Stochastic Natural Thresholding Algorithms
This work addresses sparse signal recovery for applications like medical imaging and remote sensing, but it is incremental as it extends an existing method to stochastic versions.
The paper tackles the sparse signal recovery problem by proposing stochastic natural thresholding algorithms, extending deterministic natural thresholding to stochastic settings with general objective functions, and demonstrates their performance through numerical experiments on linear and nonlinear measurements.
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.