Image compressions have a number of applications in various fields where the processing throughput and/or latency is a crucial attribute and the main limitation with state of the art implementations of compression algorithms. At the same time the contemporary GPUs provide a tremendous processing power applicable to the image compression acceleration but it calls for a specific algorithm design. We discuss the key components of successful GPU algorithm design and demonstrate this on JPEG2000 compression chain, which contains several types of algorithms: from DWT which is inherently well suited to GPU, through context modeling requiring reformulation in order to perform well on GPU, to arithmetic coding which does not fit the paradigm well but can be optimized to perform faster than CPU versions. Performance evaluation of the optimized JPEG2000 chain will be used to demonstrate the importance of various aspects of GPU programming, especially with respect to real-time applications.