Optical tomography using reverse differentiation

Optical tomography is a way to see inside the human body using infrared light. But unlike ultrasound, the light beams used are strongly scattered at infrared frequencies. So the relatively straightforward methods used for ultrasound do not apply. A way to obtain optical properties from the body from the scattered light is to simulate the process with a finite number points a then optimizing them to get an output that matches the measured output. A fast way of doing this is with conjugate gradient descent. What is needed is a Jacobian of the optical properties with respect to some error measure between the measured and simulated outputs. The fastest way of doing this is by reverse differentiating the numerical algorithm used in the simulation.

Here is a presentation for a medical imaging course that describes the algorithm and an example case obtained from a MATLAB implementation of the algorithm. More information is given in one of my whitepapers. The equations in the presentation are displayed from LaTex using the Power Point plug in called TexPoint.