The Gauss--Newton Method for Phase Retrieval from Coded Diffraction Patterns
Abstract
We study the minimum-norm Gauss--Newton method for phase retrieval from random coded diffraction patterns with additive intensity noise. For bounded symmetric masks satisfying the standard complex moment conditions, we establish convergence guarantees with quadratic error recursions in both the resampled and fixed-data settings. In the resampled setting, O(log2 n) masks per independent block suffice to obtain a spectral initializer within a constant-relative-radius neighborhood and to establish a local quadratic error recursion with an additive noise term. Consequently, in the noiseless case, the method achieves relative accuracy ε using O(loglog(1/ε)log2 n) masks. In the fixed-data setting, O(log6(en)) masks suffice for spectral initialization within a neighborhood whose relative radius is proportional to log−5/2(nL). Within this neighborhood, the method satisfies a linear contraction bound and eventually a quadratic error recursion. In particular, in the noiseless case, the method initially converges linearly and enters a quadratic convergence phase after O(log n) iterations, without acquiring additional masks. Numerical experiments on synthetic signals and a natural image demonstrate the method's efficiency relative to state-of-the-art algorithms.
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BibTeX
@misc{huang2026gaussnewton,
title = {{The Gauss--Newton Method for Phase Retrieval from Coded Diffraction Patterns}},
author = {Meng Huang and Tianjiao Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18021},
eprint = {2610.18021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18021},
}
RIS
TY - UNPB
TI - The Gauss--Newton Method for Phase Retrieval from Coded Diffraction Patterns
AU - Meng Huang
AU - Tianjiao Wang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18021
UR - https://arxiv.org/abs/2610.18021
AB - We study the minimum-norm Gauss--Newton method for phase retrieval from random coded diffraction patterns with additive intensity noise. For bounded symmetric masks satisfying the standard complex moment conditions, we establish convergence guarantees with quadratic error recursions in both the resampled and fixed-data settings. In the resampled setting, O(log^2 n) masks per independent block suffice to obtain a spectral initializer within a constant-relative-radius neighborhood and to establish a local quadratic error recursion with an additive noise term. Consequently, in the noiseless case, the method achieves relative accuracy ε using O(loglog(1/ε)log^2 n) masks. In the fixed-data setting, O(log^6(en)) masks suffice for spectral initialization within a neighborhood whose relative radius is proportional to log^−5/2(nL). Within this neighborhood, the method satisfies a linear contraction bound and eventually a quadratic error recursion. In particular, in the noiseless case, the method initially converges linearly and enters a quadratic convergence phase after O(log n) iterations, without acquiring additional masks. Numerical experiments on synthetic signals and a natural image demonstrate the method's efficiency relative to state-of-the-art algorithms.
ER -