3D Phaseless Imaging at Nano-scale: Challenges and Possible Solutions

In a variety of scientific applications we are interested in imaging 3D objects at very fine resolutions. However, we typically can not measure the object or its footprint directly. Rather restricted by fundamental laws governing the propagation of light we have access to 2D magnitude-only measurements of the 3D object through highly nonlinear projection mappings. Therefore, reconstructing the object requires inverting highly nonlinear and seemingly non-invertible mappings. In this paper we discuss some of the challenges that arises in such three dimensional phaseless imaging problems and offer possible solutions for 3D reconstruction. In particular we demonstrate how variants of the recently proposed Accelerated Wirtinger Flow (AWF) algorithm can enable precise 3D reconstruction at unprecedented resolutions. This extended abstract is based on a summary of [2], [46], and forthcoming work by the author and collaborators with parts of the text directly adapted.