Embedding Prior Knowledge Within Compressed Sensing by Neural Networks

In the compressed sensing framework, different algorithms have been proposed for sparse signal recovery from an incomplete set of linear measurements. The most known can be classified into two categories: ℓ 1 norm minimization-based algorithms and ℓ 0 pseudo-norm minimization with greedy matching pu...

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Vydáno v:	IEEE transactions on neural networks Ročník 22; číslo 10; s. 1638 - 1649
Hlavní autoři:	Merhej, D., Diab, C., Khalil, M., Prost, R.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.10.2011 Institute of Electrical and Electronics Engineers
Témata:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Artificial Intelligence Compressed Compressed sensing Computer science; control theory; systems Computer simulation Computer systems performance. Reliability Connectionism. Neural networks Correlation Data Compression - methods Decoding Exact sciences and technology Greedy algorithms Humans Indexes Matching Matching pursuit algorithms Models, Neurological Neural networks Neural Networks (Computer) Neurons orthogonal matching pursuit Recovery Signal processing Software Software Design Theoretical computing Training Random signal Probabilistic approach neural networks Minimization Decoding Case based reasoning Neural network orthogonal matching pursuit Inverse problem Restoration Greedy algorithm Probability density function Signal reconstruction Compressed sensing
ISSN:	1045-9227, 1941-0093, 1941-0093
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Popis
Shrnutí:	In the compressed sensing framework, different algorithms have been proposed for sparse signal recovery from an incomplete set of linear measurements. The most known can be classified into two categories: ℓ 1 norm minimization-based algorithms and ℓ 0 pseudo-norm minimization with greedy matching pursuit algorithms. In this paper, we propose a modified matching pursuit algorithm based on the orthogonal matching pursuit (OMP). The idea is to replace the correlation step of the OMP, with a neural network. Simulation results show that in the case of random sparse signal reconstruction, the proposed method performs as well as the OMP. Complexity overhead, for training and then integrating the network in the sparse signal recovery is thus not justified in this case. However, if the signal has an added structure, it is learned and incorporated in the proposed new OMP. We consider three structures: first, the sparse signal is positive, second the positions of the non zero coefficients of the sparse signal follow a certain spatial probability density function, the third case is a combination of both. Simulation results show that, for these signals of interest, the probability of exact recovery with our modified OMP increases significantly. Comparisons with ℓ 1 based reconstructions are also performed. We thus present a framework to reconstruct sparse signals with added structure by embedding, through neural network training, additional knowledge to the decoding process in order to have better performance in the recovery of sparse signals of interest.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	1045-9227 1941-0093 1941-0093
DOI:	10.1109/TNN.2011.2164810