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