Computational Mathematics Seminar - Victor Churchill

November 15, 2019
Tuesday, December 3, 2019 - 1:00pm to 2:00pm
Math Tower 154
Computational Mathematics Seminar

Title: High Order Total Variation Bayesian Learning via Synthesis

Speaker: Victor ChurchillDartmouth College

Abstract: We present a sparse Bayesian learning algorithm for inverse problems in signal and image processing with a high order total variation sparsity prior that can provide both accurate estimation as well as uncertainty quantification. Sparse Bayesian learning often produces more accurate estimates than the typical maximum a posteriori Bayesian estimates for sparse signal recovery. In addition, it also provides a full posterior distribution which aids downstream processing and uncertainty quantification. However, sparse Bayesian learning is only available to problems with a direct sparsity prior or those formed via synthesis. We build upon a recent paper to demonstrate how both 1D and 2D problems with a high order total variation sparsity prior can be formulated via synthesis, and develop a synthesis-based total variation Bayesian learning algorithm. Numerical examples are provided to demonstrate how our new technique is effectively employed.

Seminar Link

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