Multi-Structural Signal Recovery for Biomedical Compressive Sensing

TL;DR

This paper introduces a novel convex optimization framework that leverages multiple structural properties of biomedical signals to improve reconstruction accuracy in compressive sensing, outperforming classical methods.

Contribution

It proposes a new multi-structural convex programming approach that exploits various signal structures simultaneously for enhanced biomedical signal recovery.

Findings

Better reconstruction accuracy in simulated data

Improved L1 and L2 error metrics

Outperforms classical methods in experiments

Abstract

Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have additional structures, such as multi-sparsity in different domains, piecewise smoothness, low rank, etc. We propose a framework to exploit all the available structure information. A new convex programming problem is generated with multiple convex structure-inducing constraints and the linear measurement fitting constraint. With additional a priori information for solving the underdetermined system, the signal recovery performance can be improved. In numerical experiments, we compare the proposed method with classical methods. Both simulated data and real-life biomedical data are used. Results show that the newly proposed method achieves better reconstruction accuracy performance in term of both L1 and L2 errors.