We introduce a new approach to get faster MRI acquisition. By reducing the number of data-samples in combination with a new MRI reconstruction method, we are able to reduce the acquisition time by a factor 20 without introducing disturbing artifacts. In order to reconstruct the image we have to iteratively apply the non-uniform fast Fourier transform. This step turns out to be a major bottleneck. Therefore, we have accelerated the NUFFT by using the GPU. The speedup achieved by the GPU acceleration now enables new options for MRI research.