In 2022, the Finnish Inverse Problems Society organized the Helsinki Tomography Challenge (HTC) 2022 with the aim of reconstructing an image using only limited-angle measurements. As part of this challenge, we implemented two methods, namely an Edge Inpainting method and a Learned Primal-Dual (LPD) reconstruction. The Edge Inpainting method consists of several successive steps: A classical reconstruction using Perona-Malik, extraction of visible edges, inpainting of invisible edges using a U-Net and a final segmentation using a U-Net. The Learned Primal-Dual approach adapts the classical LPD in two ways, namely replacing the adjoint with the generalized inverse (FBP) and using large U-Nets in the primal update. For the training of the networks we generated a synthetic dataset since only five samples were provided in the challenge. The results of the challenge showed that the Edge Inpainting Method was competitive for a viewing range up to 70 degrees. In contrast, the Learned Primal Dual approach performed well on all viewing ranges of the challenge and scored second best.

The Core Imaging Library (CIL) is a software for Computed Tomography (CT) and other inverse problems. It provides processing algorithms for CT data and tools to write optimisation problems with near math syntax. Last year the Finnish Inverse Problems Society organized the “Helsinki Tomography Challenge 2022” (HTC2022) – an open competition for researchers to submit reconstruction algorithms for a challenging series of real-data limited-angle computed tomography problems. The HTC2022 provided the perfect grounds to test the capabilities of CIL in limited angle CT.

The algorithm we submitted consists of multiple stages: first, pre-processing including beam-hardening correction and data normalization; second a purpose-built directional regularization method exploiting prior knowledge of the scanned object; and finally, a multi-Otsu segmentation method. The algorithm was fully implemented using the optimization prototyping capabilities of CIL and its performance assessed and optimized on the provided training data ahead of submission. The algorithm performed well on limited-angle data down to an angular range of 50 degrees, and in the competition was beaten only by two machine learning based strategies involving generation of very large sets of synthetic training data.

In the spirit of open science, all the data sets are available from the challenge website, https://fips.fi/HTC2022.php, and the submitted algorithm code from https://github.com/TomographicImaging/CIL-HTC2022-Algo2.

This talk explores how generative models, trained on ground-truth images, can be used as priors for inverse problems, penalizing reconstructions far from images the generator can produce. We utilize variational autoencoders that generate not only an image but also a covariance uncertainty matrix for each image. The covariance can model changing uncertainty dependencies caused by structure in the image, such as edges or objects, and provides a new distance metric from the manifold of learned images. We evaluate these novel generative regularizers on retrospectively sub-sampled real-valued MRI measurements from the fastMRI dataset.

Authors: Margaret A G Duff (Science and Technology Facilities Council (UKRI)) Ivor J A Simpson (University of Sussex) Matthias J Ehrhardt (University of Bath) Neill D F Campbell (University of Bath)

Computed tomography (CT) has become an essential part of modern science. A CT scanner consists of an X-ray source that is spun around an object of interest. On the opposite end of the X-ray source a detector captures X-rays that are not absorbed by the object. The reconstruction of an image is a linear inverse problem which is usually solved by the filtered back projection algorithm. However, when the number of measurements is too small the reconstruction problem is highly ill-posed. This is for example the case when the X-ray source is not spun completely around the object, but rather irradiates the object only from a limited angle. To tackle this problem, we present a deep neural network that performs limited-angle tomography reconstruction. The model is trained on a large amount of carefully-crafted synthetic data. Our approach won the first place in the Helsinki Tomography Challenge 2022.