The least error method for sparse solution reconstruction. (15th July 2016)

• Record Type: Journal Article
• Authors: Bredies, K; Kaltenbacher, B; Resmerita, E
• Is Part Of: Inverse problems. Volume 32:Number 9(2016:Sep.)
• Publication Date: 2016-07-15
• Subjects: ill-posed problem -- regularization -- sparsity -- least error method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/9/094001
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an ℓ 1 setting and perform the convergence analysis by choosing the discretization level according to an a priori rule, as well as two a posteriori rules, via the discrepancy principle and the monotone error rule, respectively. Depending on the setting, linear or sublinear convergence rates in the ℓ 1 -norm are obtained under a source condition yielding sparsity of the solution. A part of the study is devoted to analyzing the structure of the approximate solutions and of the involved source elements.