PACM Colloquium: The reinvention of phase retrieval

Veit Elser, Cornell University
Oct 9 2017 - 4:00pm
Event type: 
PACM Colloquium
214 Fine Hall

Phase retrieval, originally, was the idea of exploiting prior information in the reconstruction of a complex-valued signal when only its magnitude can be measured. The earliest and still most important application is the reconstruction of complex biomolecules from x-ray diffraction (magnitude) data taken from crystallized samples. Over the last few years, and in the applied math community, “phase retrieval” has become identified with a different problem: extending the reach of magnitude-only data by expanding the set of “sensing vectors” used to interrogate the signal, and the design of algorithms that in the new setting can promise a successful reconstruction. This reinvention of phase retrieval is disappointing in two respects. First, owing to the extreme smallness of the x-ray/molecule interaction, the proposal of designed sensing vectors — in the main application of structural biology — is physically unfeasible. Second, the new algorithms designed for the new phase retrieval problem do not offer, in practice, significant advantages over older algorithms developed for the original problem, even as these do not come with a guarantee of success.