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

arXiv 2606.12740 ↗First posted 10 Jun 2026cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 43 references that are in the map. First posted on arXiv 10 Jun 2026.

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17 of 43 references.

References · 17

  1. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 421
  2. 2019Why gradient clipping accelerates training: A theoretical justification for adaptivitycited by 341
  3. 2020Improved Analysis of Clipping Algorithms for Non-convex Optimizationcited by 89
  4. 2014Deep Unfolding: Model-Based Inspiration of Novel Deep Architecturescited by 77
  5. 2019Deep Unfolding for Communications Systems: A Survey and Some New Directionscited by 49
  6. 2023RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detectioncited by 44
  7. 2025Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetriescited by 14
  8. 2023Smoothing the Edges: Smooth Optimization for Sparse Regularization using Hadamard Overparametrizationcited by 11
  9. 2013Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signalscited by 10
  10. 2025Deep Unfolding: Recent Developments, Theory, and Design Guidelinescited by 7
  11. 2022Deep Learning-based Channel Estimation for Wideband Hybrid MmWave Massive MIMOcited by 5
  12. 2016Perspective Functions: Proximal Calculus and Applications in High-Dimensional Statisticscited by 3
5 more
  1. 2025Escaping saddle points without Lipschitz smoothness: the power of nonlinear preconditioningcited by 3
  2. 2025Differentiable Sparsity via D-Gating: Simple and Versatile Structured Penalizationcited by 3
  3. 2024A Convex-Nonconvex Framework for Enhancing Minimization Induced Penaltiescited by 2
  4. 2025Theoretical Validation of the Latent Optimally Partitioned-ℓ2/ℓ1 Penalty with Application to Angular Power Spectrum Estimationcited by 2
  5. 2025WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelopecited by 1

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