A signal processing model of diagnostic x-ray scatter

A model of scatter is developed from a signal processing approach. The scattering process is viewed as a nonlinear filter (NLF), which transforms a two-dimensional signal representing phantom thickness into a two-dimensional signal of scattered radiation. The NLF point spread function (PSF) is derived from a single scattering model, using the principles of Compton scattering and x-ray attenuation. The PSF is characterized by three approximations: a constant geometric shape, a volume that depends on the phantom thickness, and a width that depends on the phantom-to-detector distance. This leads to a closed form expression for the scatter-to-primary ratio as a function of phantom thickness, field size, photon energy, source-to-phantom distance, and phantom-to-detector distance. The NLF model is compared with previously reported measurements using constant thickness phantoms, and discrepancies are discussed. The good agreement found between the NLF model and measured data shows that the functional dependence of scatter on the above parameters, previously only explained in terms of empirical models or Monte Carlo simulations, can be incorporated into a signal processing model.