  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.
