Convergence of the Schulz-Snyder phase retrieval algorithm to local minima.
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.
Choi
Kerkil
K
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. kerkil@untu.edu
Lanterman
Aaron D
AD
Raich
Raviv
R