Median filtering has become a ubiquitous smoothing tool for image denoising tasks, with its complexity generally determined by the median algorithm used (usually on the order of O(n log(n)) when computing the median of n elements). Most algorithms were formulated for scalar single processor computers, with few of them successfully adapted and implemented for computers with a parallel architecture. However, the redundancy for processing neighboring pixels has not yet been fully exploited for parallel implementations. Additionally, most of the implementations are only suitable for fixed point images, but not for floating point.In this paper we propose an efficient parallel implementation of the 2D median filter, based on a multiple pixel-per-thread framework, and test its implementation on a CUDA-capable GPU either for fixed point or floating point data. Our computational results show that our proposed methods outperforms state-of the art implementations, with the difference increasing significantly as the filter size grows.