Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models

Abstract. Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or superresolution, 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 if and only if 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 spar...

• Type: Journal
• Year: 2011
• Where: SIAMIS
• Authors: Matthias W. Seeger, Hannes Nickisch
• Keywords: Image, Linear Model, Magnetic Resonance, SIAMIS 2011, Software Engineering