# Indirect Image Registration with Large Diffeomorphic Deformations

## TL;DR

This paper extends large deformation diffeomorphic image registration to indirect settings with noisy data, providing theoretical guarantees and demonstrating its effectiveness in sparse, noisy 2D tomography scenarios.

## Contribution

It introduces a novel framework for indirect image registration using diffeomorphisms, with proven existence, stability, and convergence properties.

## Key findings

- Proved existence and stability of solutions for indirect registration.
- Showed convergence as data noise approaches zero.
- Demonstrated effectiveness in sparse, noisy 2D tomography examples.

## Abstract

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.