Learning phase diversity for solving ill-posed inverse problems in imaging

Abstract Inverse problems in imaging are typically ill-posed and are solved using regularized optimization techniques or - in recent times, by employing deep neural networks. While the deep network method enables fast end-to-end reconstruction from raw measurements, it does not necessarily alter the fundamentally ill-posed nature of the underlying inverse problem. It is well known that diverse, non-redundant measurements can improve the robustness of reconstruction algorithms. However, acquiring multiple measurements typically - involves additional hardware and more complex system setups, that may not always be desirable for field deployment. In this work, we note that in both incoherent and coherent (phase retrieval) optical imaging, the irradiance patterns corresponding to two phase diverse measurements associated with the same test object have implicit local correlations, which may be learned by a suitable deep network. A physics informed data augmentation scheme is then described where a trained network is used for generating a phase diverse pseudo-data based on a ground truth data frame, typically acquired using a standard imaging system. We validate this data augmentation approach for both incoherent and coherent optical imaging - configurations, with vortex phase as a - diversity mechanism. Specifically, we observe that the generated pseudo-data closely match the corresponding ground-truth data, with comparable noise characteristics. We further demonstrate that the true data along with the augmented pseudo-data provide- high quality inverse solutions with simpler robust reconstruction algorithms. Our results may open new avenues for leaner, high-fidelity computational imaging systems across a broad range of applications.