A method and apparatus to correct for scatter in projection data by successive approximations of a primary-beam estimate and a scatter estimate. The scatter estimate is calculated by convolving a scattering function, which is a function of the primary-beam estimate, with a smoothing function that includes Rayleigh scattering and Compton scattering terms. The scattering function is greater than zero in the limit that the primary-beam estimate goes to zero. The projection data can be X-ray computed tomography projection data, and the choice of scattering function has the benefit of reducing dark-band artefacts in reconstructed computed tomography images.
