The increasing size of medical imaging data, in particular time series such as CT perfusion (CTP), requires new and fast approaches to deliver timely results for acute care. Cloud architectures based on graphics processing units (GPUs) can provide the processing capacity required for delivering fast results. However, the size of CTP datasets makes transfers to cloud infrastructures time-consuming and therefore not suitable in acute situations. To reduce this transfer time, this work proposes a fast and lossless compression algorithm for CTP data. The algorithm exploits redundancies in the temporal dimension and keeps random read-only access to the image elements directly from the compressed data on the GPU. To the best of our knowledge, this is the first work to present a GPU-ready method for medical image compression with random access to the image elements from the compressed data.