Visual pattern recognition is a key research topic in the field of image processing and computer vision. Texture analysis based on steerable Riesz wavelets is powerful, but requires computing pixel -- wise operations resulting in a run time in the order of days when large volumes of data are processed. To overcome this limitation we propose a Graphics Processing Unit (GPU) based solution. A standard CPU version is used as starting point for the development of baseline GPU versions. To further increase the performance, and to overcome compute and memory limitations we apply a series of optimization techniques, leading to five versions in total. The best performing GPU solution ensures a speed -- up of 93x for the parallelized section of the application and of 29.6x for the entire application. Furthermore, we show that a higher Riesz order and/or a higher image resolution further increases the speed -- up.