Abstract

Inverse imaging problems in practice constitute a pipeline of tasks that starts with image reconstruction, involves registration, segmentation, and a prediction task at the end. The idea of multi-tasking inverse problems is to make use of the full information in the data in every step of this pipeline by jointly optimising for all tasks. While this is not a new idea in inverse problems, the ability of deep learning to capture complex prior information paired with its computational efficiency renders an all-in-one approach practically possible for the first time.

In this talk we will discuss multi-tasking approaches to inverse problems, and their analytical and numerical challenges. This will include a variational model for joint motion estimation and reconstruction for fast tomographic imaging, joint registration and reconstruction (using a template image as a shape prior in the reconstruction) for limited angle tomography, as well as a variational model for joint image reconstruction and segmentation for MRI. These variational approaches will be put in contrast to a deep learning framework for multi-tasking inverse problems, with examples for joint image reconstruction and segmentation, and joint image reconstruction and classification from tomographic data.