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.

对于存在于图像科学中的非线性反问题，前向模型中的对称性很常见。当使用数据驱动的深度学习方法来解决这类问题时，这些内在的对称性可能导致学习困难。本文解释了这些困难是如何产生的，更重要的是，如何通过预处理训练集（即对称性破坏）来克服这些困难。我们以远场相位恢复（FFPR）为例，该方法在科学成像的许多领域中起着核心作用，并展示了对称性破坏如何显著改善数据驱动学习。我们还阐述了对称性破坏的数学原则。