A pansharpening method based on the Rudin-Osher-Fatemi model and using a reproducing kernel Hilbert space along with the approximated Heaviside function is developed. The corresponding minimisation problem is solved by the alternating direction method of multipliers. Numerous numerical experiments with Pléiades and IKONOS satellite datasets demonstrate the efficiency of the method in preserving spectral and spatial information and show its superiority to other approaches.