Uncertainty-Aware Null Space Networks for Data-Consistent Image Reconstruction

TL;DR

This paper introduces an uncertainty-aware null space network approach for image reconstruction that provides both accurate images and confidence estimates, especially useful in safety-critical applications like medical imaging.

Contribution

It combines deep null-space networks with uncertainty quantification to model data-dependent uncertainty in inverse problems, a novel approach in this domain.

Findings

Effective reconstruction from undersampled Radon measurements

Robust uncertainty estimation via input-dependent scale maps

First to model data-dependent uncertainty in inverse problems

Abstract

Reconstructing an image from noisy and incomplete measurements is a central task in several image processing applications. In recent years, state-of-the-art reconstruction methods have been developed based on recent advances in deep learning. Especially for highly underdetermined problems, maintaining data consistency is a key goal. This can be achieved either by iterative network architectures or by a subsequent projection of the network reconstruction. However, for such approaches to be used in safety-critical domains such as medical imaging, the network reconstruction should not only provide the user with a reconstructed image, but also with some level of confidence in the reconstruction. In order to meet these two key requirements, this paper combines deep null-space networks with uncertainty quantification. Evaluation of the proposed method includes image reconstruction from undersampled Radon measurements on a toy CT dataset and accelerated MRI reconstruction on the fastMRI dataset. This work is the first approach to solving inverse problems that additionally models data-dependent uncertainty by estimating an input-dependent scale map, providing a robust assessment of reconstruction quality.