Recovery Performance of IHT and HTP Algorithms under General Perturbations

Xiaobo ZHANG  Wenbo XU  Yupeng CUI  Jiaru LIN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.10   pp.1698-1702
Publication Date: 2018/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.1698
Type of Manuscript: LETTER
Category: Digital Signal Processing
compressed sensing,  matrix perturbation,  IHT algorithm,  HTP algorithm,  restricted isometry property,  

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In compressed sensing, most previous researches have studied the recovery performance of a sparse signal x based on the acquired model y=Φx+n, where n denotes the noise vector. There are also related studies for general perturbation environment, i.e., y=(Φ+E)x+n, where E is the measurement perturbation. IHT and HTP algorithms are the classical algorithms for sparse signal reconstruction in compressed sensing. Under the general perturbations, this paper derive the required sufficient conditions and the error bounds of IHT and HTP algorithms.