Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties
This work addresses signal recovery problems in domains like spectroscopy and nanopore sensing, representing an incremental improvement over existing methods.
The paper tackles the problem of recovering block-sparse signals with unknown block partitions by proposing two nonconvex regularization methods (LogLOP-l2/l1 and AdaLOP-l2/l1) that address underestimation bias in convex approaches. Numerical experiments show these methods outperform state-of-the-art baselines in estimation accuracy across synthetic data, angular power spectrum estimation, and nanopore current denoising.
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.