Deep Unfolding of Iteratively Reweighted ADMM for Wireless RF Sensing

TL;DR

This paper introduces a deep unfolding approach for iteratively reweighted ADMM to enhance defect detection in layered materials using wireless radar, combining non-convex optimization with deep learning for improved accuracy and convergence.

Contribution

It proposes a novel deep unfolding method for a non-convex joint rank and sparsity minimization problem in wireless RF sensing, outperforming traditional convex approaches.

Findings

Outperforms conventional methods in mean square error of component recovery.

Achieves faster convergence in defect detection.

Demonstrates improved accuracy through deep learning parameter tuning.

Abstract

We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose joint rank and sparsity minimization for defect detection. In particular, we propose a non-convex approach based on the iteratively reweighted nuclear and $\ell_1-$norm (a double-reweighted approach) to obtain a higher accuracy compared to the conventional nuclear norm and $\ell_1-$norm minimization. To this end, an iterative algorithm is designed to estimate the low-rank and sparse contributions. Further, we propose deep learning to learn the parameters of the algorithm (i.e., algorithm unfolding) to improve the accuracy and the speed of convergence of the algorithm. Our numerical results show that the proposed approach outperforms the conventional approaches in terms of mean square errors of the recovered low-rank and sparse components and the speed of convergence.