Model-based image reconstruction from time-resolved diffusion data

This paper addresses the issue of reconstructing the unknown eld of absorption and scattering coe cients from time-resolved measurements of di used light in a computationally e cient manner. The intended application is optical tomography, which has generated considerable interest in recent times. The inverse problem is posed in the Bayesian framework. The maximum a posteriori (MAP) estimate is used to compute the reconstruction. We use an edge-preserving generalized Gaussian Markov random eld to model the unknown image. The di usion model used for the measurements is solved forward in time using a nite-di erence approach known as the alternating-directions implicit method. This method requires the inversion of a tridiagonal matrix at each time step and is therefore of O(N ) complexity, where N is the dimensionality of the image. Adjoint di erentiation is used to compute the sensitivity of the measurements with respect to the unknown image. The novelty of our method lies in the computation of the sensitivity since we can achieve it in O(N ) time as opposed to O(N2) time required by the perturbation approach. We present results using simulated data to show that the proposed method yields superior quality reconstructions with substantial savings in computation.