Low storage space for compressive sensing: semi-tensor product approach

Jinming Wang,Chaoxiang Chen,Yue Ruan,Shiping Ye

doi:10.1186/s13640-017-0199-9

Jinming Wang, Chaoxiang Chen + Show 2 more

Open Access

https://doi.org/10.1186/s13640-017-0199-9

Copy DOI

Abstract

Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

Highlights

Compressive sensing (CS) [1] theory provides a new way to sample and compress data
Our work aimed at reducing the amount of storage space needed with conventional compressive sensing
We provided a theoretical analysis of the acquisition process with semi-tensor product (STP)-CS and that of the recovery algorithm with iteratively re-weighted least squares (IRLS)

Summary

Introduction

Compressive sensing (CS) [1] theory provides a new way to sample and compress data. The basic idea of CS is that a higher-dimensional signal is projected onto a measurement matrix, by which a low-dimensional sensed sequence is obtained. The proposed algorithm effectively reduces the storage space of a measurement matrix. Deterministic measurement matrices require little storage space and incur less computational cost, but the accuracy of the reconstruction is not as high as a random measurement matrix. To reconstruct the original signals, the Kronecker algorithm must generate an M × N dimensional measurement matrix, and this requires large-scale memory space. The aim is to propose an algorithm that can maintain the same reconstruction performance as conventional compressive sensing, but requires less required storage for the measurement matrix and less memory for reconstructing. Our algorithm generates a random matrix, with dimensions that are smaller than M and N, where M is the length of the sampling vector and N is the length of signal that we want to reconstruct. The STP of matrices was introduced by Cheng [21, 22]

Semi-tensor product

Conventional CS algorithm

Comparisons with two-dimensional signals

Findings

Conclusions