Fast thresholding algorithms with feedbacks for sparse signal recovery

TL;DR

This paper introduces a new class of fast, feedback-based thresholding algorithms for sparse signal recovery, demonstrating their effectiveness and rapid convergence, especially in large-scale problems.

Contribution

It presents novel iterative algorithms combining thresholding, feedback, and null space tuning, with proven finite-step convergence under restricted isometry conditions.

Findings

Algorithms are highly effective for large-scale sparse recovery.

Convergence is guaranteed in finite steps under certain conditions.

Numerical results show superior speed and accuracy.

Abstract

We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various feedbacks are derived, which are seen as exceedingly effective and fast. Convergence results are also provided. The core algorithm is shown to converge in finite many steps under a (preconditioned) restricted isometry condition. The algorithms are seen as particularly effective for large scale problems. Numerical studies about the effectiveness and the speed of the algorithms are also presented.