SEMINARS IN BIOMEDICAL ENGINEERING
Geometrically Convergent Monte Carlo Algorithms for Radiative Transport Problems
Dr. Jerome Spanier
Monte Carlo simulations of the radiative transport equation provide a “gold standard” of computational accuracy for many problems in biomedical optics, but their slow convergence (as dictated by the central limit theorem) prevents their routine use. In the past decade, there has been a concerted effort to develop adaptively modified Monte Carlo algorithms that converge geometrically to solutions of radiative transport equations. Our group has concentrated on algorithms that extend to integral equations methods first proposed for matrix equations by Halton in 1962. This was accomplished by expanding the solution in suitable basis functions and estimating a finite number of expansion coefficients by random variables, based on either correlated sampling or importance sampling, and designing strategies to lower the variance recursively. Geometric convergence has been rigorously established for these “first generation” adaptive algorithms, but their practical utility is degraded by the expansion technique itself. More recently we have developed new adaptive algorithms that overcome most of the computations shortcomings of the earlier algorithms, and we have demonstrated the geometric convergence of these “second generation” algorithms. We will outline the major ideas involved and illustrate their advantages over conventional Monte Carlo methods. These algorithms will play a significant role in providing real‐time computational support for biophotonics applications at the Beckman Laser Institute and Medical Clinic.
sponsored by
The Laser Microbeam and Medical Program (LAMMP)
a NIH biotechnology resource facility at the Beckman Laser Institute