Ring artifacts are a very common problem in tomographic reconstruction, and numerous methods exist to either pre-process the sinogram or correct the reconstructed slice. A novel approach to perform the correction as part of the reconstruction process is presented. It is shown that for iterative techniques, which amount to optimizing an objective function, the ring artifacts correction can be easily integrated in the formalism, enabling simultaneous slice reconstruction and ring artifacts correction. This method is tested and compared with mainstream correction techniques for both simulated and experimental data. Results show that the correction is efficient, especially for undersampled datasets. This technique is included in the PyHST2 code which is used at the European Synchrotron Radiation Facility for tomographic reconstruction.