3-D reconstruction in macro- and micro-worlds: Challenges and Solutions
Data Science Seminar
Yunpeng Shi (Princeton University)
You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.
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.