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.

1. Introduction

Compressive Sensing (CS) has attracted tremendous interest in recent years, which provides the possibility of recovering a signal at sub-Nyquist rate [1]–[5]. It declares that a signal with sparse representations under some domain can be reconstructed with high probability from very few measurements, which are obtained via linearly projecting the original signal onto a random basis. CS theory depicts a new paradigm for signal acquisition, which conducts sampling and compression at the same time, rather than sequentially performing these two steps as the traditional methodology does. CS-based compression has an asymmetric design: simple encoder and complex decoder, which is quite conductive to some image processing applications where the data acquisition devices have to be simple (e.g. inexpensive resource-deprived sensors), or oversampling may harm the object being captured (e.g. X-ray imaging) [6].