Compressive sensing on manifolds using a nonparametric mixture of factor analyzers: Algorithm and performance bounds

Minhua Chen, Jorge Silva, John Paisley, Chunping Wang, David Dunson, Lawrence Carin

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Abstract

Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x∈ℝN that are of high dimension N but are constrained to reside in a low-dimensional subregion of ℝN. 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. © 2010 IEEE.
Original languageEnglish (US)
Pages (from-to)6140-6155
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume58
Issue number12
DOIs
StatePublished - Dec 1 2010
Externally publishedYes

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