Image compressive-sensing recovery using structured laplacian sparsity in DCT domain and multi-hypothesis prediction

In compressive sensing (CS), the seeking of a fair domain is of essentially significance to achieve a high enough degree of signal sparsity. Most methods in the literature, however, use a fixed transform domain or prior information that cannot exhibit enough sparsity for various images. Superiorly, we propose an algorithm to explore the structured Laplacian sparsity of DCT coefficients, which can adapt to the non-stationarity of natural images. Better sparsity is achieved by utilizing the nonlocal similarity of natural images and constructing structured image patch groups. Meanwhile, multiple hypotheses for each pixel could be obtained owing to the overlapping of the structured groups and similar patches. Additionally, for solving the optimization problem formulated from the techniques above, we design an efficient iterative method based on split Bregman iteration (SBI) algorithm. Experimental results demonstrate that the proposed algorithm outperforms the other state-of-the-art methods in both objective and subjective recovery quality.