Approaching phase retrieval with deep learning

Phase retrieval is the process of reconstructing images from only magnitude measurements. The problem is particularly challenging as most of the information about the image is contained in the missing phase. An important phase retrieval problem is Fourier phase retrieval, where the magnitudes of the Fourier transform are given. This problem is relevant in many areas of science, e.g., in X-ray crystallography, astronomy, microscopy, array imaging, and optics. In addition to Fourier phase retrieval, we also take a closer look at two additional phase retrieval problems: Fourier phase retrieval with a reference image and compressive Gaussian phase retrieval. Most methods for phase retrieval, e.g., the error-reduction algorithm or Fienup's hybrid-input output algorithms are optimization-based algorithms which solely minimize an error-function to reconstruct the image. These methods usually make strong assumptions about the measured magnitudes which do not always hold in practice. Thus, they only work reliably for easy instances of the phase retrieval problems but fail drastically for difficult instances. With the recent advances in the development of graphics processing units (GPUs), deep neural networks (DNNs) have become fashionable again and have led to breakthroughs in many research areas. In this thesis, we show how DNNs can be applied to solve the more difficult instances of phase retrieval problems when training data is available. On the one hand, we show how supervised learning can be used to greatly improve the reconstruction quality when training images and their corresponding measurements are available. We analyze the ability of these methods to generalize to out-of-distribution data. On the other hand, we take a closer look at an existing unsupervised method that relies on generative models. Unsupervised methods are agnostic toward the measurement process which is particularly useful for Gaussian phase retrieval. We apply this method to the Fourier phase retrieval problem and demonstrate how the reconstruction performance can be further improved with different initialization schemes. Furthermore, we demonstrate how optimizing intermediate representations of the underlying generative model can help overcoming the limited range of the model and, thus, can help to reach better solutions. Finally, we show how backpropagation can be used to learn reference images using a modification of the well-established error-reduction algorithm and discuss whether learning a reference image is always efficient. As it is common in machine learning research, we evaluate all methods on benchmark image datasets as it allows for easy reproducibility of the experiments and comparability to related methods. To better understand how the methods work, we perform extensive ablation experiments, and also analyze the influence of measurement noise and missing measurements

Limited-Angle Tomography Reconstruction via Deep End-To-End Learning on Synthetic Data

Computed tomography (CT) has become an essential part of modern science and medicine. 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 filtered back projection. However, when the number of measurements is small, the reconstruction problem is 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 is trained on a large amount of carefully-crafted synthetic data and can perform limited-angle tomography reconstruction even for only 30{\deg} or 40{\deg} sinograms. With our approach we won the first place in the Helsinki Tomography Challenge 2022

A Survey on Self-Supervised Representation Learning

Learning meaningful representations is at the heart of many tasks in the field of modern machine learning. Recently, a lot of methods were introduced that allow learning of image representations without supervision. These representations can then be used in downstream tasks like classification or object detection. The quality of these representations is close to supervised learning, while no labeled images are needed. This survey paper provides a comprehensive review of these methods in a unified notation, points out similarities and differences of these methods, and proposes a taxonomy which sets these methods in relation to each other. Furthermore, our survey summarizes the most-recent experimental results reported in the literature in form of a meta-study. Our survey is intended as a starting point for researchers and practitioners who want to dive into the field of representation learning