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.
Highlights
Discrete Fourier analysis is very common in digital signal and image processing, and it is a fundamental tool in many applications
As the basis functions (BF) are adapted to the spatial domain of the data, window functions for handling the boundaries of the domain can be omitted, which is another advantage of spatial harmonic analysis (SPHARA)
In this paper we have introduced SpharaPy, a Python implementation of SPHARA, which is a new method for spatial harmonic analysis of multisensor data
Summary
Discrete Fourier analysis is very common in digital signal and image processing, and it is a fundamental tool in many applications. In common digital image data, the pixels are arranged on a flat surface in a Cartesian or rectangular grid. For such data, the basis functions (BF) for the Fourier transformation are usually implicitly specified by the transformation rule (cf [1]). The sensors for data acquisition are not located on a flat surface and cannot be represented by Cartesian or regular grids. Because of the non-regular sensor arrangement, standard 2D Fourier analysis cannot be used for the spatial analysis of these multisensor data. Eigensystems of Laplace operators and Laplace– Beltrami operators are applied in graph theory [3] as well as computer graphics and shape analysis [4,5,6,7,8,9]
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