological representation for image patches in each cluster by using the Gaussians that represent the different features to model the morphological components. Using the simple alternating iteration, the developed piecewise morphological diversity estimation (PMDE) algorithm can effectively estimate the MAP of morphological components, thus resulting in the nonlinear estimation for image patches. We extend the PMDE to a piecewise morphological diversity sparse estimation by using the constrained Gaussians with the low-rank covariance matrices, to gain the performance improvements. We report the experimental results on image compressed sensing in the case of sensing nonoverlapping patches with Gaussian random matrices. The results demonstrate that our algorithms can suppress undesirable block artifacts efficiently, and delivers reconstructed images with higher qualities than other state-of-the-art methods.