A MATLAB Package for Partition of Unity Based Signal Interpolation and Approximation on Graphs
The package contains several MATLAB functions for the generation of a partition of unity on graphs and an implementation of a kernel-based interpolation scheme based on a Partition of Unity Method (PUM).
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The routines GBF_Jcenters_greedy.m, GBF_domainaugment.m and GBF_genPUM.m are used to generate a partition of unity on the underlying graph
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The routines GBF_genGBF.m and GBF_RLSGBF.m contain the code for the solution of the local interpolation problems. The function GBF_RLSGBFPUM.m calculates the global GBFPUM interpolant or approxiamant of a graph signal.
A simple example for the usage of the routines is provided in the script example.m. It demonstrates how a partition of unity is generated on the Minnesota graph and how this partition of unity can be used to merge local GBF approximants to a global interpolation signal.
If you are using this code, please cite the following articles:
- [1] Cavoretto, R., De Rossi, A., Erb, W.
Partition of Unity Methods for Signal Processing on Graphs
J. Fourier Anal. Appl. 27 (2021), Art. 66
The theory on graph basis functions (GBFs) for kernel-based interpolation of graph signals can be found in
- [2] Erb, W.
Graph Signal Interpolation with Positive Definite Graph Basis Functions
Appl. Comput. Harmon. Anal. 60 (2022), 368-395
Copyright (C) 2022 R. Cavoretto, A. De Rossi, W Erb
GBFPUM is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.