Compressive sensing by learning a Gaussian mixture model from measurements.

Published

Journal Article

Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.

Full Text

Duke Authors

Cited Authors

  • Yang, J; Liao, X; Yuan, X; Llull, P; Brady, DJ; Sapiro, G; Carin, L

Published Date

  • January 2015

Published In

Volume / Issue

  • 24 / 1

Start / End Page

  • 106 - 119

PubMed ID

  • 25361508

Pubmed Central ID

  • 25361508

Electronic International Standard Serial Number (EISSN)

  • 1941-0042

International Standard Serial Number (ISSN)

  • 1057-7149

Digital Object Identifier (DOI)

  • 10.1109/tip.2014.2365720

Language

  • eng