Image/video compressive sensing recovery using joint adaptive sparsity measure

Compressive sensing (CS) is a recently emerging technique and an extensively studied problem in signal and image processing, which enables joint sampling and compression into a unified approach. Recently, local smoothness and nonlocal self-similarity have both led to superior sparsity priors for CS image restoration. In this paper, first, a new sparsity measure called joint adaptive sparsity measure (JASM) is introduced. The proposed JASM enforces both local sparsity and nonlocal 3D sparsity in transform domain, concurrently, providing a powerful mechanism for characterizing the structured sparsities of natural image. More precisely, the local sparsity depicts the local smoothness redundancies exploited by an adaptively learned sparsifying basis, and the nonlocal 3D sparsity corresponds to the nonlocal self-similarity constraint achieved by a new proposed nonlocal statistical sparse modeling. Then, two novel techniques for high-fidelity CS image and video recovery via JASM are proposed. The proposed methods are formulated in the form of minimization functional under regularization-based framework which is solved via an efficient alternating minimization algorithm based on split Bregman framework. Comprehensive experimental results are reported to manifest the effectiveness of the proposed methods compared with the current state-of-the-art methods in CS image/video restoration. HighlightsA new sparsity measure called joint adaptive sparsity measure (JASM) is established.The proposed JASM enforces both local and nonlocal 3D sparsity in transform domain.Two novel techniques for high-fidelity CS image/video recovery via JASM are proposed.Extensive experimental results validate the effectiveness of the proposed methods.