Unsupervised Deep Learning for Inverse Problems in Computed Tomography

Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this, in this study we assume it is unknown how to solve the imaging problem of Computed Tomography. We introduce an unsupervised deep learning framework that leverages the inherent similarities between iterative reconstruction, Deep Image Prior (DIP), and unrolled optimization schemes. Our specific contribution is a training framework for amortized reconstruction: After training on a dataset without any image-domain ground truth, reconstruction of an unseen scan reduces to a single network forward pass. We demonstrate the feasibility of reconstructing images from measurement data by pure network inference, without additional gradient steps for unseen samples. Our method is evaluated on the two-dimensional 2DeteCT dataset. Within a controlled, geometry-matched benchmark, our reconstructions are competitive with, or better than, filtered back-projection, maximum-likelihood reconstruction, and a supervised network of identical architecture. Compared to a per-image DIP baseline, our method reaches similar quality while replacing the costly per-instance optimization with a single forward pass, yielding a speed-up of about four orders of magnitude. This makes it a promising candidate for time-critical imaging applications. Future work will address multi-dataset adaptability, counter-measures against over-smoothing, advanced uncertainty quantification, and further medical-imaging inverse problems.