Abstract
The null vector method, based on a simple linear algebraic concept, is proposed as an initialization method for nonconvex approaches to the phase retrieval problem. For the stylized measurement with random complex Gaussian matrices, a nonasymptotic error bound is derived, stronger than that of the spectral vector method. Numerical experiments show that the null vector method also has a superior performance for the realistic measurement of coded diffraction patterns in coherent diffractive imaging.
| Original language | English |
|---|---|
| Pages (from-to) | 854-868 |
| Number of pages | 15 |
| Journal | SIAM Journal on Matrix Analysis and Applications |
| Volume | 38 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2017 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Analysis
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Phase retrieval by linear algebra. / Chen, Pengwen; Fannjiang, Albert; Liu, Gi Ren.
In: SIAM Journal on Matrix Analysis and Applications, Vol. 38, No. 3, 01.01.2017, p. 854-868.Research output: Contribution to journal › Article
TY - JOUR
T1 - Phase retrieval by linear algebra
AU - Chen, Pengwen
AU - Fannjiang, Albert
AU - Liu, Gi Ren
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The null vector method, based on a simple linear algebraic concept, is proposed as an initialization method for nonconvex approaches to the phase retrieval problem. For the stylized measurement with random complex Gaussian matrices, a nonasymptotic error bound is derived, stronger than that of the spectral vector method. Numerical experiments show that the null vector method also has a superior performance for the realistic measurement of coded diffraction patterns in coherent diffractive imaging.
AB - The null vector method, based on a simple linear algebraic concept, is proposed as an initialization method for nonconvex approaches to the phase retrieval problem. For the stylized measurement with random complex Gaussian matrices, a nonasymptotic error bound is derived, stronger than that of the spectral vector method. Numerical experiments show that the null vector method also has a superior performance for the realistic measurement of coded diffraction patterns in coherent diffractive imaging.
UR - http://www.scopus.com/inward/record.url?scp=85031772669&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85031772669&partnerID=8YFLogxK
U2 - 10.1137/16M1107747
DO - 10.1137/16M1107747
M3 - Article
AN - SCOPUS:85031772669
VL - 38
SP - 854
EP - 868
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
SN - 0895-4798
IS - 3
ER -