On a scalable nonparametric denoising of time series signals

Denoising and filtering of time series signals is a problem emerging in many areas of computational science. Here we demonstrate how the non- parametric computational methodology called Finite Element Method of time series analysis with H1 regularization can be extended for denoising of very long and noisy time series signals. The main computational bottleneck is in- duced by the cost of the inner Quadratic programming problem. Analyzing the solvability and utilizing the problem structure, we suggest an adapted version of the Spectral Projected Gradient method (SPG-QP) to resolve the problem. This approach increases the granularity of parallelization, making the proposed methodology highly suitable for Graphics Processing Unit (GPU) computing. We demonstrate the scalability of our open-source implementation based on PETSc for the Piz Daint supercomputer of the Swiss Supercomputing Centre CSCS, by solving large-scaled data denoising problems and comparing their computational scaling and performance to the performance of the standard denoising methods.