An empirical eigenvalue-threshold test for sparsity level estimation from compressed measurements
Author
Lavrenko, A.
Römer, F.
Del Galdo, G.
Thoma, R.
Arıkan, Orhan
Date
2014Source Title
Proceedings of the 22nd European Signal Processing Conference, EUSIPCO 2014
Print ISSN
2219-5491
Publisher
IEEE
Pages
1761 - 1765
Language
English
Type
Conference PaperItem Usage Stats
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Abstract
Compressed sensing allows for a significant reduction of the number of measurements when the signal of interest is of a sparse nature. Most computationally efficient algorithms for signal recovery rely on some knowledge of the sparsity level, i.e., the number of non-zero elements. However, the sparsity level is often not known a priori and can even vary with time. In this contribution we show that it is possible to estimate the sparsity level directly in the compressed domain, provided that multiple independent observations are available. In fact, one can use classical model order selection algorithms for this purpose. Nevertheless, due to the influence of the measurement process they may not perform satisfactorily in the compressed sensing setup. To overcome this drawback, we propose an approach which exploits the empirical distributions of the noise eigenvalues. We demonstrate its superior performance compared to state-of-the-art model order estimation algorithms numerically.
Keywords
DetectionEigenvalues and eigenfunctions
Error detection
Mathematical models
Signal processing
Signal reconstruction
Compressed domain
Computationally efficient
Empirical distributions
Measurement process
Model-order selection
Signal of interests
Sparsity level
Compressed sensing