October 29, 2024

A general framework of rotational sparse approximation in uncertainty quantification

This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the gPC expansion of a set of random variables after the rotation has a sparser representation. However, this rotational approach alters the underlying linear system to be solved, which makes finding the sparse coefficients more difficult than the case without rotation. To solve this problem, we examine several popular nonconvex regularizations in compressive sensing (CS) that perform better than the classic l1 approach empirically. All these regularizations can be minimized by the alternating direction method of multipliers (ADMM). Numerical examples show superior performance of the proposed combination of rotation and nonconvex sparse promoting regularizations over the ones without rotation and with rotation but using the convex l1 approach. 

About the speaker

Dr. Mengqi Hu is a Postdoc Research Associate at University of North Carolina at Chapel Hill. In 2016, he graduated with a MS in Mathematics from The University of Texas Rio Grande Valley, formerly known as The University of Texas-Pan American. After that he continued his graduate study and graduated in mathematics for a PhD at the University of Texas at Dallas at 2021. He worked as a postdoc at Lehigh University from 2021-2022 and then to UNC at Chapel Hill where he is now.  

His reseach interest includes Sparse recovery, signal processing and imaging from different sources in general.