Zu Chongzhi Research Seminar

Date and Time (China standard time): Thursday, Aug 21, 2:00 pm – 3:00 pm

Location: IB 2028

Zoom: 969 7235 5170, Passcode: dkumath

Title: Fast Image Denoising and Alignment via Steerable Transforms

Speaker: Yunpeng Shi (University of California, Davis)

Abstract: In this talk, we explore two classical image processing tasks motivated by cryo-electron microscopy imaging: tomographic image denoising and rigid image registration. Both tasks inherently involve operations of 2D rotations, where leveraging specific transforms can significantly enhance the speed and robustness of the algorithms.

In the first part of the talk, I will introduce an unsupervised image denoiser based on estimating the covariance matrix of clean images. A key insight is that if the image manifold is invariant under global in-plane rotations, this symmetry can be exploited to accelerate computations and reduce dimensionality. I will discuss recent advances in fast expansion into steerable bases that allow us to efficiently utilize this rotational symmetry, leading to a thousandfold improvement in the speed of covariance estimation over existing methods. This technique has been successfully applied to joint deconvolution and denoising of large-scale, real-world cryo-EM images.

In the second part, I will present a fast algorithm for aligning images using optimal transport. Our method leverages the sliced Wasserstein distance by computing the 1D Wasserstein distance between radial line projections of input images. By applying a special transform to the frequency domain, we achieve efficient alignment of two L by L images in O(L^2 log L) operations — matching the complexity of alignment using Euclidean distance. I will demonstrate the robustness of our method to translations and deformations.

Finally, I will comment on the practical limitations of both methods and discuss open questions that remain, highlighting areas for future exploration.

Bio: Dr. Yunpeng Shi is an Assistant Professor in the Department of Mathematics at the University of California, Davis, where he has served since 2023. From 2020 to 2023, he was a postdoctoral research associate in the Program in Applied and Computational Mathematics at Princeton University under the supervision of Professor Amit Singer. He received his Ph.D. in Mathematics from the University of Minnesota, advised by Professor Gilad Lerman. His research focuses on the mathematical foundations and the development of fast, robust algorithms for 3D computer vision and image processing, with applications to large-scale 3D reconstruction problems, including cryo-electron microscopy for protein molecules.