Optical imaging in medicine .2. Modelling and reconstruction

The desire for a diagnostic optical imaging modality has motivated the development of image reconstruction procedures involving solution of the inverse problem. This approach is based on the assumption that, given a set of measurements of transmitted light between pairs of points on the surface of an object, there exists a unique three-dimensional distribution of internal scatterers and absorbers which would yield that set. Thus imaging becomes a task of solving an inverse problem using an appropriate model of photon transport. In this paper we examine the models that have been developed for this task, and review current approaches to image reconstruction. Specifically, we consider models based on radiative transfer theory and its derivatives, which are either stochastic in nature (random walk, Monte Carlo, and Markov processes) or deterministic (partial differential equation models and their solutions). Image reconstruction algorithms are discussed which are based on either direct backprojection, perturbation methods, nonlinear optimization, or Jacobian calculation. Finally we discuss some of the fundamental problems that must be addressed before optical tomography can be considered to be an understood problem, and before its full potential can be realized.