spharapy 1.3.0

SPHARA-based spatial harmonic analysis and filtering

Sphara Implementation in Python

SpharaPy is a Python implementation of the SPHARA framework (Spatial Harmonic Analysis), an extension of classical spatial Fourier analysis to non-uniformly positioned samples on arbitrary surfaces in R^3. For details, see Graichen et al. (2015).

The basis functions used by SPHARA are obtained from the eigenanalysis of a discrete Laplace–Beltrami operator defined on a triangular mesh of the spatial sample locations.

The SpharaPy toolbox provides:

• Tools to compute SPHARA basis functions

• Routines to perform SPHARA analysis and synthesis (SPHARA transform)

• Methods for spatial filtering in the SPHARA domain

• Additional helper functions to design SPHARA-domain filters (ideal, Gaussian and Butterworth; low-pass, high-pass and band-pass)

These filters can be used directly with the class spharapy.spharafilter.SpharaFilter.

Requirements and Installation

Required software and packages:

• Python >= 3.10

• NumPy >= 1.23.5

• SciPy >= 1.14

• Matplotlib >= 3.6

Installation via pip:

pip install spharapy

Examples and Usage

Minimal examples are included within the source code. More detailed tutorial examples are provided in the documentation.

Citing SpharaPy

If you find this toolbox useful and publish results obtained using it, please consider citing the following publications:

• Graichen, U., Eichardt, R., & Haueisen, J. (2019). SpharaPy: A Python toolbox for spatial harmonic analysis of non-uniformly sampled data. SoftwareX, 10, Article 100289. https://doi.org/10.1016/j.softx.2019.100289

• Graichen, U., Eichardt, R., Fiedler, P., Strohmeier, D., Zanow, F., & Haueisen, J. (2015). SPHARA – A generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: Application to EEG. PLOS ONE, 10(4), e0121741. https://doi.org/10.1371/journal.pone.0121741