Aggregation of regularized solutions from multiple observation models. (17th June 2015)

• Record Type: Journal Article
• Authors: Chen, Jieyang; Pereverzyev Jr, Sergiy; Xu, Yuesheng
• Is Part Of: Inverse problems. Volume 31:Number 7(2015:Jul.)
• Publication Date: 2015-06-17
• Subjects: joint inversion -- aggregation -- multi-parameter regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/7/075005
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Joint inversion of multiple observation models has important applications in many disciplines including geoscience, image processing and computational biology. One of the methodologies for joint inversion of ill-posed observation equations naturally leads to multi-parameter regularization, which has been intensively studied over the last several years. However, problems such as the choice of multiple regularization parameters remain unsolved. In the present study, we discuss a rather general approach to the regularization of multiple observation models, based on the idea of the linear aggregation of approximations corresponding to different values of the regularization parameters. We show how the well-known linear functional strategy can be used for such an aggregation and prove that the error of a constructive aggregator differs from the ideal error value by a quantity of an order higher than the best guaranteed accuracy from the most trustable observation model. The theoretical analysis is illustrated by numerical experiments with simulated data.