Vol. 13, No. 1, 2018

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ISSN: 2157-5452 (e-only)
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On a scalable nonparametric denoising of time series signals

Lukáš Pospíšil, Patrick Gagliardini, William Sawyer and Illia Horenko

Vol. 13 (2018), No. 1, 107–138
Abstract

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 H1 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
Mathematical Subject Classification 2010
Primary: 37M10, 62-07, 62H30, 65Y05, 90C20
Milestones
Received: 20 June 2017
Accepted: 30 October 2017
Published: 17 February 2018
Authors
Lukáš Pospíšil
Università della Svizzera italiana
Lugano
Switzerland
Patrick Gagliardini
Università della Svizzera italiana
Lugano
Switzerland
William Sawyer
Swiss National Supercomputing Centre
Lugano
Switzerland
Illia Horenko
Università della Svizzera italiana
Lugano
Switzerland