# Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties

arXiv: https://arxiv.org/abs/2603.01304 · HTML: https://mlsanity.com/paper/2603.01304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 65 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [A survey of sparse representation: algorithms and applications](https://mlsanity.com/paper/1602.07017/) (2016)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Support recovery without incoherence: A case for nonconvex regularization](https://mlsanity.com/paper/1412.5632/) (2014)
- [A Survey on Nonconvex Regularization Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning](https://mlsanity.com/paper/1808.05403/) (2018)
- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [The proximal alternating direction method of multipliers in the nonconvex setting: convergence analysis and rates](https://mlsanity.com/paper/1801.01994/) (2018)
- [Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals](https://mlsanity.com/paper/1311.2150/) (2013)
- [Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function](https://mlsanity.com/paper/2206.13506/) (2022)
- [Linearly Involved Generalized Moreau Enhanced Models and Their Proximal Splitting Algorithm under Overall Convexity Condition](https://mlsanity.com/paper/1910.10337/) (2019)
- [Block Sparse Bayesian Learning: A Diversified Scheme](https://mlsanity.com/paper/2402.04646/) (2024)
- [A Convex-Nonconvex Framework for Enhancing Minimization Induced Penalties](https://mlsanity.com/paper/2407.14819/) (2024)
- [Theoretical Validation of the Latent Optimally Partitioned-ℓ2/ℓ1 Penalty with Application to Angular Power Spectrum Estimation](https://mlsanity.com/paper/2509.13745/) (2025)
- [Hybrid data and model driven algorithms for angular power spectrum estimation](https://mlsanity.com/paper/2005.14003/) (2020)
- [Adaptive Block Sparse Regularization under Arbitrary Linear Transform](https://mlsanity.com/paper/2401.15292/) (2024)

## Abstract (arXiv)

We propose two nonconvex regularization methods, LogLOP-l2/l1 and AdaLOP-l2/l1, for recovering block-sparse signals with unknown block partitions. These methods address the underestimation bias of existing convex approaches by extending log-sum penalty and the Minimax Concave Penalty (MCP) to the block-sparse domain via novel variational formulations. Unlike Generalized Moreau Enhancement (GME) and Bayesian methods dependent on the squared-error data fidelity term, our proposed methods are compatible with a broad range of data fidelity terms. We develop efficient Alternating Direction Method of Multipliers (ADMM)-based algorithms for these formulations that exhibit stable empirical convergence. Numerical experiments on synthetic data, angular power spectrum estimation, and denoising of nanopore currents demonstrate that our methods outperform state-of-the-art baselines in estimation accuracy.