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Conference Paper

Compressed Sensing and Bayesian Experimental Design

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84205

Seeger,  MW
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84109

Nickisch,  H
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Seeger, M., & Nickisch, H. (2008). Compressed Sensing and Bayesian Experimental Design. Proceedings of the 25th International Conference on Machine Learning (ICML 2008), 912-919.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C839-3
Abstract
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 amp;amp;amp; 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.