In this paper, we shall continue a study of the CS-recovery of signals studied in [1]. Under the assumption that a m × n matrix A obeys the RIP of order s we decompose the space of unknown vectors into sets M0; M1; · · · ;M7 de ned by a bias function px on a good location T0 = {1...
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Research Article10.9734/BJMCS/2015/18237
Our goal is to reconstruct an unknown sparse signal. In this paper, we consider the feature of the sparse signal and research good conditions for the recovery of sparse signals. In detail, we assume that h ≡ x*−x and h = (h1; h2; · · · ; hn), where x is an unknown signal and x* i...
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Research Article10.9734/BJMCS/2015/13998
The main purpose of this paper is to establish the sufficient condition for the restricted isometry constant δs in compressed sensing by using T. Cai and A. Zhang idea. Let h ≡ x* − x and h = (h1; h2; _ _ _ ; hn), where x is an unknown signal and x* is the CS-solution. For simpli...
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Research Article10.9734/BJMCS/2014/9002
The first purpose of this paper is to give a sufficient condition under which A obeys the weak RIP and to evaluate the solution of CS using this result. The second is to show that when an m x n random matrix A satisfies the isotropy property: for every row vector A{k} of A, al...
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Research Article10.9734/BJMCS/2014/7298
In this paper we define the k-restrictly norm constant rk(A) of a matrix A to be used in compressed sensing and give better error estimations on recovering compressive signals with noise using the matrix A~ _ A rk(A) . Furthermore, we define the notion of k-restricted invertibili...
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Research Article10.9734/BJMCS/2014/6171