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 *** the problem of sparse signal recovery,SBL often produces more accurate estimates than maximum a posteriori estimates,including those that useℓ1 ***,rather than a single signal estimate,SBL yields a full posterior density estimate which can be used for uncertainty ***,SBL is only immediately applicable to problems having a direct sparsity prior,or to those that can be formed via *** paper demonstrates how a problem with an HOTV sparsity prior can be formulated via synthesis,and then utilizes *** 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 *** examples are provided to demonstrate how this new technique is effectively employed.