SEMINARS IN BIOMEDICAL ENGINEERING

A fast solver for radiative transport equation with applications

Hongkai Zhao, PhD

Presenting an efficient forward solver for steady-state or frequency-domain radiative transfer equation (RTE) on 2D and 3D structured and unstructured meshes with vacuum boundary condition or reflection boundary condition. Due to high dimensionality the key issue is to construct an efficient iterative scheme that can deal with various behaviors of the solution in different regimes, such as transport, diffusion, optical thick, and forward peaking. In our algorithm we use a angular and spatial discretization that preserves properties of both scattering and differential operators of RTE. To solve the large linear system after discretization, we develop an efficient multigrid method in both angular and physical space. Our algorithm can deal with different scattering regimes efficiently. Efficiency and accuracy of our algorithm is demonstrated by comparison with both analytical solutions and Monte Carlo solutions, and various numerical tests in optical imaging. Based on this algorithm, a multi-level imaging algorithm is developed for optical tomorgraphy. If time permits, I will also talk about our recent work on compressive sensing (CS) in bioluminescence tomography (BLT) based on RTE. Shown much improved results over standard reconstruction method.

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sponsored by

The Laser Microbeam and Medical Program (LAMMP)
a NIH biotechnology resource facility at the Beckman Laser Institute