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Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds.

Publication ,  Journal Article
Chen, M; Silva, J; Paisley, J; Wang, C; Dunson, D; Carin, L
Published in: IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society
December 2010

Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x ∈ ℝ N that are of high dimension N but are constrained to reside in a low-dimensional subregion of ℝ N . The number of mixture components and their rank are inferred automatically from the data. The resulting algorithm can be used for learning manifolds and for reconstructing signals from manifolds, based on compressive sensing (CS) projection measurements. The statistical CS inversion is performed analytically. We derive the required number of CS random measurements needed for successful reconstruction, based on easily-computed quantities, drawing on block-sparsity properties. The proposed methodology is validated on several synthetic and real datasets.

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Published In

IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society

DOI

ISSN

1053-587X

Publication Date

December 2010

Volume

58

Issue

12

Start / End Page

6140 / 6155

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Chen, M., Silva, J., Paisley, J., Wang, C., Dunson, D., & Carin, L. (2010). Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds. IEEE Transactions on Signal Processing : A Publication of the IEEE Signal Processing Society, 58(12), 6140–6155. https://doi.org/10.1109/tsp.2010.2070796
Chen, Minhua, Jorge Silva, John Paisley, Chunping Wang, David Dunson, and Lawrence Carin. “Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds.IEEE Transactions on Signal Processing : A Publication of the IEEE Signal Processing Society 58, no. 12 (December 2010): 6140–55. https://doi.org/10.1109/tsp.2010.2070796.
Chen M, Silva J, Paisley J, Wang C, Dunson D, Carin L. Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds. IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society. 2010 Dec;58(12):6140–55.
Chen, Minhua, et al. “Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds.IEEE Transactions on Signal Processing : A Publication of the IEEE Signal Processing Society, vol. 58, no. 12, Dec. 2010, pp. 6140–55. Epmc, doi:10.1109/tsp.2010.2070796.
Chen M, Silva J, Paisley J, Wang C, Dunson D, Carin L. Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds. IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society. 2010 Dec;58(12):6140–6155.

Published In

IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society

DOI

ISSN

1053-587X

Publication Date

December 2010

Volume

58

Issue

12

Start / End Page

6140 / 6155

Related Subject Headings

  • Networking & Telecommunications