The advent of Wide Field Adaptive Optics (WFAO) systems marks the beginning of a new era in high spatial resolution imaging. The newly commissioned Gemini South Multi-Conjugate Adaptive Optics System (GeMS) combined with the infrared camera Gemini South Adaptive Optics Imager (GSAOI), delivers quasi diffraction-limited images over a field of similar to 2 arc-minutes across. However, despite this excellent performance, some variable residues still limit the quality of the analyses. In particular, distortions severely affect GSAOI and become a critical issue for high-precision astrometry and photometry. In this paper, we investigate an optimal way to correct for the distortion following an inverse problem approach. Formalism as well as applications on GeMS data are presented.