In this paper we describe an investigation into the application of deep learning methods for low-dose and sparse angle computed tomography using small training datasets. To motivate our work we review some of the existing approaches and obtain quantitative results after training them with different amounts of data. We find that the learned primal-dual method has an outstanding performance in terms of reconstruction quality and data efficiency. However, in general, end-to-end learned methods have two deficiencies: (a) a lack of classical guarantees in inverse problems and (b) the lack of generalization after training with insufficient data. To overcome these problems, we introduce the deep image prior approach in combination with classical regularization and an initial reconstruction. The proposed methods achieve the best results in the low-data regime in three challenging scenarios.

Deep learning approaches for tomographic image reconstruction have become very effective and have been demonstrated to be competitive in the field. Comparing these approaches is a challenging task as they rely to a great extent on the data and setup used for training. With the Low-Dose Parallel Beam (LoDoPaB)-CT dataset, we provide a comprehensive, open-access database of computed tomography images and simulated low photon count measurements. It is suitable for training and comparing deep learning methods as well as classical reconstruction approaches. The dataset contains over 40000 scan slices from around 800 patients selected from the LIDC/IDRI database. The data selection and simulation setup are described in detail, and the generating script is publicly accessible. In addition, we provide a Python library for simplified access to the dataset and an online reconstruction challenge. Furthermore, the dataset can also be used for transfer learning as well as sparse and limited-angle reconstruction scenarios.

The reconstruction of computed tomography (CT) images is an active area of research. Following the rise of deep learning methods, many data-driven models have been proposed in recent years. In this work, we present the results of a data challenge that we organized, bringing together algorithm experts from different institutes to jointly work on quantitative evaluation of several data-driven methods on two large, public datasets during a ten day sprint. We focus on two applications of CT, namely, low-dose CT and sparse-angle CT. This enables us to fairly compare different methods using standardized settings. As a general result, we observe that the deep learning-based methods are able to improve the reconstruction quality metrics in both CT applications while the top performing methods show only minor differences in terms of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). We further discuss a number of other important criteria that should be taken into account when selecting a method, such as the availability of training data, the knowledge of the physical measurement model and the reconstruction speed.

Over recent years, deep learning methods have become an increasingly popular choice for solving tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point estimates for the reconstruction. However, especially in the analysis of ill-posed inverse problems, the study of uncertainties is essential. In our work, we apply generative flow-based models based on invertible neural networks to two challenging medical imaging tasks, i.e., low-dose computed tomography and accelerated medical resonance imaging. We test different architectures of invertible neural networks and provide extensive ablation studies. In most applications, a standard Gaussian is used as the base distribution for a flow-based model. Our results show that the choice of a radial distribution can improve the quality of reconstructions.

Deep image prior (DIP) was recently introduced as an effective unsupervised approach for image restoration tasks. DIP represents the image to be recovered as the output of a deep convolutional neural network, and learns the network's parameters such that the model output matches the corrupted observation. Despite its impressive reconstructive properties, the approach is slow when compared to supervisedly learned, or traditional reconstruction techniques. To address the computational challenge, we bestow DIP with a two-stage learning paradigm: (i) perform a supervised pretraining of the network on a simulated dataset; (ii) fine-tune the network's parameters to adapt to the target reconstruction task. We provide a thorough empirical analysis to shed insights into the impacts of pretraining in the context of image reconstruction. We showcase that pretraining considerably speeds up and stabilizes the subsequent reconstruction task from real-measured 2D and 3D micro computed tomography data of biological specimens. The code and additional experimental materials are available at https://educateddip.github.io/docs.educated_deep_image_prior/ educateddip.github.io/docs.educated_deep_image_prior/.

Imaging problems such as the one in nanoCT require the solution of an inverse problem, where it is often taken for granted that the forward operator, i.e., the underlying physical model, is properly known. In the present work we address the problem where the forward model is inexact due to stochastic or deterministic deviations during the measurement process. We particularly investigate the performance of non-learned iterative reconstruction methods dealing with inexactness and learned reconstruction schemes, which are based on U-Nets and conditional invertible neural networks. The latter also provide the opportunity for uncertainty quantification. A synthetic large data set in line with a typical nanoCT setting is provided and extensive numerical experiments are conducted evaluating the proposed methods.