Optimized Compressed Sensing Matrix Design for Noisy Communication Channels

TL;DR

This paper presents a novel power-constrained sensing matrix design for compressed sensing in noisy communication channels, optimizing MSE performance and offering low-complexity solutions that outperform existing methods.

Contribution

It introduces a new matrix design approach based on minimizing a lower-bound on MSE, with closed-form solutions and a stochastic optimization method for reduced computational complexity.

Findings

Proposed design improves sparse source reconstruction accuracy.

Low-complexity stochastic method outperforms traditional approaches.

Numerical experiments validate the effectiveness of the proposed scheme.

Abstract

We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel and the sensor-to-decoder communication channel are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE. Under certain conditions, we derive closed-form solutions to the optimization problem. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the strength of the proposed scheme by comparing it with other relevant methods. We discuss the computational complexity of our design method, and develop an equivalent stochastic optimization method to the problem of interest that can be solved approximately with a significantly less computational burden. We illustrate that the low-complexity method still outperforms the popular competing methods.