This paper discusses an OpenCL version of a volumetric JPEG 2000 codec that runs on GPUs, multi-core processors or a combination of both. Since the performance critical part consists of a fine-grained (discrete wavelet transform) and coarse-grained algorithm (Tier-1), the best performance is obtained with a hybrid execution in which the discrete wavelet transform is executed on a GPU and Tier-1 on a multi-core. Using an Intel i7 multi-core in combination with a modest NVIDIA Quadro K620 GPU yields speedups greater than 10 compared with the original sequential code. The performance bottlenecks that arise on GPUs when parallelizing algorithms that are coarse-grained by nature are discussed and also the optimizations that are possible. A performance analysis reveals the inefficiencies and explains the deviations from the GPU peak performance.