Robust Image Reconstruction for Block-Based Compressed Sensing Using a Binary Measurement Matrix

Abstract

Nowadays, there are still difficulties in the implementation of Compressed Sensing (CS) sensors due to the nature of the measurement matrix. A binary measurement matrix can simplify the CS procedure significantly. However, due to the singularity of this class of measurement matrices, the convergence of some of existing CS reconstruction algorithms, such as the well-known block-based CS with smoothed-projected Landweber reconstruction (BCS-SPL) algorithm, is not guaranteed and can lead to an inaccurate recovery. In this paper we propose a simple, fast and efficient CS recovery algorithm that is able to recover the original image from compressed samples which are obtained using a binary measurement. Singular value decomposition (SVD) is coupled with the BCS-SPL algorithm in order to improve its recovery capability when a binary matrix is employed. The experimental results show that the proposed recovery algorithm has a better performance in terms of reconstruction quality when compared with existing reconstruction algorithm and yields images with quality that matches or exceeds those produced by the BCS-SPL algorithm. Additionally, the proposed algorithm is the most efficient in terms of recovery time, especially at high subrates.