Research
A Unified Fractional Regularization Framework for Sparse Recovery
arXiv:2604.23184v1 Announce Type: cross Abstract: We propose a unified fractional regularization framework for sparse signal recovery based on the ell_1/ell_p^q model. Our main theoretical contributio
arXiv:2604.23184v1 Announce Type: cross Abstract: We propose a unified fractional regularization framework for sparse signal recovery based on the ell_1/ell_p^q model. Our main theoretical contribution is the characterization of the equivalence between the first-order stationary points of the ell_1/ell_p^q formulation and the subtractive ell_1 - alpha ell_p model, providing a unified perspective on these nonconvex regularizers. In addition, we establish a new sufficient recovery condition under the Restricted Isometry Property (RIP), showing that the framework's robustness even under high-coherence sensing matrices. To solve the resulting problem, we develop a majorization-minimization (MM) algorithm and prove its convergence via the Kurdyka-Lojasiewicz (KL) property. Numerical experiments on different sensing matrices and MRI reconstruction demonstrate that the proposed approach consistently outperforms existing methods.
Related
Source: arXiv cs.LG | 2026-04-28