Speaker: Yunpeng Shi
Title: 3-D reconstruction in macro- and micro-worlds: Challenges and Solutions
Abstract: In this talk I will discuss two problems of 3-D reconstruction: structure from motion (SfM) and cryo-electron microscopy (cryo-EM) imaging, which respectively solves the 3-D structure of, for example, architectures and protein molecules. My talk will be focused on two mathematical subproblems respectively in SfM and cryo-EM: robust group synchronization and image covariance estimation, and their extensions and applications. Both problems are closely related to low-rank approximations of certain matrices, but they are also challenging in very different ways. In the first half of the talk, I will introduce the group synchronization problem given highly corrupted data, and its applications in SfM. In the meantime, a fast and accurate solution that leverages the cycle-consistency constraints will be discussed. In the second half, I will focus on the covariance estimation problem given high-resolution images with varying contrast, and its applications in cryo-EM image restoration. Our method of covariance estimation achieves several order of magnitude speed up compared to the previous methods. Based on the fast covariance solver, I will introduce our image restoration method, called fast covariance Wiener filtering, that is completely ab-initio and unsupervised. Our method conducts a non-blind image deconvolution, image contrast estimation and image denoising in a joint way.