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A tight bound of modified iterative hard thresholding algorithm for compressed sensing

Jinyao Ma; Haibin Zhang; Shanshan Yang; Jiaojiao Jiang — 2023

Applications of Mathematics

We provide a theoretical study of the iterative hard thresholding with partially known support set (IHT-PKS) algorithm when used to solve the compressed sensing recovery problem. Recent work has shown that IHT-PKS performs better than the traditional IHT in reconstructing sparse or compressible signals. However, less work has been done on analyzing the performance guarantees of IHT-PKS. In this paper, we improve the current RIP-based bound of IHT-PKS algorithm from $δ_{3 s - 2 k} < \frac{1}{\sqrt{32}} \approx 0.1768$ to $δ_{3 s - 2 k} < \frac{\sqrt{5} - 1}{4} \approx 0.309$ , where $δ_{3 s - 2 k}$ is the restricted...

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