Gauss–Newton Optimization for Phase Recovery From the Bispectrum
Gauss–Newton Optimization for Phase Recovery From the Bispectrum
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DOI：
10.1109/tci.2019.2948784
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发表时间：
2018-12
影响因子：
5.4
通讯作者：
James Herring;J. Nagy;Lars Ruthotto
中科院分区：
文献类型：
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作者：
James Herring;J. Nagy;Lars Ruthotto
从双谱中恢复相位是散斑干涉测量中的一个核心问题，它可以归结为一个最小化加权非线性最小二乘目标函数的优化问题。我们看两个不同的配方的相位恢复问题的文献，这两个可以最小化相对于恢复的相位或恢复的图像。以前，解决这些公式的策略仅限于梯度下降或拟牛顿法。本文探讨了高斯-牛顿优化方案的问题，从双谱的相位恢复。我们实施有效的高斯-牛顿优化方案的所有配方。对于这两个配方，相对于恢复的图像进行优化，我们还扩展到投影高斯-牛顿，以强制执行恢复的图像的像素强度上的元素的下限和上限。我们表明，我们的高效高斯-牛顿计划的结果在更好的图像重建没有或有限的额外的计算成本相比，以前实施的一阶优化方案的相位恢复从双谱。所有方法和模拟的MATLAB实现都在Github上的BiBox存储库中公开提供。
Phase recovery from the bispectrum is a central problem in speckle interferometry which can be posed as an optimization problem minimizing a weighted nonlinear least-squares objective function. We look at two different formulations of the phase recovery problem from the literature, both of which can be minimized with respect to either the recovered phase or the recovered image. Previously, strategies for solving these formulations have been limited to gradient descent or quasi-Newton methods. This article explores Gauss–Newton optimization schemes for the problem of phase recovery from the bispectrum. We implement efficient Gauss–Newton optimization schemes for all the formulations. For the two of these formulations which optimize with respect to the recovered image, we also extend to projected Gauss–Newton to enforce element-wise lower and upper bounds on the pixel intensities of the recovered image. We show that our efficient Gauss–Newton schemes result in better image reconstructions with no or limited additional computational cost compared to previously implemented first-order optimization schemes for phase recovery from the bispectrum. MATLAB implementations of all methods and simulations are made publicly available in the BiBox repository on Github.