Ranked Sparse Signal Support Detection

This paper considers the problem of detecting the support (sparsity pattern) of a sparse vector from random noisy measurements. Conditional power of a component of the sparse vector is defined as the energy conditioned on the component being nonzero. Analysis of a simplified version of orthogonal ma...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2012-11, Vol.60 (11), p.5919-5931
Main Authors: Fletcher, A. K., Rangan, S., Goyal, V. K.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Compressed sensing
Conditioning
convex optimization
Detection, estimation, filtering, equalization, prediction
Dynamic range
Exact sciences and technology
Heuristic algorithms
Information, signal and communications theory
lasso
Matching pursuit algorithms
Mathematical analysis
Maximum likelihood estimation
orthogonal matching pursuit
random matrices
Sampling, quantization
Signal and communications theory
Signal processing
Signal to noise ratio
Signal, noise
sparse Bayesian learning
sparsity
Telecommunications and information theory
thresholding
Transaction processing
Vectors
Vectors (mathematics)
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Summary:This paper considers the problem of detecting the support (sparsity pattern) of a sparse vector from random noisy measurements. Conditional power of a component of the sparse vector is defined as the energy conditioned on the component being nonzero. Analysis of a simplified version of orthogonal matching pursuit (OMP) called sequential OMP (SequOMP) demonstrates the importance of knowledge of the rankings of conditional powers. When the simple SequOMP algorithm is applied to components in nonincreasing order of conditional power, the detrimental effect of dynamic range on thresholding performance is eliminated. Furthermore, under the most favorable conditional powers, the performance of SequOMP approaches maximum likelihood performance at high signal-to-noise ratio.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2012.2208957