Parallel Statistical Multi-resolution Estimation

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.