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  Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models

Seeger, M., & Nickisch, H. (2011). Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models. SIAM Journal on Imaging Sciences, 4(1), 166-199. doi:10.1137/090758775.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-BC5E-3 Version Permalink: http://hdl.handle.net/21.11116/0000-0001-BA64-D
Genre: Journal Article

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https://epubs.siam.org/doi/10.1137/090758775 (Publisher version)
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 Creators:
Seeger, M1, 2, Author              
Nickisch, H1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density‘s mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

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 Dates: 2011-03
 Publication Status: Published in print
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 Identifiers: DOI: 10.1137/090758775
BibTex Citekey: 6886
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Title: SIAM Journal on Imaging Sciences
Source Genre: Journal
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Pages: - Volume / Issue: 4 (1) Sequence Number: - Start / End Page: 166 - 199 Identifier: -