In many applications of compressed sensing the signal is block sparse, i.e., the non-zero elements of the sparse signal are clustered in blocks. Here, we propose a family of iterativealgorithms for the recovery of bl...
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In many applications of compressed sensing the signal is block sparse, i.e., the non-zero elements of the sparse signal are clustered in blocks. Here, we propose a family of iterativealgorithms for the recovery of block sparse signals. These algorithms, referred to as iterative reweighted l(2)/l(1) minimization algorithms (IR-l(2)/l(1)), solve a weighted l(2)/l(1) minimization in each iteration. Our simulation and analytical results on the recovery of both ideally and approximately block sparse signals show that the proposed iterativealgorithms have significant advantages in terms of accuracy and the number of required measurements over non-iterative approaches as well as existing iterative methods. In particular, we demonstrate that, by increasing the block length, the performance of the proposed algorithms approaches the Wu-Verdu theoretical limit. The improvement in performance comes at a rather small cost in complexity increase. Further improvement in performance is achieved by using a priori information about the location of non-zero blocks, even if such a priori information is not perfectly reliable.
In this paper, we derive an efficient iterative algorithm for the recovery of block-sparse signals given the finite data alphabet and the non-zero block probability. The non-zero block number is supposed to be far sma...
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In this paper, we derive an efficient iterative algorithm for the recovery of block-sparse signals given the finite data alphabet and the non-zero block probability. The non-zero block number is supposed to be far smaller than the total block number (block-sparse). The key principle is the separation of the unknown signal vector into an unknown support vector s and an unknown data symbol vector a. Both number (parallel to s parallel to(0)) and positions (s(i) is an element of{0, 1}) of non-zero blocks are unknown. The proposed algorithms use an iterative two-stage LASSO procedure consisting in optimizing the recovery problem alternatively with respect to a and with respect to s. The first algorithm resorts on l(1)-norm of the support vector and the second one applies reweighted l(1)-norm, which further improves the recovery performance. Performance of proposed algorithms is illustrated in the context of sporadic multiuser communications. Simulations show that the reweighted-l(1) algorithm performs close to its lower bound (perfect knowledge of the support vector). (C) 2018 Elsevier B.V. All rights reserved.
In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recoveryalgorithms in the context of compressed sensing. These algorithms are particularly interesting due ...
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In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recoveryalgorithms in the context of compressed sensing. These algorithms are particularly interesting due to their low complexity (linear in the signal dimension n). The asymptotic analysis predicts the fraction of unverified signal elements at each iteration l in the asymptotic regime where n -> l. The analysis is similar in nature to the well-known density evolution technique commonly used to analyze iterative decoding algorithms. To perform the analysis, a message-passing interpretation of NB-VB algorithms is provided. This interpretation lacks the extrinsic nature of standard message-passing algorithms to which density evolution is usually applied. This requires a number of nontrivial modifications in the analysis. The analysis tracks the average performance of the recoveryalgorithms over the ensembles of input signals and sensing matrices as a function of l. Concentration results are devised to demonstrate that the performance of the recoveryalgorithms applied to any choice of the input signal over any realization of the sensing matrix follows the deterministic results of the analysis closely. Simulation results are also provided which demonstrate that the proposed asymptotic analysis matches the performance of recoveryalgorithms for large but finite values of n. Compared to the existing technique for the analysis of NB-VB algorithms, which is based on numerically solving a large system of coupled differential equations, the proposed method is more accurate and simpler to implement.
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