Fast Phase Retrieval: A Robust and Efficient Multidimensional Phase Retrieval Algorithm

We present the first phase retrieval algorithm with a set of deterministic recovery guarantees. We show that for a class of objects known as "Schwarz Objects", the algorithm is guaranteed to reconstruct the object given only the magnitudes of its discrete Fourier transform. We present numerical evidence that the algorithm additionally succeeds quite often for non-Schwarz objects. We also present a set of measurement matrices for which the algorithm is guaranteed to recover any object. We derive the algorithm by converting instances of the phase-retrieval problem to the Schwarz problem and refine the solution with local optimization. The result is an algorithm that is fast, universal and robust against noise.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Brabec, Cole

Advisor dc:contributor.advisor

• Englund, Dirk R.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/153788

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/153788