Convergence of the Schulz-Snyder phase retrieval algorithm to local minima
Document Type
Article
Publication Date
1-1-2006
Abstract
The Schulz-Snyder iterative algorithm for phase retrieval attempts to recover a nonnegative function from its autocorrelation by minimizing the I-divergence between a measured autocorrelation and the autocorrelation of the estimated image. We illustrate that the Schulz-Snyder algorithm can become trapped in a local minimum of the I-divergence surface. To show that the estimates found are indeed local minima, sufficient conditions involving the gradient and the Hessian matrix of the I-divergence are given. Then we build a brief proof showing how an estimate that satisfies these conditions is a local minimum. The conditions are used to perform numerical tests determining local minimality of estimates. Along with the tests, related numerical issues are examined, and some interesting phenomena are discussed. © 2006 Optical Society of America.
Publication Title
Journal of the Optical Society of America A: Optics and Image Science, and Vision
Recommended Citation
Choi, K.,
Lanterman, A.,
&
Raich, R.
(2006).
Convergence of the Schulz-Snyder phase retrieval algorithm to local minima.
Journal of the Optical Society of America A: Optics and Image Science, and Vision,
23(8), 1835-1845.
http://doi.org/10.1364/JOSAA.23.001835
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/13300
