Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography.

Area of Science:

• Computational physics
• Optical imaging
• Numerical analysis

Background:

• The radiative transfer equation (RTE) offers superior accuracy for tomographic reconstruction compared to diffusion approximation (DA).
• High computational cost of RTE-based methods limits their practical use in complex scenarios.

Purpose of the Study:

• To develop an efficient method for solving the RTE forward problem with multiple light sources simultaneously.
• Introduce a novel linear solver, block BiCGStab, to accelerate convergence by leveraging shared information.

Main Methods:

• Implementation of a novel block biconjugate gradient stabilized (block BiCGStab) method for solving the RTE forward problem.
• Development of two parallelized block BiCGStab variants for enhanced performance with limited threads.
• Performance evaluation using numerical simulations with the Delta-Eddington approximation.

Main Results:

• The single-threaded block RTE solver demonstrated a 1.5-3x reduction in computation time compared to traditional sequential methods.
• Parallel block solvers achieved a 1.5x speedup over traditional parallel sequential methods.
• The block linear solver's independence from discretization schemes and preconditioners allows for further optimization.

Conclusions:

• The proposed block BiCGStab method offers a significant computational speedup for RTE-based tomographic reconstruction.
• This efficient solver enhances the practical applicability of accurate RTE methods in optical imaging.
• The solver's modularity enables integration with existing techniques for potentially greater accuracy and speed.