Descending iterative hard thresholding: A robust approach to sparse recovery under heavy-tailed noise

Compressed sensing has emerged as a powerful technique for signal recovery in various fields, from medical imaging to communication systems. Among the plethora of algorithms devised for this purpose, the Adaptive Iterative Hard Thresholding ([Formula: see text]) algorithm has garnered attention for its simplicity and efficiency. However, it is not without limitations, especially when applied to real-world scenarios characterized by heavy-tailed noise and a relatively small number of observations. In this paper, we address this challenge by introducing a novel approach called the Descending Iterative Hard Thresholding algorithm. Our method builds upon the foundation of the [Formula: see text] algorithm and incorporates the concept of a backtracking line search method. The motivation behind this development is to enhance the stability and accelerate the convergence rate of compressed sensing, particularly in the presence of heavy-tailed noise. We present theoretical analyses and experimental validations to support the results of our approach.