Density evolution analysis of node-based verification-based algorithms in compressed sensing

In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recovery algorithms in the context of compressive sensing. These algorithms are particularly interesting due to their low complexity (linear in the signal dimension n). The asymptotic analysi...

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Bibliographic Details
Published in:2011 IEEE International Symposium on Information Theory Proceedings pp. 474 - 478
Main Authors: Eftekhari, Y., Heidarzadeh, A., Banihashemi, A. H., Lambadaris, I.
Format: Conference Proceeding
Language:English
Published: IEEE 01.07.2011
Subjects:
Algorithm design and analysis
Compressed sensing
Decoding
Differential equations
Niobium
Sensors
Simulation
ISBN:1457705966, 9781457705960
ISSN:2157-8095
Online Access:Get full text
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Summary:In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recovery algorithms 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 → ∞. 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 non-trivial modifications in the analysis. The analysis tracks the average performance of the recovery algorithms 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 recovery algorithms 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 recovery algorithms 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 much simpler and more accurate.
ISBN:1457705966
9781457705960
ISSN:2157-8095
DOI:10.1109/ISIT.2011.6034172