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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. <\/jats:p>","DOI":"10.1142\/s0219691325500122","type":"journal-article","created":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T04:26:58Z","timestamp":1743827218000},"source":"Crossref","is-referenced-by-count":0,"title":["Descending iterative hard thresholding: A robust approach to sparse recovery under heavy-tailed noise"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-4375-9218","authenticated-orcid":false,"given":"Guowei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, (School of Artificial Intelligence), Zhejiang Sci-Tech University, Hangzhou 310018, P. R. 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