首页> 外文期刊>Journal of the Optical Society of America, A. Optics, image science, and vision >Convergence of the Schulz-Snyder phase retrieval algorithm to local minima
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Convergence of the Schulz-Snyder phase retrieval algorithm to local minima

机译:Schulz-Snyder相位检索算法收敛于局部极小值

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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.
机译:用于相位检索的Schulz-Snyder迭代算法尝试通过使所测得的自相关与估计图像的自相关之间的I差异最小化,从自相关中恢复非负函数。我们说明了Schulz-Snyder算法可以陷入I-散度表面的局部最小值中。为了证明找到的估计确实是局部最小值,给出了涉及梯度和I-散度的Hessian矩阵的充分条件。然后,我们建立一个简短的证据,证明满足这些条件的估计值是局部最小值。这些条件用于执行确定局部估计最小值的数值测试。除测试外,还研究了相关的数值问题,并讨论了一些有趣的现象。

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