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—In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing with the well-known ℓ1-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of(More)
Recently, Dimakis, Smarandache, and Vontobel indicated that the parity-check matrices of good LDPC codes can be used as provably good measurement matrices for compressed sensing (CS) under basis pursuit (BP). In this paper, we consider the parity-check matrix H(r, q) of the array codes, one of the most important kind of structured LDPC codes. The spark,(More)
Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as provably good measurement matrices for compressed sensing(More)
Binary 0-1 measurement matrices, especially those from coding theory, were introduced to compressed sensing (CS) recently. Good measurement matrices with preferred properties, e.g., the restricted isometry property (RIP) and nullspace property (NSP), have no known general ways to be efficiently checked. Khajehnejad et al. made use of girth to certify the(More)
—For a measurement matrix in compressed sensing, its spark (or the smallest number of columns that are linearly dependent) is an important performance parameter. The matrix with spark greater than 2k guarantees the exact recovery of k-sparse signals under an l0-optimization, and the one with large spark may perform well under approximate algorithms of the(More)
As the rapid growth of data, many storage systems have used erasure codes instead of replication to reduce the storage cost under the same level of reliability. Maximum-Distance- Separable (MDS) codes have been the most widely adopted, due to their optimal storage efficiency. It is well understood that the application of codes in storage systems, where the(More)
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their hardware realization convenient and easy. Firstly, using the famous Johnson bound for binary constant weight codes, we(More)
On a binary erasure channel (BEC) with erasing probability e, the performance of a binary linear code is determined by the incorrigible sets of the code. The incorrigible set distribution (ISD) {I<sub>i</sub>}<sub>i=0</sub><sup>n</sup> enumerates the number of incorrigible sets with size i of the code. The probability of unsuccessful decoding under optimal(More)
We propose a new iterative greedy algorithm to reconstruct sparse signals in compressed sensing. By a simple combination of subspace pursuit and iterative hard thresholding, the proposed algorithm, called subspace thresholding pursuit (STP) shows well improved empirical performance, while still keeps a strong theoretical guarantee in terms of restricted(More)