An apparatus is provided to reconstruct an image using combined third-generation energy-integrating computed tomography projection data and fourth-generation spectrally resolved computed tomography projection data. The apparatus includes processing circuitry configured to obtain first projection data representing projection data from an energy-integrating detector obtain second projection data representing projection data from a photon-counting spectrally discriminating detector and reconstruct a first combined-system basis image and a second combined-system basis image by solving a combined-system matrix equation using the first projection data and the second projection data.
