Seminar by Fei Lu

Speaker

Fei Lu (Johns Hopkins University)

Title

Adaptive RKHS regularization for ill-posed linear inverse problems

Date

• March 19, 2024 15:00 CET+0100 (Europe/Rome)

• March 19, 2024 10:00 EDT-0400 (US/Eastern)

• March 19, 2024 09:00 CDT-0500 (US/Central)

• March 19, 2024 07:00 PDT-0700 (US/Pacific)

Abstract

Reguarlization is crucial to produce stable accurate solutions for ill-posed inverse problems in the form of Ax=b. Although regularization has been intensively studied for more than a century, a remaining challgene to properly regularize the problem with varying A and b. Such problems arise in data-driven modeling, where even the space of x is either unknown or depends on the basis functions and discretization. We introduce a data-adaptive RKHS for regularization. The RKHS is determined by the inverse problem and the data, and it can be either finite or infinite dimension. We will discuss a direct method based on matrix decomposition, as well as a scalable iterative method based on a new generalized Golub-Kahan bidiagonalization. In both direct and iterative methods, the RKHS regularizer leads to convergent estimators that are robust to noise, outperforming the widely used L2 or l2 regularizers. We demonstrate the applications in learning kernels in operators, solving Fredholm equations of the first kind, and image deblurring.

Recording

Watch the recording on our YouTube channel.