Dual-grid parameter choice method with application to image deblurring
Journal:
arXiv
Published Date:
Apr 14, 2025
Abstract
Variational regularization of ill-posed inverse problems is based on
minimizing the sum of a data fidelity term and a regularization term. The
balance between them is tuned using a positive regularization parameter, whose
automatic choice remains an open question in general. A novel approach for
parameter choice is introduced, based on the use of two slightly different
computational models for the same inverse problem. Small parameter values
should give two very different reconstructions due to amplification of noise.
Large parameter values lead to two identical but trivial reconstructions.
Optimal parameter is chosen between the extremes by matching image similarity
of the two reconstructions with a pre-defined value. Efficacy of the new method
is demonstrated with image deblurring using measured data and two different
regularizers.
