SpharaPy: A Python toolbox for spatial harmonic analysis of non-uniformly sampled data

Uwe Graichen; Roland Eichardt; Jens Haueisen

doi:10.1016/j.softx.2019.100289

SpharaPy: A Python toolbox for spatial harmonic analysis of non-uniformly sampled data

Uwe Graichen^*, Roland Eichardt, Jens Haueisen

^*Corresponding author for this work

Research output: Journal article (peer-reviewed) › Journal article

2 Citations (Scopus)

Abstract

SpharaPy is a Python implementation of a new approach for spatial harmonic analysis (SPHARA). SPHARA extends the classical spatial Fourier analysis to non-uniformly positioned samples on arbitrary surfaces in R³. The basis functions (BF) used by SPHARA are determined by the eigenanalysis of the discrete Laplace–Beltrami operator, which is defined on a triangular mesh specified by the spatial sampling points. The SpharaPy Python toolbox provides classes and functions to compute the SPHARA BF for data analysis and synthesis as well as classes to design and apply spatial filters. An illustrative example of applying the SpharaPy package in the field of biosignal processing using electroencephalography data is presented.

Original language	English
Article number	100289
Journal	SoftwareX
Volume	10
DOIs	https://doi.org/10.1016/j.softx.2019.100289
Publication status	Published - 01 Jul 2019
Externally published	Yes

Keywords

EEG Data Processing
Eigenanalysis of the discrete Laplace–Beltrami operator
Generalized spatial Fourier analysis
Online filtering
Spatial filtering
Spatial harmonic analysis

ASJC Scopus subject areas

Software
Computer Science Applications

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10.1016/j.softx.2019.100289

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title = "SpharaPy: A Python toolbox for spatial harmonic analysis of non-uniformly sampled data",

abstract = "SpharaPy is a Python implementation of a new approach for spatial harmonic analysis (SPHARA). SPHARA extends the classical spatial Fourier analysis to non-uniformly positioned samples on arbitrary surfaces in R3. The basis functions (BF) used by SPHARA are determined by the eigenanalysis of the discrete Laplace–Beltrami operator, which is defined on a triangular mesh specified by the spatial sampling points. The SpharaPy Python toolbox provides classes and functions to compute the SPHARA BF for data analysis and synthesis as well as classes to design and apply spatial filters. An illustrative example of applying the SpharaPy package in the field of biosignal processing using electroencephalography data is presented.",

keywords = "EEG Data Processing, Eigenanalysis of the discrete Laplace–Beltrami operator, Generalized spatial Fourier analysis, Online filtering, Spatial filtering, Spatial harmonic analysis",

author = "Uwe Graichen and Roland Eichardt and Jens Haueisen",

note = "Funding Information: This project has received funding from the German Research Foundation under grand number Gr 5251/1-1 , from the European Union Horizon 2020 research and innovation programme under grant agreement No 686865 (project BREAKBEN), and from Marie Sk{\l}odowska-Curie, Germany Innovative Training Network under grant agreement No 813483 (project INFANS). We acknowledge support for the Article Processing Charge from the German Research Foundation and the Open Access Publication Fund of the Technische Universit{\"a}t Ilmenau. Publisher Copyright: {\textcopyright} 2019 The Authors",

year = "2019",

month = jul,

day = "1",

doi = "10.1016/j.softx.2019.100289",

language = "English",

volume = "10",

journal = "SoftwareX",

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publisher = "Elsevier B.V.",

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T2 - A Python toolbox for spatial harmonic analysis of non-uniformly sampled data

AU - Graichen, Uwe

AU - Eichardt, Roland

AU - Haueisen, Jens

N1 - Funding Information: This project has received funding from the German Research Foundation under grand number Gr 5251/1-1 , from the European Union Horizon 2020 research and innovation programme under grant agreement No 686865 (project BREAKBEN), and from Marie Skłodowska-Curie, Germany Innovative Training Network under grant agreement No 813483 (project INFANS). We acknowledge support for the Article Processing Charge from the German Research Foundation and the Open Access Publication Fund of the Technische Universität Ilmenau. Publisher Copyright: © 2019 The Authors

PY - 2019/7/1

Y1 - 2019/7/1

N2 - SpharaPy is a Python implementation of a new approach for spatial harmonic analysis (SPHARA). SPHARA extends the classical spatial Fourier analysis to non-uniformly positioned samples on arbitrary surfaces in R3. The basis functions (BF) used by SPHARA are determined by the eigenanalysis of the discrete Laplace–Beltrami operator, which is defined on a triangular mesh specified by the spatial sampling points. The SpharaPy Python toolbox provides classes and functions to compute the SPHARA BF for data analysis and synthesis as well as classes to design and apply spatial filters. An illustrative example of applying the SpharaPy package in the field of biosignal processing using electroencephalography data is presented.

AB - SpharaPy is a Python implementation of a new approach for spatial harmonic analysis (SPHARA). SPHARA extends the classical spatial Fourier analysis to non-uniformly positioned samples on arbitrary surfaces in R3. The basis functions (BF) used by SPHARA are determined by the eigenanalysis of the discrete Laplace–Beltrami operator, which is defined on a triangular mesh specified by the spatial sampling points. The SpharaPy Python toolbox provides classes and functions to compute the SPHARA BF for data analysis and synthesis as well as classes to design and apply spatial filters. An illustrative example of applying the SpharaPy package in the field of biosignal processing using electroencephalography data is presented.

KW - EEG Data Processing

KW - Eigenanalysis of the discrete Laplace–Beltrami operator

KW - Generalized spatial Fourier analysis

KW - Online filtering

KW - Spatial filtering

KW - Spatial harmonic analysis

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DO - 10.1016/j.softx.2019.100289

M3 - Journal article

AN - SCOPUS:85070341382

SN - 2352-7110

VL - 10

JO - SoftwareX

JF - SoftwareX

M1 - 100289

ER -

SpharaPy: A Python toolbox for spatial harmonic analysis of non-uniformly sampled data

Abstract

Keywords

ASJC Scopus subject areas

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