In this work, we demonstrate that the ptychographic phase problem can be solved in a live fashion during scanning, while data is still being collected. We propose a generally applicable modification of the widespread projection-based algorithms such as Error Reduction (ER) and Difference Map (DM). This novel variant of ptychographic phase retrieval enables immediate visual feedback during experiments, reconstruction of arbitrary-sized objects with a fixed amount of computational resources, and adaptive scanning. By building upon the Real-Time Iterative Spectrogram Inversion (RTISI) family of algorithms from the audio processing literature, we show that live variants of projection-based methods such as DM can be derived naturally and may even achieve higher-quality reconstructions than their classic non-live counterparts with comparable effective computational load.

In this work, we utilize the high-fidelity generation abilities of diffusion models to solve blind JPEG restoration at high compression levels. We propose an elegant modification of the forward stochastic differential equation of diffusion models to adapt them to this restoration task and name our methodDriftRec. Comparing DriftRec against anL2regression baseline with the same network architecture and state-of-the-art techniques for JPEG restoration, we show that our approach can escape the tendency of other methods to generate blurry images, and recovers the distribution of clean images significantly more faithfully. For this, only a dataset of clean/corrupted image pairs and no knowledge about the corruption operation is required, enabling wider applicability to other restoration tasks. In contrast to other conditional and unconditional diffusion models, we utilize the idea that the distributions of clean and corrupted images are much closer to each other than each is to the usual Gaussian prior of the reverse process in diffusion models. Our approach therefore requires only low levels of added noise and needs comparatively few sampling steps even without further optimizations. We show that DriftRec naturally generalizes to realistic and difficult scenarios such as unaligned double JPEG compression and blind restoration of JPEGs found online, without having encountered such examples during training.

One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only possible given the full complex-valued diffraction data, i.e. magnitude and phase. However, in diffractive imaging, generally only magnitudes can be directly measured while the phase needs to be estimated. In this work we specifically consider ptychography, a sub-field of diffractive imaging, where objects are reconstructed from multiple overlapping diffraction images. We pro-pose an augmentation of existing iterative phase retrieval algorithms with a neural network designed for refining the result of each iteration. For this purpose we adapt and extend a recently proposed architecture from the speech processing field. Evaluation results show the proposed approach delivers improved convergence rates in terms of both iteration count and algorithm runtime.