The Overcomplete Dictionary-Based Directional Estimation Model and Nonconvex Reconstruction Methods

Abstract

In this paper, it is proposed the directional estimation model on the overcomplete dictionary, which bridges the compressed measurements of the image blocks and the directional structures of the dictionary. In the model, it is established the analytical method to estimate the structure type of a block as either smooth, single-oriented, or multioriented. Furthermore, the structures of each type of blocks are described by the structured subdictionaries. Then based on the obtained estimations and the constrains on the sparse dictionaries, the original image will be estimated. To verify the model, the nonconvex methods are designed for compressed sensing. Specifically, the greedy pursuit-based methods are established to search the subdictionaries obtained by the model, which achieve better local structural estimation than the methods without the directional estimation. More importantly, it is proposed the nonconvex image reconstruction method with direction-guided dictionaries and evolutionary searching strategies (NR_DG), where the evolutionary searching strategies are delicately designed for each type of the blocks based on the directional estimation. By the experimental results, it is shown that the NR_DG method performs better than the available two-stage evolutionary reconstruction method.