Sorted L1/L2 Minimization for Sparse Signal Recovery

TL;DR

This paper proposes a new sorted L1/L2 minimization technique for sparse signal recovery, effectively handling noise and outperforming existing methods in support detection and accuracy.

Contribution

It introduces a novel weighted minimization model that improves sparse signal recovery and provides rigorous solution existence proofs for both noise-free and noisy cases.

Findings

Outperforms state-of-the-art methods in support detection

Effective in both noise-free and noisy scenarios

Demonstrates superior recovery accuracy

Abstract

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively preserving the most significant contributions to the signal while promoting sparsity. We present models for both noise-free and noisy scenarios, and rigorously prove the existence of solutions for each case. To solve these models, we adopt a linearization approach inspired by the difference of convex functions algorithm. Our experimental results demonstrate the superiority of our method over state-of-the-art approaches in sparse signal recovery across various circumstances, particularly in support detection.