Image reconstruction through metamorphosis
This work addresses image reconstruction challenges in fields like medical imaging by enabling more robust registration when intensity templates are inaccurate, though it is incremental as it builds on existing metamorphosis frameworks.
The paper tackles the inverse problem of reconstructing images from noisy, indirect observations by jointly estimating both geometric deformations and intensity changes through metamorphosis, demonstrating good results even with poorly chosen template intensities and proving the method's well-defined regularization properties.
This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving intensities and the other a deformation of intensity values itself, which, e.g., allows for appearance of a new structure. The idea developed here is to reconstruct an image from noisy and indirect observations by registering, via metamorphosis, a template to the observed data. Unlike a registration with only geometrical changes, this framework gives good results when intensities of the template are poorly chosen. We show that this method is a well-defined regularisation method (proving existence, stability and convergence) and present several numerical examples.