Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T12:51:19.374Z Has data issue: false hasContentIssue false

9 - Phase Retrieval with the Nonnegativity Constraint

from Part II - Analysis of Algorithms for Phase Retrieval

Published online by Cambridge University Press:  21 April 2022

Alexander H. Barnett ,
Charles L. Epstein ,
Leslie Greengard  and
Jeremy Magland
Alexander H. Barnett
Affiliation:
Flatiron Institute
Charles L. Epstein
Affiliation:
Flatiron Institute
Leslie Greengard
Affiliation:
Courant Institute
Jeremy Magland
Affiliation:
Flatiron Institute
Get access

Summary

This chapter repeats much of the analysis of the previous chapter but using the assumption that the image is nonnegative, and its autocorrelation image has sufficiently small support rather than an estimate for the support of the image itself. In this case the auxiliary set is B+, the set consisting of nonnegative images, and the intersections of A and B+ lie on the boundary of B+, which is convex but not smooth. This complicates the notion of transversality, as was discussed in Chapter 4. We then present many numerical examples exploring the behavior of algorithms using nonnegativty and also the assumption that the unknown image has a given l1-norm. The chapter concludes with an appendix describing an efficient algorithm for finding the l2-nearest point on the boundary of an l1-ball.

Type
Chapter
Information
Geometry of the Phase Retrieval Problem
Graveyard of Algorithms
 , pp. 191 - 204
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×