Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773597 | Applied and Computational Harmonic Analysis | 2017 | 28 Pages |
Abstract
In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this paper we present a recent approach which determines the approximant from shift invariant subspaces by minimizing an â1-regularized least squares problem which makes additional use of the wavelet frame transform in order to preserve sharp edges. We give a detailed analysis of this approach, i.e., how the approximation error behaves dependent on data density and noise level. Moreover, a link to wavelet frame based image restoration models is established and the convergence of these models is analyzed. In the end, we present some numerical examples, for instance how to apply this approach to handle coarse-grained models in molecular dynamics.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jianbin Yang, Dominik Stahl, Zuowei Shen,