Accelerating nonlinear reconstruction in laminar optical tomography by use of recursive SVD inversion

Image reconstruction in the most model-based biophotonic imaging modalities essentially poses an ill-posed nonlinear inverse problem, which has been effectively tackled in the diffusion-approximation-satisfied scenarios such as diffuse optical tomography. Nevertheless, a nonlinear implementation in high-resolution laminar optical tomography (LOT) is normally computationally-costly due to its strong dependency on a dense source-detector configuration and a physically-rigorous photon-transport model. To circumvent the adversity, we herein propose a practical nonlinear LOT approach to the absorption reconstruction. The scheme takes advantage of the numerical stability of the singular value decomposition (SVD) for the ill-posed linear inversion, and is accelerated by adopting an explicitly recursive strategy for the time-consuming repeated SVD inversion, which is based on a scaled expression of the sensitivity matrix. Experiments demonstrate that the proposed methodology can perform as well as the traditional nonlinear one, while the computation time of the former is merely 26.27% of the later on average.