File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1016/j.acha.2022.01.002
- Scopus: eid_2-s2.0-85123203669
- WOS: WOS:000798823200004
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Solving phase retrieval with random initial guess is nearly as good as by spectral initialization
Title | Solving phase retrieval with random initial guess is nearly as good as by spectral initialization |
---|---|
Authors | |
Keywords | Geometric landscape Nonconvex Phase retrieval Phaseless measurements |
Issue Date | 2022 |
Citation | Applied and Computational Harmonic Analysis, 2022, v. 58, p. 60-84 How to Cite? |
Abstract | The problem of recovering a signal x∈Rn from a set of magnitude measurements yi=|〈ai,x〉|,i=1,…,m is referred as phase retrieval, which has many applications in fields of physical sciences and engineering. In this paper we show that the smoothed amplitude flow based model for phase retrieval has benign geometric structure under the optimal sampling complexity. In particular, we show that when the measurements ai∈Rn are Gaussian random vectors and the number of measurements m≥Cn, our smoothed amplitude flow based model has no spurious local minimizers with high probability, i.e., the target solution x is the unique global minimizer (up to a global phase) and the loss function has a negative directional curvature around each saddle point. Due to this benign geometric landscape, the phase retrieval problem can be solved by the gradient descent algorithms without spectral initialization. Numerical experiments show that the gradient descent algorithm with random initialization performs well even comparing with state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed. |
Persistent Identifier | http://hdl.handle.net/10722/327383 |
ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 2.231 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Cai, Jian Feng | - |
dc.contributor.author | Huang, Meng | - |
dc.contributor.author | Li, Dong | - |
dc.contributor.author | Wang, Yang | - |
dc.date.accessioned | 2023-03-31T05:30:56Z | - |
dc.date.available | 2023-03-31T05:30:56Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Applied and Computational Harmonic Analysis, 2022, v. 58, p. 60-84 | - |
dc.identifier.issn | 1063-5203 | - |
dc.identifier.uri | http://hdl.handle.net/10722/327383 | - |
dc.description.abstract | The problem of recovering a signal x∈Rn from a set of magnitude measurements yi=|〈ai,x〉|,i=1,…,m is referred as phase retrieval, which has many applications in fields of physical sciences and engineering. In this paper we show that the smoothed amplitude flow based model for phase retrieval has benign geometric structure under the optimal sampling complexity. In particular, we show that when the measurements ai∈Rn are Gaussian random vectors and the number of measurements m≥Cn, our smoothed amplitude flow based model has no spurious local minimizers with high probability, i.e., the target solution x is the unique global minimizer (up to a global phase) and the loss function has a negative directional curvature around each saddle point. Due to this benign geometric landscape, the phase retrieval problem can be solved by the gradient descent algorithms without spectral initialization. Numerical experiments show that the gradient descent algorithm with random initialization performs well even comparing with state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed. | - |
dc.language | eng | - |
dc.relation.ispartof | Applied and Computational Harmonic Analysis | - |
dc.subject | Geometric landscape | - |
dc.subject | Nonconvex | - |
dc.subject | Phase retrieval | - |
dc.subject | Phaseless measurements | - |
dc.title | Solving phase retrieval with random initial guess is nearly as good as by spectral initialization | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.acha.2022.01.002 | - |
dc.identifier.scopus | eid_2-s2.0-85123203669 | - |
dc.identifier.volume | 58 | - |
dc.identifier.spage | 60 | - |
dc.identifier.epage | 84 | - |
dc.identifier.eissn | 1096-603X | - |
dc.identifier.isi | WOS:000798823200004 | - |