Signal and Image Recovery with Scale and Signed Permutation Invariant Sparsity-Promoting Functions

2025/11/08 by Jia, Jianqing, Prater-Bennette, Ashley, Shen, Lixin · 1 citation
Computer Science · Engineering · #Advanced Image Processing Techniques #FOS: Electrical engineering #FOS: Mathematics #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2511.05777

openalex publication_date 2025/11/08 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of ℓ₁ to ℓ₂ norms, (ℓ₁/ℓ₂)², has been introduced as a sparsity-prompting function, showing superior performance compared to traditional ℓ₁ minimization, particularly in challenging scenarios with high coherence and dynamic range. This paper explores the integration of the proximity operator of (ℓ₁/ℓ₂)² and ℓ₁/ℓ₂ into efficient optimization frameworks, including the Accelerated Proximal Gradient (APG) and Alternating Direction Method of Multipliers (ADMM). We rigorously analyze the convergence properties of these algorithms and demonstrate their effectiveness in compressed sensing and image restoration applications. Numerical experiments highlight the advantages of our proposed methods in terms of recovery accuracy and computational efficiency, particularly under noise and high-coherence conditions.

Citations

• Analysis and algorithms for some compressed sensing models based on L1/L2 minimization
• A Scale Invariant Approach for Sparse Signal Recovery
• Fast L1-L2 minimization via a proximal operator
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
• Estimating Unknown Sparsity in Compressed Sensing
• Coherence-Pattern Guided Compressive Sensing with Unresolved Grids

Cited by

• Transformed ℓ₁ Gradient Regularization for Image Denoising
• An efficient proximal algorithm for squared L1 over L2 regularized sparse recovery

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