In this paper, we present a new approach for the analysis of iterative node-based verification-based (nb-vb) recoveryalgorithms in the context of compressive sensing. These algorithms are particularly interesting due...
详细信息
ISBN:
(纸本)9781457705953
In this paper, we present a new approach for the analysis of iterative node-based verification-based (nb-vb) recoveryalgorithms in the context of compressive 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 -> infinity. 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-vbalgorithms 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 non-trivial 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-vbalgorithms, which is based on numerically solving a large system of coupled differential equations, the proposed method is much simpler and more accurate.
暂无评论