Unlocking Inverse Problems Using Deep Learning: Breaking Symmetries in Phase Retrieval

Kshitij Tayal, Chieh-Hsin Lai, Raunak Manekar, Zhong Zhuang, Vipin Kumar, Ju Sun

Keywords: Phase Retrieval, Inverse problems, Symmetry, Deep Learning

Abstract: In many physical systems, inputs related by intrinsic system symmetries generate the same output. So when inverting such systems, an input is mapped to multiple symmetry-related outputs. This causes fundamental difficulty in tackling these inverse problems by the emerging end-to-end deep learning approach. Taking phase retrieval as an illustrative example, we show that careful symmetry breaking on the training data can help get rid of the difficulty and significantly improve learning performance on real data.