Through the Wall Radar Imaging via Kronecker-structured Huber-type RPCA

TL;DR

This paper introduces a novel robust low-rank plus sparse matrix decomposition method using Kronecker-structured RPCA for improved through-the-wall radar imaging, effectively handling noise and outliers to enhance target detection.

Contribution

It reformulates TWRI as a Kronecker-structured RPCA problem with robust noise handling and develops an efficient ADMM-based solution with tailored steps for wall removal and target recovery.

Findings

Enhanced detection performance in complex scenarios

Robustness to heterogeneous noise and outliers

Effective wall clutter removal and target localization

Abstract

The detection of multiple targets in an enclosed scene, from its outside, is a challenging topic of research addressed by Through-the-Wall Radar Imaging (TWRI). Traditionally, TWRI methods operate in two steps: first the removal of wall clutter then followed by the recovery of targets positions. Recent approaches manage in parallel the processing of the wall and targets via low rank plus sparse matrix decomposition and obtain better performances. In this paper, we reformulate this precisely via a RPCA-type problem, where the sparse vector appears in a Kronecker product. We extend this approach by adding a robust distance with flexible structure to handle heterogeneous noise and outliers, which may appear in TWRI measurements. The resolution is achieved via the Alternating Direction Method of Multipliers (ADMM) and variable splitting to decouple the constraints. The removal of the front wall is achieved via a closed-form proximal evaluation and the recovery of targets is possible via a tailored Majorization-Minimization (MM) step. The analysis and validation of our method is carried out using Finite-Difference Time-Domain (FDTD) simulated data, which show the advantage of our method in detection performance over complex scenarios.