Scatter Correction in PET Using the Transport Equation

In the presence of a strong scatterer, it is inappropriate to perform scatter correction by subtracting scattered from measured events and work on unscattered events only. Take, for example, a strong scatterer that completely surrounds the reconstruction volume. In this case, all events are scattered and removal simply would leave nothing. We propose an algorithm for PET reconstruction that is based on modeling the scanning process by the full transport equation, incorporating (multiple) scatter and attenuation. Then, a solution to the full forward model is sought. The concept sounds simple, but it is hard to implement since the forward model becomes arbitrarily complex. Also, care has to be taken to use expectation maximization techniques to retain image quality.