Correlation plenoptic imaging (CPI) is a novel technological imaging modality enabling to overcome drawbacks of standard plenoptic devices, while preserving their advantages. However, a major challenge in view of real-time application of CPI is related to the relevant amount of required frames and the consequent computational-intensive processing algorithm. In this work, we describe the design and implementation of an optimized processing algorithm that is portable to an efficient computational environment and exploits the highly parallel algorithm offered by GPUs. Improvements by a factor ranging from 20X, for correlation measurement, to 500X, for refocusing, are demonstrated. Exploration of the relation between the improvement in performance achieved and actual GPU capabilities also indicates the feasibility of near-real-time processing capability, opening up to the potential use of CPI for practical real-time application.