File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1137/15M1029357
- Scopus: eid_2-s2.0-85007124236
- WOS: WOS:000391853100024
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Phase retrieval from incomplete magnitude information via total variation regularization
Title | Phase retrieval from incomplete magnitude information via total variation regularization |
---|---|
Authors | |
Keywords | Total variation Phase retrieval Partial magnitudes Alternative directional multiplier method |
Issue Date | 2016 |
Citation | SIAM Journal on Scientific Computing, 2016, v. 38, n. 6, p. A3672-A3695 How to Cite? |
Abstract | © 2016 Society for Industrial and Applied Mathematics. The phase retrieval problem has drawn considerable attention, as many optical detection devices can only measure magnitudes of the Fourier transform of the underlying object (signal or image). This paper addresses the phase retrieval problem from incomplete data, where only partial magnitudes of Fourier transform are obtained. In particular, we consider structured illuminated patterns in holography and find that noninteger values used in designing such patterns often yield better reconstruction than the conventional integer-valued ones. Furthermore, we demonstrate theoretically and numerically that three diffracted sets of (complete) magnitude data are sufficient to recover the object. To compensate for incomplete information, we incorporate a total variation regularization a priori to guarantee that the reconstructed image satisfies some desirable properties. The proposed model can be solved efficiently by an alternative directional multiplier method with provable convergence. Numerical experiments validate the theoretical finding and demonstrate the effectiveness of the proposed method in recovering objects from noisy and incomplete data. |
Persistent Identifier | http://hdl.handle.net/10722/277049 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 1.803 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chang, Huibin | - |
dc.contributor.author | Lou, Yifei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Zeng, Tieyong | - |
dc.date.accessioned | 2019-09-18T08:35:27Z | - |
dc.date.available | 2019-09-18T08:35:27Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | SIAM Journal on Scientific Computing, 2016, v. 38, n. 6, p. A3672-A3695 | - |
dc.identifier.issn | 1064-8275 | - |
dc.identifier.uri | http://hdl.handle.net/10722/277049 | - |
dc.description.abstract | © 2016 Society for Industrial and Applied Mathematics. The phase retrieval problem has drawn considerable attention, as many optical detection devices can only measure magnitudes of the Fourier transform of the underlying object (signal or image). This paper addresses the phase retrieval problem from incomplete data, where only partial magnitudes of Fourier transform are obtained. In particular, we consider structured illuminated patterns in holography and find that noninteger values used in designing such patterns often yield better reconstruction than the conventional integer-valued ones. Furthermore, we demonstrate theoretically and numerically that three diffracted sets of (complete) magnitude data are sufficient to recover the object. To compensate for incomplete information, we incorporate a total variation regularization a priori to guarantee that the reconstructed image satisfies some desirable properties. The proposed model can be solved efficiently by an alternative directional multiplier method with provable convergence. Numerical experiments validate the theoretical finding and demonstrate the effectiveness of the proposed method in recovering objects from noisy and incomplete data. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Scientific Computing | - |
dc.subject | Total variation | - |
dc.subject | Phase retrieval | - |
dc.subject | Partial magnitudes | - |
dc.subject | Alternative directional multiplier method | - |
dc.title | Phase retrieval from incomplete magnitude information via total variation regularization | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/15M1029357 | - |
dc.identifier.scopus | eid_2-s2.0-85007124236 | - |
dc.identifier.volume | 38 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | A3672 | - |
dc.identifier.epage | A3695 | - |
dc.identifier.eissn | 1095-7200 | - |
dc.identifier.isi | WOS:000391853100024 | - |