Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index: Part 2. Inverse model

This paper is the second part of the study of optical tomography based on radiative transfer equation considering refractive index, namely the inverse model which reconstruct the image from the data obtained from the forward model in the first part of this study. In the forward model, we divided the problem into two cases: one is the uniform refractive index and the other is the gradient refractive index. We also use the human brain phantom which contains void-like region to test the forward model, the experiment result shows that the simulation agrees well with the theoretical model.Similarly, in the inverse model, we also consider the reconstruct scheme in two cases as above. In the case of uniform refractive index, we use the adjoint difference method to calculate the gradient of the objective function. In the case of gradient refractive index, we use Lagrangian formalism method to obtain the formula of the gradient.In order to test the reconstruct algorithm, we use the image which was used in the forward model as the predicted data. From the reconstruct image, we can see the case of gradient refractive index agrees with the original image more closer. This shows that the reconstruct algorithm we used is robust and effective.