Maximum likelihood estimation under partial sparsity constraints

We consider the problem of estimating two deterministic vectors in a linear Gaussian model where one of the unknown vectors is subject to a sparsity constraint. We derive the maximum likelihood estimator for this problem and develop the Projected Orthogonal Matching Pursuit (POMP) algorithm for its...

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Bibliographic Details
Published inProceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) pp. 6421 - 6425
Main Authors Routtenberg, Tirza, Eldar, Yonina C., Lang Tong
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2013
Subjects
Compressed sensing
constrained Cramér-Rao
Matching pursuit algorithms
Maximum likelihood estimation
Signal to noise ratio
Sparse matrices
Sparsity
Vectors
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Summary:We consider the problem of estimating two deterministic vectors in a linear Gaussian model where one of the unknown vectors is subject to a sparsity constraint. We derive the maximum likelihood estimator for this problem and develop the Projected Orthogonal Matching Pursuit (POMP) algorithm for its practical implementation. The corresponding constrained Cramér-Rao bound (CCRB) on the mean-square-error is developed under the sparsity constraint. We then show that estimation in linear dynamical systems with a sparse control can be formulated as a special case of this problem.
ISSN:1520-6149
DOI:10.1109/ICASSP.2013.6638902