Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis

Details Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis

2010-03-17

arxiv.org/abs/1003.3323v7

Mathematics

Statistics Theory

Scientific paper

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics of projections of the residuals on a given set of sub-spaces in the image-space of the operator. We prove general consistency and convergence rate results in the framework of Bregman-divergences which allows for a vast range of penalty functionals. Various examples that indicate the applicability of our approach will be discussed. We will illustrate in the context of signal and image processing that the presented method constitutes a locally adaptive reconstruction method.

Affiliated with

Also associated with

No associations

Rating

Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shape Constrained Regularisation by Statistical Multiresolution for Inverse Problems: Asymptotic Analysis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233631