Year: 2023
Author: V. Churchill, A. Gelb
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 246–262
Abstract
This paper presents an application of the sparse Bayesian learning (SBL) algorithm to linear inverse problems with a high order total variation (HOTV) sparsity prior. For the problem of sparse signal recovery, SBL often produces more accurate estimates than maximum a posteriori estimates, including those that use $\ell_1$ regularization. Moreover, rather than a single signal estimate, SBL yields a full posterior density estimate which can be used for uncertainty quantification. However, SBL is only immediately applicable to problems having a direct sparsity prior, or to those that can be formed via synthesis. This paper demonstrates how a problem with an HOTV sparsity prior can be formulated via synthesis, and then utilizes SBL. This expands the class of problems available to Bayesian learning to include, e.g., inverse problems dealing with the recovery of piecewise smooth functions or signals from data. Numerical examples are provided to demonstrate how this new technique is effectively employed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2110-m2021-0157
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 246–262
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: High order total variation regularization Sparse Bayesian learning Analysis and synthesis Piecewise smooth function recovery.
Author Details
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