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

Abstract

Projection-based neurodynamic systems have recently been used for sparse reconstruction, but most existing designs focus on convex

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<q<1

) 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.