Work

A projection-based neurodynamic system method with convergence guarantees for 𝐿 𝑞 -regularized (0 < 𝑞 < 1) sparse recovery problem

Year: 2026

Type: article

Abstract: Projection-based neurodynamic systems have recently been used for sparse reconstruction, but most existing designs focus on convex L 1 L_{1} models and may be suboptimal for highly sparse signals. This paper develops an inertial projection-based neurodynamic system (PBNS) for the nonconvex L q L_{q} -regularized ( 0 < q < 1 0 ) sparse recovery problem. By applying a standard variable splitting and introducing a smooth absolute-value regularization, we transform the original model into the minimization of a continuously differentiable objective over a closed convex set, which enables a rigorous dynamical-system formulation. We design a two-layer inertial PBNS driven by the projected gradient mapping and obtain an implementable reconstruction algorithm via time discretization. The proposed dynamics is shown to be globally well-posed (existence and uniqueness of trajectories), and its trajectory converges asymptotically to the equilibrium set under a cocoercivity-type condition, with an additional local convergence result under local cocoercivity. Extensive experiments on synthetic compressed sensing data and real fetal ECG signals demonstrate that the proposed PBNS- L q L_{q} method is stable and achieves improved reconstruction accuracy and efficiency compared with representative convex and nonconvex baselines.

Source: Journal of Inverse and Ill-Posed Problems

DOI: 10.1515/jiip-2023-0005

Authors: Wei Ma, Xiaojing Liu, Ting Han, Xiaohu Luo

Institutions: Xinhua College of Ningxia University, Ningxia Normal University

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: Natural Science Foundation of Ningxia Province, Ningxia Normal University