In this project, optimization methods based on Mean Field Annealing , as developed at North Carolina State University are applied to the problem of reconstruction of PET data from measurements. The new techniques take into account the statistics of the noise (Poisson), the nature of the blur process, and prior models of the image itself; to construct a much higher resolution image, from the same measured data. The images below illustrate this by comparing an image constructed using conventional filtered back projection with an image reconstructed using Mean Field Annealing
By changing the filter used by FBP algorithm, the left image can be made sharper, but with increased sensitivity to noise.
A paper has been written which carefully compares the results of maximum likelihood, MAP (our version), and FBP.