Image reconstruction with imperfect forward models and applications in deblurring

TL;DR

This paper introduces a novel image reconstruction method using partially ordered spaces to handle errors in forward models, with applications demonstrated in deblurring tasks involving imperfect kernels.

Contribution

It develops a lattice-based approach to model errors in forward models and analyzes the convexity of the feasible set for improved image reconstruction.

Findings

Effective deblurring with imperfect kernels demonstrated

Feasible set convexity analyzed in various settings

Method outperforms traditional approaches in handling model errors

Abstract

We present and analyse an approach to image reconstruction problems with imperfect forward models based on partially ordered spaces - Banach lattices. In this approach, errors in the data and in the forward models are described using order intervals. The method can be characterised as the lattice analogue of the residual method, where the feasible set is defined by linear inequality constraints. The study of this feasible set is the main contribution of this paper. Convexity of this feasible set is examined in several settings and modifications for introducing additional information about the forward operator are considered. Numerical examples demonstrate the performance of the method in deblurring with errors in the blurring kernel.