Year: 2015
Type: article
Abstract: Nonlinear parametric inverse problems appear in several prominent applications; one such application is diffuse optical tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly due to the need for solving a sequence of large-scale discretized, parametrized partial differential equations in the forward model. In this paper, we show how interpolatory parametric model reduction can significantly reduce the cost of the inversion process in DOT by drastically reducing the computational cost of solving the forward problems. The key observation is that function evaluations for the underlying optimization problem may be viewed as transfer function evaluations along the imaginary axis; a similar observation holds for Jacobian evaluations as well. This motivates the use of system-theoretic model order reduction methods. We discuss the construction and use of interpolatory parametric reduced models as surrogates for the full forward model. Within the DOT setting, these surrogate models can approximate both the cost functional and the associated Jacobian with very little loss of accuracy while significantly reducing the cost of the overall inversion process. Four numerical examples illustrate the efficiency of the proposed approach.
DOI: 10.1137/130946320
Authors: Eric de Sturler, Serkan Gugercin, Misha E. Kilmer, Saifon Chaturantabut, Christopher Beattie, Meghan O'Connell
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Collaborative Research: Innovative Integrated Strategies for Nonlinear Parametric Inversion, Near-infrared spectral imaging of the breast for cancer detection and monitoring, CAREER: Reduced-order Modeling and Controller Design for Large-scale Dynamical Systems via Rational Krylov Methods, Collaborative Research: Innovative Integrative Strategies for Nonlinear Parametric Inversion, CMG COLLABORATIVE RESEARCH: Quantum Monte Carlo Calculations of Deep Earth Materials
OpenAlex ID: W1595822959