Denoising and filtering of time series signals is a problem emerging in many
areas of computational science. Here we demonstrate how the nonparametric
computational methodology of the finite element method of time series analysis with
regularization can be extended for denoising of very long and noisy time series
signals. The main computational bottleneck is 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-scale data denoising problems and comparing their
computational scaling and performance to the performance of the standard denoising
methods.
Keywords
time series analysis, quadratic programming, SPG-QP,
regularization