A method for reconstructing image data from x-ray data measured with an imaging system having at least one photon-counting detector includes obtaining a representation of data measured by the photon-counting detector. The method also includes generating first image data based on a projection based first functional using a first algorithm, the projection based first functional being dependent on the representation of data. The method also includes updating, based on a second functional that includes a model of at least one physical effect not included in the projection based first functional, the first image data to obtain second image data. The invention also provides an image processing device configured to reconstruct image data from x-ray data measured with an imaging system including at least one photon-counting detector as well as a corresponding computer program product.