Reconstructing image differences from tomographic Poisson data

Given two measurements of an image and a modified version of the image, we seek reconstructions of both the original image and the difference of the images. The data are assumed to be Poisson, with known nonnegative forward operator and nonnegative images. A penalized likelihood is minimized with the penalty equal to the sum of the absolute difference between the images. An alternating minimization algorithm is developed by reformulating the penalized maximum likelihood problem as a double minimization of I-divergence plus the penalty. This algorithm guarantees monotonic decrease in the objective function for each iteration. Simulations with random images and tomographic data are presented to demonstrate properties of the algorithm. Convergence properties of the algorithm are studied both theoretically and in simulations.