A stochastic gradient approach on compressive sensing signal reconstruction based on adaptive filtering framework

TL;DR

This paper introduces a stochastic gradient adaptive filtering framework for compressive sensing signal reconstruction, employing zero attraction methods to enhance convergence and robustness, and proposes algorithms that outperform existing methods.

Contribution

It presents a novel stochastic gradient approach based on adaptive filtering for sparse signal reconstruction, including new algorithms with improved convergence and noise robustness.

Findings

Algorithms converge faster than existing methods.

Enhanced robustness against noise demonstrated.

Effective acceleration of convergence rates.

Abstract

Based on the methodological similarity between sparse signal reconstruction and system identification, a new approach for sparse signal reconstruction in compressive sensing (CS) is proposed in this paper. This approach employs a stochastic gradient-based adaptive filtering framework, which is commonly used in system identification, to solve the sparse signal reconstruction problem. Two typical algorithms for this problem: $l_0$-least mean square ($l_0$-LMS) algorithm and $l_0$-exponentially forgetting window LMS ($l_0$-EFWLMS) algorithm are hence introduced here. Both the algorithms utilize a zero attraction method, which has been implemented by minimizing a continuous approximation of $l_0$ norm of the studied signal. To improve the performances of these proposed algorithms, an $l_0$-zero attraction projection ($l_0$-ZAP) algorithm is also adopted, which has effectively accelerated their convergence rates, making them much faster than the other existing algorithms for this problem. Advantages of the proposed approach, such as its robustness against noise etc., are demonstrated by numerical experiments.