Local regularization of linear inverse problems via variational filtering. (7th June 2017)

• Record Type: Journal Article
• Authors: Lamm, Patricia K
• Is Part Of: Inverse problems. Volume 33:Number 8(2017:Aug.)
• Publication Date: 2017-06-07
• Subjects: inverse problem -- regularization method -- filtering -- fast algorithm -- localization -- image deblurring; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa7426
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We develop local regularization methods for ill-posed linear inverse problems governed by general Fredholm integral operators. The methods are executed as filtering algorithms which are simple to implement and computationally efficient for a large class of problems. We establish a convergence theory and give convergence rates for such methods, and illustrate their computational speed in numerical tests for inverse problems in geomagnetic exploration and imaging.