提出新方法提升未知分块稀疏信号恢复精度
Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties
- 用对数和极小极大凹惩罚扩展分块稀疏建模
- 在合成数据和纳米孔电流去噪中优于现有方法
- 适用于多种数据保真项，算法收敛稳定
我们提出两种非凸正则化方法：LogLOP-l2/l1 和 AdaLOP-l2/l1，用于恢复未知分块结构的稀疏信号。通过新颖的变分形式，将对数和惩罚与极小极大凹惩罚（MCP）拓展至分块稀疏域，克服了现有凸方法的低估偏差问题。与依赖平方误差保真项的广义Moreau增强（GME）和贝叶斯方法不同，本方法兼容多种数据保真项。我们开发了基于交替方向乘子法（ADMM）的高效算法，具有稳定的实证收敛性。在合成数据、角功率谱估计及纳米孔电流去噪任务上的数值实验表明，所提方法在估计精度上优于当前最优基线。
原文摘要 · Abstract (English)
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.
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