Robust method for finding sparse solutions to linear inverse problems using an L2 regularization

TL;DR

This paper presents a robust, biologically inspired algorithm called CPA that uses L2 regularization to accurately identify sparse components in signals, outperforming other methods especially under noisy conditions.

Contribution

It introduces a novel CPA algorithm with an analytical binary indicator for atom presence, leveraging L2 regularization for robustness and real-time implementation.

Findings

CPA outperforms existing methods in noisy environments

The algorithm provides an analytical expression for atom detection

CPA is robust to strong noise and novel signal components

Abstract

We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete dictionary. By changing the geometry of the estimation problem, CPA gives an analytical expression for a binary variable that indicates the presence or absence of a dictionary atom using an L2 regularizer. The regularized solution can be implemented using an efficient real-time Kalman-filter type of algorithm. The smoother L2 regularization of CPA makes it very robust to noise, and CPA outperforms other methods in identifying known atoms in the presence of strong novel atoms in the signal.