Joint Design of Measurement Matrix and Sparse Support Recovery Method via Deep Auto-encoder

TL;DR

This paper introduces a deep learning auto-encoder approach to jointly design measurement matrices and support recovery methods for complex sparse signals, outperforming traditional methods especially when sparsity patterns are unknown or complex.

Contribution

It proposes a novel data-driven auto-encoder framework that jointly optimizes measurement matrices and support recovery, effectively exploiting sparsity properties without requiring explicit models.

Findings

Achieves better support recovery performance than classic methods.

Reduces computational complexity significantly.

Effective in scenarios with complex or unknown sparsity structures.

Abstract

Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity patterns for improving performance. In this letter, we propose a data-driven approach to jointly design the measurement matrix and support recovery method for complex sparse signals, using auto-encoder in deep learning. The proposed architecture includes two components, an auto-encoder and a hard thresholding module. The proposed auto-encoder successfully handles complex signals using standard auto-encoder for real numbers. The proposed approach can effectively exploit properties of sparsity patterns, and is especially useful when these underlying properties do not have analytic models. In addition, the proposed approach can achieve sparse support recovery with low computational complexity. Experiments are conducted on an application ex-ample, device activity detection in grant-free massive access for massive machine type communications (mMTC). Numerical results show that the proposed approach achieves significantly better performance with much less computation time than classic methods, in the presence of extra structures in sparsity patterns.