Sparse regularization of inverse problems by operator-adapted frame thresholding
Abstract
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame thresholding approach which we show to provide a convergent regularization method with linear convergence rates. These results will be compared to the well-known analysis and synthesis variants of sparse -regularization which are usually implemented thorough iterative schemes. If the frame is a basis (non-redundant case), the three versions of sparse regularization, namely synthesis and analysis variants of regularization as well as the DFD thresholding are equivalent. However, in the redundant case, those three approaches are pairwise different.
Cite
@article{arxiv.1909.09364,
title = {Sparse regularization of inverse problems by operator-adapted frame thresholding},
author = {Jürgen Frikel and Markus Haltmeier},
journal= {arXiv preprint arXiv:1909.09364},
year = {2019}
}