Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models




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.

Author(s): Seeger, M. and Nickisch, H.
Journal: SIAM Journal on Imaging Sciences
Volume: 4
Number (issue): 1
Pages: 166-199
Year: 2011
Month: March
Day: 0

Department(s): Empirical Inference
Research Project(s): Medical and Neuroscientific Imaging
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1137/090758775
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models},
  author = {Seeger, M. and Nickisch, H.},
  journal = {SIAM Journal on Imaging Sciences},
  volume = {4},
  number = {1},
  pages = {166-199},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = mar,
  year = {2011},
  month_numeric = {3}