Efficient Projection for Compressed Sensing

Compressed sensing (CS), a joint compression and sensing process, is a emerging field of activity in which the signal is sampled and simultaneously compressed at a greatly reduced rate. In CS, the projection matrix is chosen at random which would lead to inefficient performance of CS. Recently, an optimized projection (OP) was chosen such that it leads to better coherence of the effective dictionary, leading substantially better CS reconstruction performance. This is the only recent work related to the optimization of projection matrix, but the major drawback of this approach is that its algorithm is an iterative and high complexity one. It is considered that an efficient and lightweight algorithm for designing projection matrix would usefully supplement and enhance the performance of CS. In this paper, we propose an algorithm to obtain such an projection matrix called efficient projection (EP) which is designed in such a way that the new projected dictionary will have the structure as much similar as the original dictionary. For this purpose, we use multidimensional scaling (MDS) technique which helps to find a low-dimensional new projected dictionary such that the pairwise distances between new atoms in this new projected dictionary match as well as possible the original atoms in original dictionary. This leads to a solution for EP which is very simple and can be obtained by doing singular value decomposition of original dictionary. The experiments show the novelty of our approach when it can gain a comparative performance with a very low complexity compared to that of OP.