The JPEG compression format has been the standard for lossy image compression for over multiple decades, offering high compression rates at minor perceptual loss in image quality. For GPU-accelerated computer vision and deep learning tasks, such as the training of image classification models, efficient JPEG decoding is essential due to limitations in memory bandwidth. As many decoder implementations are CPU-based, decoded image data has to be transferred to accelerators like GPUs via interconnects such as PCI-E, implying decreased throughput rates. JPEG decoding therefore represents a considerable bottleneck in these pipelines. In contrast, efficiency could be vastly increased by utilizing a GPU-accelerated decoder. In this case, only compressed data needs to be transferred, as decoding will be handled by the accelerators. In order to design such a GPU-based decoder, the respective algorithms must be parallelized on a fine-grained level. However, parallel decoding of individual JPEG files represents a complex task. In this paper, we present an efficient method for JPEG image decompression on GPUs, which implements an important subset of the JPEG standard. The proposed algorithm evaluates codeword locations at arbitrary positions in the bitstream, thereby enabling parallel decompression of independent chunks. Our performance evaluation shows that on an A100 (V100) GPU our implementation can outperform the state-of-the-art implementations libjpeg-turbo (CPU) and nvJPEG (GPU) by a factor of up to 51 (34) and 8.0 (5.7). Furthermore, it achieves a speedup of up to 3.4 over nvJPEG accelerated with the dedicated hardware JPEG decoder on an A100.