A playground for looking at Fourier phase retrieval (from an observation of the squared norm of a Fourier transform) in microscopy applications.

• David W. Hogg (SCDA) (NYU) (MPIA)

This project is heavily influenced by discussions with

• Charlie Epstein (Penn)
• Leslie Greengard (SCDA) (NYU)
• Jeremy Magland (SCDA)

Copyright 2015 David W. Hogg. Any code in this repository is licensed for use and re-use under the open-source MIT License. See the file LICENSE for more details.

• The problem of inferring the phase of a Fourier transform (of, say, an image) from an observation of the squared-norm of that Fourier transform comes up in problems of x-ray diffraction and diffraction microscopy. In principle it also might arise in adaptive optics.
• The problem is analogous to (or identical to, in some sense) inferring a function from an observation of its auto-correlation.
• We will concentrate on methods that involve either explicit optimization of a justified objective function or else some kind of probabilistic inference.