What is Wrong with End-to-End Learning for Phase Retrieval?
This addresses a fundamental issue in scientific imaging for researchers, though it is incremental as it builds on existing methods.
The paper tackles the learning difficulties in deep learning for nonlinear inverse problems like far-field phase retrieval, caused by symmetries in the forward model, and shows that symmetry breaking preprocessing substantially improves data-driven learning.
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.