ESTIMATION AND UNCERTAINTY QUANTIFICATION FOR PIECEWISE SMOOTH SIGNAL RECOVERY

作     者：Victor Churchill Anne Gelb Victor Churchill;Anne Gelb

作者机构：Department of MathematicsThe Ohio State UniversityColumbusOHUSA Department of MathematicsDartmouth CollegeHanoverNHUSA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2023年第41卷第2期

页      面：246-262页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported in part by NSF-DMS 1502640,NSF-DMS 1912685,AFOSR FA9550-18-1-0316 Office of Naval Research MURI grant N00014-20-1-2595. 

主　　题：High order total variation regularization Sparse Bayesian learning Analysis and synthesis Piecewise smooth function recovery 

摘      要：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 useℓ1 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.