A Unified Fractional Regularization Framework for Sparse Recovery

• URL: http://arxiv.org/abs/2604.23184v1
• Date: Sat, 25 Apr 2026 07:32:39 GMT
• Title: A Unified Fractional Regularization Framework for Sparse Recovery
• Abstract summary: We propose a unified fractional regularization framework for sparse signal recovery based on the $ell_pq$ model.<n> Numerical experiments demonstrate that the proposed framework consistently outperforms existing methods.
• Score: 6.9812173056207705
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\ell_1 - α\ell_p$ 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.

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