What is Wrong with End-to-End Learning for Phase Retrieval?
Wenjie Zhang Yuxiang Wan Zhong Zhuang Ju Sun
For nonlinear inverse problems that are prevalent in imaging science,
symmetries in the forward model are common. When data-driven deep learning
approaches are used to solve such problems, these intrinsic symmetries can
cause substantial learning difficulties. In this paper, we explain how such
difficulties arise and, more importantly, how to overcome them by preprocessing
the training set before any learning, i.e., symmetry breaking. We take
far-field phase retrieval (FFPR), which is central to many areas of scientific
imaging, as an example and show that symmetric breaking can substantially
improve data-driven learning. We also formulate the mathematical principle of
symmetry breaking.