Title: High Order Total Variation Bayesian Learning via Synthesis
Speaker: Victor Churchill - Dartmouth 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.
