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Compressed Sensing and Bayesian Experimental Design

2008

Conference Paper

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We relate compressed sensing (CS) with Bayesian experimental design and provide a novel efficient approximate method for the latter, based on expectation propagation. In a large comparative study about linearly measuring natural images, we show that the simple standard heuristic of measuring wavelet coefficients top-down systematically outperforms CS methods using random measurements; the sequential projection optimisation approach of (Ji & Carin, 2007) performs even worse. We also show that our own approximate Bayesian method is able to learn measurement filters on full images efficiently which ouperform the wavelet heuristic. To our knowledge, ours is the first successful attempt at "learning compressed sensing" for images of realistic size. In contrast to common CS methods, our framework is not restricted to sparse signals, but can readily be applied to other notions of signal complexity or noise models. We give concrete ideas how our method can be scaled up to large signal representations.

Author(s): Seeger, MW. and Nickisch, H.
Book Title: ICML 2008
Journal: Proceedings of the 25th International Conference on Machine Learning (ICML 2008)
Pages: 912-919
Year: 2008
Month: July
Day: 0
Editors: Cohen, W. W., A. McCallum, S. Roweis
Publisher: ACM Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1145/1390156.1390271
Event Name: 25th International Conference on Machine Learning
Event Place: Helsinki, Finland

Address: New York, NY, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5135,
  title = {Compressed Sensing and Bayesian Experimental Design},
  author = {Seeger, MW. and Nickisch, H.},
  journal = {Proceedings of the 25th International Conference on Machine Learning (ICML 2008)},
  booktitle = {ICML 2008},
  pages = {912-919},
  editors = {Cohen, W. W., A. McCallum, S. Roweis},
  publisher = {ACM Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {New York, NY, USA},
  month = jul,
  year = {2008},
  month_numeric = {7}
}