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.

中文翻译：

---

双谱相恢复的高斯-牛顿优化

双谱的相位恢复是散斑干涉测量中的一个核心问题，它可以作为一个优化问题来最小化加权非线性最小二乘目标函数。我们从文献中查看相位恢复问题的两种不同形式，这两种形式都可以相对于恢复相位或恢复图像最小化。以前，解决这些公式的策略仅限于梯度下降或拟牛顿方法。本文探讨了针对双谱相位恢复问题的 Gauss-Newton 优化方案。我们为所有公式实施了高效的高斯-牛顿优化方案。对于针对恢复图像进行优化的这两个公式，我们还扩展到投影 Gauss-Newton，以对恢复图像的像素强度实施逐元素的下限和上限。我们表明，与之前实现的用于双谱相位恢复的一阶优化方案相比，我们的高效高斯-牛顿方案可以在没有额外计算成本或额外计算成本有限的情况下实现更好的图像重建。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。