Speaker
Description
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include computations of inner-products, which becomes costly when the number of iterations is high, are a bottleneck for parallelization, and can cause the algorithms to break down due to information loss in the projections.
In this talk, I will describe two new approaches to handle expensive inner-product computations in the context of solving large-scale inverse problems. First, we describe new iterative solvers based on the randomized Golub-Kahan approach, where sketched inner products are used to estimate inner products of high-dimensional vectors. Second, we describe new inner-product-free Krylov solvers that avoid inner-products completely. For both approaches, we also describe hybrid methods that combine iterative projection methods with Tikhonov regularization, where regularization parameters can be selected automatically during the iterative process. Numerical results from image reconstruction show the potential benefits of these approaches.