Image reconstruction with imperfect forward models and applications in deblurring
This work addresses image deblurring problems where forward models are inaccurate, which is a common issue in practical applications, but it appears incremental as it builds on existing lattice-based methods.
The paper tackles image reconstruction with imperfect forward models, such as deblurring with errors in the blurring kernel, by proposing an approach based on Banach lattices and order intervals to handle errors, and demonstrates its performance through numerical examples.
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.