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

Abstract

It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.

Overview of diffuse optical tomography and its clinical applications

“…97,101 Even with current advanced computer technology, however, the heavy computational load is still the biggest drawback with the RTE. A variety of fast solvers of the RTE have been proposed, [102][103][104][105] and among these a hybrid model-based the RTE and DE is one of the most promising approaches. The hybrid model is based on the idea that the DE is an accurate model for measurements far from a light source.…”

Application of diffusion approximation in quantitative photoacoustic tomography in the presence of low-scattering regions

“…However, due to computationally expensive nature of these models, utilizing them in high dimensional tomographic inverse problems is often not feasible in practice. Although many computational challenges related to these models have been overcome by development of computational resources and numerical methods, such as usage of efficient parallel computing [39] or preconditioned Krylov subspace methods [40,41], their utilization is still limited in tomographic imaging.…”

Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

“…The other components are expanded by finite series of Legendre polynomials and used as the phase function in the dEM. The dEM has been widely employed in the field of biomedical optics since Klose and coworkers have introduced from the field of astrophysics [18][19][20][21][22]. It has been shown that the numerical solutions of the dEM agree with those of the RTE while the number of the discrete angular directions is reduced to approximately one-sixth of the required number for the RTE-calculations.…”

“…It has been shown that the numerical solutions of the dEM agree with those of the RTE while the number of the discrete angular directions is reduced to approximately one-sixth of the required number for the RTE-calculations. Nevertheless, a validity of the dEM is still unclear; Klose and coworkers showed that the second order dEM can provide the accurate results the same as the RTE [21], while Jia and coworkers stated that the zeroth order dEM is sufficient [22], and Boulet and coworkers employed the zeroth and first order dEM [20]. These differences probably come from the fact that the validity of the dEM depends on the SD distances, times after light incidence, and the optical properties, like the validity of the PDE.…”