Fast algorithms for Hyperspectral Diffuse Optical Tomography

Arvind Krishna Saibaba

Tufts University

Diffuse Optical Tomography (DOT) is an imaging technique that uses near infrared light to image highly scattering media, and is useful for breast cancer detection and brain imaging. The image reconstruction of chromophore concentrations using DOT data can be described mathematically as an ill-posed inverse problem. Recent work has shown that the use of hyperspectral DOT (hyDOT) data, has the potential for improving the quality of the reconstructions. The use of this data in the formulation and solution of the inverse problem poses a significant computational burden. The forward operator is, in actuality, nonlinear. However, under certain assumptions, the Born approximation provides a suitable surrogate for the forward operator, and we assume this to be true in the present work. Computation of the Born matrix requires the solution of thousands of large scale discrete PDEs, which we tackle using a novel recycling Krylov subspace approach, and the reconstruction problem requires matrix-vector products with the (dense) Born matrix, which we tackle by developing a recursive compression algorithm for the Born matrix. In this talk, I will address both of these difficulties, thus demonstrating a computational viable approach for hyDOT reconstruction. I will provide a detailed analysis of the accuracy and computational costs of the resulting algorithms and demonstrate the validity of our approach by detailed numerical experiments on a realistic geometry.

Joint work with Misha Kilmer, Eric Miller and Sergio Fantini.

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