Fast L1-Minimization Algorithm for Sparse Approximation Based on an Improved LPNN-LCA framework

TL;DR

This paper introduces a fast, real-time sparse approximation algorithm combining LPNN, LCA, and projection theorem, achieving stable solutions with satisfactory accuracy for applications like data analytics and image processing.

Contribution

The paper presents a novel sparse approximation algorithm that integrates LPNN, LCA, and projection theorem to enable real-time solutions with guaranteed stability.

Findings

Achieves real-time sparse approximation with stable dynamics.

Provides solutions with satisfactory mean squared errors.

Demonstrates effectiveness through simulation results.

Abstract

The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has been done in this area, and many off-the-shelf algorithms have been proposed. However, most of them cannot offer a real-time solution. To some extent, this shortcoming limits its application prospects. To address this issue, we devise a novel sparse approximation algorithm based on Lagrange programming neural network (LPNN), locally competitive algorithm (LCA), and projection theorem. LPNN and LCA are both analog neural network which can help us get a real-time solution. The non-differentiable objective function can be solved by the concept of LCA. Utilizing the projection theorem, we further modify the dynamics and proposed a new system with global asymptotic stability. Simulation results show that the proposed sparse approximation method has the real-time solutions with satisfactory MSEs.