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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. [ABSTRACT FROM AUTHOR]

Abstract: Optical tomography belongs to the promising set of non-invasive methods for probing applications of semi-transparent media. This covers a wide range of fields. Nowadays, it is mainly driven by medical imaging in search of new less aggressive and affordable diagnostic means. This paper aims at presenting the most recent research accomplished in the authors’ laboratories as well as that of collaborative institutions concerning the development of imaging algorithms. The light transport modelling is not a difficult question as it used to be. Research is now focused on data treatment and reconstruction. Since the turn of the century, the rapid expansion of low cost computing has permitted the development of enhanced imaging algorithms with great potential. Some of these developments are already on the verge of clinical applications. This paper presents these developments and also provides some insights on still unresolved challenges. Intrinsic difficulties are identified and promising directions for solutions are discussed. [Copyright &y& Elsevier]