Phase retrieval

Jameson Cahill; Peter G. Casazza; John Jasper; Lindsey M. Woodland

doi:10.1117/12.2185187

14 September 2015 Phase retrieval

Jameson Cahill, Peter G. Casazza, John Jasper, Lindsey M. Woodland

Proceedings Volume 9597, Wavelets and Sparsity XVI; 95970O (2015) https://doi.org/10.1117/12.2185187
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

Abstract

We answer a number of open problems concerning phase retrieval and phase retrieval by projections. In particular, one main theorem classifies phase retrieval by projections via collections of sequences of vectors allowing norm retrieval. Another key result computes the minimal number of vectors needed to add to a frame in order for it to possess the complement property and hence allow phase retrieval. In furthering this idea, in a third main theorem we show that when a collection of subspaces is one subspace short from allowing phase retrieval, then any partition of these subspaces spans two hyperplanes. We offer many more results in this area as well as provide a large number of examples showing the limitations of the theory.

Citation Download Citation

Jameson Cahill, Peter G. Casazza, John Jasper, and Lindsey M. Woodland "Phase retrieval", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970O (14 September 2015); https://doi.org/10.1117/12.2185187

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available