X-ray computed tomography is a widely used, non-destructive imaging technique that computes cross-sectional images of an object from a set of X-ray absorption profiles (the so-called sinogram). The computation of the image from the sinogram is an ill-posed inverse problem, which becomes underdetermined when we are only able to collect insufficiently many X-ray measurements. We are here interested in solving X-ray tomography image reconstruction problems where we are unable to scan the object from all directions, but where we have prior information about the object’s shape. We thus propose a method that reduces image artefacts due to limited tomographic measurements by inferring missing measurements using shape priors. Our method uses a Generative Adversarial Network that combines limited acquisition data and shape information. While most existing methods focus on evenly spaced missing scanning angles, we propose an approach that infers a substantial number of consecutive missing acquisitions. We show that our method consistently improves image quality compared to images reconstructed using the previous state-of-the-art sinogram-inpainting techniques. In particular, we demonstrate a 7 dB Peak Signal-to-Noise Ratio improvement compared to other methods.

We address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring acquisitions into an estimated measurement at an intermediate angle. This procedure yields an enhanced sequence of measurements that can be reconstructed using standard methods, or further enhanced using regularisation approaches.Unlike methods that improve the sequence of acquisitions using an initial deterministic interpolation followed by machinelearning enhancement, we focus on inferring one measurement at once. This allows the method to scale to 3D, the computation to be faster and crucially, the interpolation to be significantly better than the current methods, when they exist. We also establish that a sequence of measurements must be processed as such, rather than as an image or a volume. We do so by comparing interpolation and up-sampling methods, and find that the latter significantly under-perform.We compare the performance of the proposed method against deterministic interpolation and up-sampling procedures and find that it outperforms them, even when used jointly with a stateof-the-art projection-data enhancement approach using machinelearning. These results are obtained for 2D and 3D imaging, on large biomedical datasets, in both projection space and image space.

Compensating scarce measurements by inferring them from computational models is a way to address ill-posed inverse problems. We tackle Limited Angle Tomography by completing the set of acquisitions using a generative model and prior-knowledge about the scanned object. Using a Generative Adversarial Network as model and Computer-Assisted Design data as shape prior, we demonstrate a quantitative and qualitative advantage of our technique over other state-of-the-art methods. Inferring a substantial number of consecutive missing measurements, we offer an alternative to other image inpainting techniques that fall short of providing a satisfying answer to our research question: can X-Ray exposition be reduced by using generative models to infer lacking measurements?