Stochastic Natural Thresholding Algorithms

TL;DR

This paper introduces stochastic natural thresholding algorithms for sparse signal recovery, providing convergence guarantees and demonstrating improved performance through numerical experiments on linear and nonlinear measurements.

Contribution

It extends the deterministic Natural Thresholding method to a stochastic version with convergence guarantees and evaluates its effectiveness.

Findings

Convergence guarantees for stochastic natural thresholding algorithms.

Enhanced performance demonstrated on linear and nonlinear measurement experiments.

Extension of NT to stochastic settings with general objective functions.

Abstract

Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the sparse signal recovery problem. More recently, Natural Thresholding (NT) has been proposed with improved computational efficiency. This paper proposes and discusses convergence guarantees for stochastic natural thresholding algorithms by extending the NT from the deterministic version with linear measurements to the stochastic version with a general objective function. We also conduct various numerical experiments on linear and nonlinear measurements to demonstrate the performance of StoNT.