Research - Overview

Computational Inverse Problems

My research centers on the advancement of computational techniques and relevant theory for the solution of inverse problems that arise in computationally demanding contexts such as medical and industrial imaging, as well as data science. The focus of my research and my student's is on the integration of modern scientific computing practices with mathematically rigorous data-aware approaches to solve inverse problems.

Accelerated Numerical Methods

Accelerated numerical techniques for discrete inverse problems often center on developing efficient iterative methods utilizing strategies such as mixed-to-low precision computing, randomization, and optimized data movement in memory. Low-to-mixed precision shows particular promise in preconditioning, where, because inverse problems have limits on achievable solution quality under realistic noise, computing low-rank Kronecker product preconditioners in low precision for iterative solvers like LSQR can achieve significant speedups without loss of accuracy. The unifying goal across these themes is the development of precision and communication aware iterative solvers for inverse problems that are robust, efficient, and architecture conscious.

All things discrete ill-posed problems [!]

A consistent theme of my research in discrete inverse problems is developing a deeper fundamental understanding of why methods and techniques work the way they do. This often involves investigating questions at either the fundamental linear algebraic or optimization level.