Deep Unfolded Latent Optimally Partitioned-l2/l1 Networks for Data-driven Block-Sparse Recovery

2026-06-10

AI Summary

This work addresses the challenges of recovering block-sparse signals under unknown partitions and the limitations of conventional LOP-ℓ²/ℓ¹ methods, which suffer from manual parameter tuning and numerical instability. To overcome these issues, the authors propose a novel deep unfolding framework that integrates implicit differentiation with deep weight factorization (DWF). This architecture achieves both numerical stability—ensured by implicit differentiation—and enhanced modeling flexibility through DWF, which enables the use of non-convex smooth data fidelity terms, thereby circumventing the parameter sensitivity and structural constraints of existing approaches. Experimental results demonstrate that the proposed method matches the recovery performance of state-of-the-art algorithms while exhibiting remarkable robustness against impulsive noise.

Abstract

The convex Latent Optimal Partition (LOP)-l2/l1 approach enables block-sparse signal recovery with unknown partitions but relies on manual hyperparameter tuning. Additionally, numerical instability in differentiating its proximal operator prevents its automatic parameter tuning via Deep Unfolding (DU). To address these limitations, we propose two architectures: a stable framework utilizing implicit differentiation and a flexible variant leveraging Deep Weight Factorization (DWF). The DWF-based approach also supports nonconvex smooth data fidelity terms. Numerical experiments demonstrate that DU-LOP-l2/l1 yields competitive performance and high resilience against impulsive noise.

Problem

• block-sparse recovery
• hyperparameter tuning
• proximal operator
• numerical instability
• deep unfolding

Innovation

• Deep Unfolding
• Latent Optimal Partition
• Block-Sparse Recovery
• Implicit Differentiation
• Deep Weight Factorization