A method and apparatus is provided to reconstruct a collective image of a multiple method/geometry imaging system (e.g., a hybrid computed tomography system having energy-integrating detectors arranged in a third-generation geometry and photon-counting detectors arranged in a fourth generation geometry), wherein a splitting-based iterative algorithm using modified dual variables is used in the image reconstruction. Whereas a separate image for each method/geometry of the multiple method/geometry imaging system can be obtained by solving the distinct system-matrix equation corresponding to each respective method/geometry, the collective image is obtained by simultaneously solving a collective optimization problem including all respective system-matrix. The collective image is obtained more efficiently using variable splitting to subdivide the optimization into subproblems that are solved in an iterative fashion. For some applications, the collective image can be further improved by including a beam-hardening correction step.
