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