Oblique Iterative Hard Thresholding 알고리즘을 이용한 압축 센싱의 보장된 Sparse 복원

Abstract

It has been shown in compressive sensing that every s-sparse x∈Rⁿ can be recovered from the measuremen tvector y=Ax or the noisy vector y=Ax＋e via l₁-minimization as soon as the 3s-restricted isometry constant ofthe sensing matrix A is smaller than 1/2 or smaller than 1/√3 by 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.