Improved bounds on restricted isometry constant for orthogonal matching pursuit
نویسندگان
چکیده
منابع مشابه
Improved Bounds on the Restricted Isometry Constant for Orthogonal Matching Pursuit
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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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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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) is a natural extension of OMP algorithm where unlike OMP, it may select N(≥ 1) atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a K-sparse signal from a compressed measurement y = Φx by K iteration if the sensing matrix Φ satisfies restricted isometry property (RIP) of order NK where δNK < √ N √ K+2 √ N ...
متن کاملImproved Bounds on Restricted Isometry Constants
The restricted isometry constant (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the 2 norm. Specifically, the upper and lower RICs of a matrix A of size n×N are the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all (N k ) matrices formed by taki...
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ژورنال
عنوان ژورنال: Electronics Letters
سال: 2013
ISSN: 0013-5194,1350-911X
DOI: 10.1049/el.2013.2222