Phase Retrieval in Imaging and Speech Enhancement

Supervisors: Prof. Henry Chapman (DESY, UHH), Prof. Timo Gerkmann (UHH)

Advanced sources such as free-electron lasers produce intense and coherent beams of X-rays that are opening up new possibilities to image biological materials, such as single molecules, at atomic resolution. Since atomic-resolution lenses do not exist, such methods usually rely upon retrieving the structural information encoded in the far-field coherent diffraction pattern [Shechtman et al, 2015].
This intensity pattern corresponds to the Fourier magnitude of the object, and is thus an incomplete measurement since the spectral phase cannot be measured. To reconstruct the original structure, the missing phase information needs to be retrieved. A very similar problem of phase retrieval is encountered in speech source separation and enhancement, and has received increasing attention recently [Gerkmann et al, 2015]. Many recent contributions to the field of speech processing are based on modern machine learning techniques. Such techniques have also been applied to the phase problem and have been shown to provide fast and accurate results.
The goal of this project is to explore common concepts in X-ray imaging and speech enhancement. Recent advances in the application of machine learning in speech analysis will be transferred and adapted to X-ray imaging, obtaining deeper insights into this challenging inverse problem and providing new opportunities for high-resolution structure determination of biological systems. The successful candidate has a solid background in machine learning and signal processing.