  We discuss several strategies to implement Dykstra's projection algorithm on
NVIDIA's compute unified device architecture (CUDA). Dykstra's algorithm is the
central step in and the computationally most expensive part of statistical
multi-resolution methods. It projects a given vector onto the intersection of
convex sets. Compared with a CPU implementation our CUDA implementation is one
order of magnitude faster. For a further speed up and to reduce memory
consumption we have developed a new variant, which we call incomplete Dykstra's
algorithm. Implemented in CUDA it is one order of magnitude faster than the
CUDA implementation of the standard Dykstra algorithm. As sample application we
discuss using the incomplete Dykstra's algorithm as preprocessor for the
recently developed super-resolution optical fluctuation imaging (SOFI) method
(Dertinger et al. 2009). We show that statistical multi-resolution estimation
can enhance the resolution improvement of the plain SOFI algorithm just as the
Fourier-reweighting of SOFI. The results are compared in terms of their power
spectrum and their Fourier ring correlation (Saxton and Baumeister 1982). The
Fourier ring correlation indicates that the resolution for typical second order
SOFI images can be improved by about 30 per cent. Our results show that a
careful parallelization of Dykstra's algorithm enables its use in large-scale
statistical multi-resolution analyses.
