Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illumination of the object, which is shifted after each illumination to cover its whole domain. As in the resulting measurements the phase information is lost, ptychography gives rise to solving a phase retrieval problem. In this work, we consider ptychographic measurements corrupted with background noise, a type of additive noise that is independent of the shift, i.e., it is the same for all diffraction patterns. Two algorithms are provided, for arbitrary objects and for so-called phase objects that do not absorb the light but only scatter it. For the second type, a uniqueness of reconstruction is established for almost every object. Our approach is based on the Wigner Distribution Deconvolution, which lifts the object to a higher-dimensional matrix space where the recovery can be reformulated as a linear problem. Background noise only affects a few equations of the linear system that are therefore discarded. The lost information is then restored using redundancy in the higher-dimensional space. Keywords: phase retrieval, ptychography, background noise, Wigner Distribution Deconvolution, uniqueness of reconstruction.

翻译：叠层成像是一种计算成像技术，旨在从一组衍射图案中重建感兴趣的物体。每个衍射图案通过物体的局部照明获得，每次照明后移动照明区域以覆盖整个物体域。由于测量中相位信息丢失，叠层成像需要求解相位恢复问题。本文考虑背景噪声污染的叠层成像测量，这是一种与移位无关的加性噪声类型，即所有衍射图案中的噪声相同。针对任意物体和所谓的不吸收光仅散射光的相位物体，我们提供了两种算法。对于第二类物体，几乎对于所有物体均可建立重建的唯一性。我们的方法基于维格纳分布反卷积，该方法将物体提升到高维矩阵空间，其中恢复问题可重构为线性问题。背景噪声仅影响线性系统中的少数方程，因此这些方程被舍弃。随后利用高维空间中的冗余性恢复丢失的信息。关键词：相位恢复，叠层成像，背景噪声，维格纳分布反卷积，重建唯一性。