Guaranteed Sparse Recovery Using Oblique Iterative Hard Thresholding Algorithm in Compressive Sensing 


Vol. 39,  No. 12, pp. 739-745, Dec.  2014


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  Abstract

It has been shown in compressive sensing that every s-sparse x∈R<SUP>N</SUP> can be recovered from the measurement vector y=Ax or the noisy vector y=Ax+e via ℓ₁-minimization as soon as the 3s-restricted isometry constant of the sensing matrix A is smaller than 1/2 or smaller than 1/√3by applying the Iterative Hard Thresholding (IHT) algorithm. However, recovery can be guaranteed by practical algorithms for some certain assumptions of acquisition schemes. One of the key assumption is that the sensing matrix must satisfy the Restricted Isometry Property (RIP), which is often violated in the setting of many practical applications. In this paper, we studied a generalization of RIP, called Restricted Biorthogonality Property (RBOP) for anisotropic cases, and the new recovery algorithms called oblique pursuits. Then, we provide an analysis on the success of sparse recovery in terms of restricted biorthogonality constant for the IHT algorithms.

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  Cite this article

[IEEE Style]

T. L. N. Nguyen, H. Jung, Y. Shin, "Guaranteed Sparse Recovery Using Oblique Iterative Hard Thresholding Algorithm in Compressive Sensing," The Journal of Korean Institute of Communications and Information Sciences, vol. 39, no. 12, pp. 739-745, 2014. DOI: .

[ACM Style]

Thu L. N. Nguyen, Honggyu Jung, and Yoan Shin. 2014. Guaranteed Sparse Recovery Using Oblique Iterative Hard Thresholding Algorithm in Compressive Sensing. The Journal of Korean Institute of Communications and Information Sciences, 39, 12, (2014), 739-745. DOI: .

[KICS Style]

Thu L. N. Nguyen, Honggyu Jung, Yoan Shin, "Guaranteed Sparse Recovery Using Oblique Iterative Hard Thresholding Algorithm in Compressive Sensing," The Journal of Korean Institute of Communications and Information Sciences, vol. 39, no. 12, pp. 739-745, 12. 2014.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880