We consider blind ptychography, an imaging technique which aims to reconstruct an object of interest from a set of its diffraction patterns, each obtained by a local illumination. As the distribution of the light within the illuminated region, called the window, is unknown, it also has to be estimated as well. For the recovery, we consider gradient and stochastic gradient descent methods for the minimization of amplitude-base squared loss. In particular, this includes extended Ptychographic Iterative Engine as a special case of stochastic gradient descent. We show that all methods converge to a critical point at a sublinear rate with a proper choice of step sizes. We also discuss possibilities for larger step sizes.

翻译：我们考虑盲光刻术，这是一种成像技术，旨在从一组衍射图案中重建感兴趣的物体，每个图案均通过局部照明获得。由于照明区域（称为窗口）内的光分布未知，因此也必须对其进行估计。对于重建，我们考虑采用梯度下降法和随机梯度下降法来最小化基于振幅的平方损失。特别地，这包括扩展型光刻迭代引擎作为随机梯度下降法的一个特例。我们证明，在适当选择步长的情况下，所有方法均以亚线性速率收敛到临界点。我们还讨论了采用更大步长的可能性。