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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Bibliographic Details
Published in:IEEE transactions on neural networks Vol. 22; no. 10; pp. 1638 - 1649
Main Authors: Merhej, D., Diab, C., Khalil, M., Prost, R.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2011
Institute of Electrical and Electronics Engineers
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1045-9227
1941-0093
1941-0093
DOI:10.1109/TNN.2011.2164810