期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 58, 期 12, 页码 6140-6155出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2070796
关键词
Beta process; compressive sensing; Dirichlet process; low-rank Gaussian; manifold learning; mixture of factor analyzers; nonparametric Bayes
资金
- NIEHS NIH HHS [R01 ES017240, R01 ES017436] Funding Source: Medline
Nonparametric Bayesian methods are employed to constitute a mixture of low-rank Gaussians, for data x is an element of 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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