title: Compressive Sensing on Manifolds Using a Nonparametric Mixture of Factor Analyzers: Algorithm and Performance Bounds.
abstract: Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for datax∈ ℝNthat are of high dimensionNbut 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.
authors.affiliation: Electrical and Computer Engineering Department, Duke University, Durham, NC 27708-0291 USA.
authors.forename: Minhua
authors.initials: M
authors.lastname: Chen
authors.forename: Jorge
authors.initials: J
authors.lastname: Silva
authors.forename: John
authors.initials: J
authors.lastname: Paisley
authors.forename: Chunping
authors.initials: C
authors.lastname: Wang
authors.forename: David
authors.initials: D
authors.lastname: Dunson
authors.forename: Lawrence
authors.initials: L
authors.lastname: Carin
keywords: Beta process; Dirichlet process; compressive sensing; low-rank Gaussian; manifold learning; mixture of factor analyzers; nonparametric Bayes
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