Near optimal bound of orthogonal matching pursuit using restricted isometric constant
نویسندگان
چکیده
منابع مشابه
Near optimal bound of orthogonal matching pursuit using restricted isometric constant
As a paradigm for reconstructing sparse signals using a set of under sampled measurements, compressed sensing has received much attention in recent years. In identifying the sufficient condition under which the perfect recovery of sparse signals is ensured, a property of the sensing matrix referred to as the restricted isometry property (RIP) is popularly employed. In this article, we propose t...
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We shall show that if the restricted isometry constant (RIC) δs+1(A) of the measurement matrix A satisfies δs+1(A) < 1 √ s+ 1 , then the greedy algorithm Orthogonal Matching Pursuit(OMP) will succeed. That is, OMP can recover every s-sparse signal x in s iterations from b = Ax. Moreover, we shall show the upper bound of RIC is sharp in the following sense. For any given s ∈ N, we shall construc...
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In this letter, we first construct a counter example to show that for any given positive integer K ≥ 2 and for any 1 √ K+1 ≤ t < 1, there always exist a K−sparse x and a matrix A with the restricted isometry constant δK+1 = t such that the OMP algorithm fails in K iterations. Secondly, we show that even when δK+1 = 1 √ K+1 , the OMP algorithm can also perfectly recover every K−sparse vector x f...
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This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary D in a Hilbert space H. Given an element f ∈ H, OMP generates a sequence of approximations fn, n = 1, 2, . . ., each of which is a linear combination of n dictionary elements chosen by a greedy criterion. It is studied whether the approximations fn are in some sense comparable to...
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Generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of orthogonal matching pursuit. It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry const...
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ژورنال
عنوان ژورنال: EURASIP Journal on Advances in Signal Processing
سال: 2012
ISSN: 1687-6180
DOI: 10.1186/1687-6180-2012-8