tight_frame {gasper} | R Documentation |
Tight-Frame Computation
Description
Constructs a tight-frame wavelet on graphs
Usage
tight_frame(
evalues,
evectors,
b = 2,
filter_func = zetav,
filter_params = list()
)
Arguments
evalues |
Numeric vector containing the eigenvalues of the Laplacian matrix. |
evectors |
Matrix of the corresponding eigenvectors of the Laplacian matrix. |
b |
Numeric scalar. Parameter that controls the number of scales in the wavelet decomposition. |
filter_func |
Function used to compute the filter values. By default, it uses the |
filter_params |
List of additional parameters required by filter_func. Default is an empty list. |
Value
Matrix of the tight-frame wavelet coefficients.
Note
tight_frame
can be adapted for other filters by passing a different filter function to the filter_func
parameter.
The computation of using
and
applies primarily to the default
zetav
filter. It can be overridden by providing it in the filter_params
list for other filters.
References
Coulhon, T., Kerkyacharian, G., & Petrushev, P. (2012). Heat kernel generated frames in the setting of Dirichlet spaces. Journal of Fourier Analysis and Applications, 18(5), 995-1066.
Göbel, F., Blanchard, G., von Luxburg, U. (2018). Construction of tight frames on graphs and application to denoising. In Handbook of Big Data Analytics (pp. 503-522). Springer, Cham.
Leonardi, N., & Van De Ville, D. (2013). Tight wavelet frames on multislice graphs. IEEE Transactions on Signal Processing, 61(13), 3357-3367.
de Loynes, B., Navarro, F., Olivier, B. (2021). Data-driven thresholding in denoising with Spectral Graph Wavelet Transform. Journal of Computational and Applied Mathematics, Vol. 389.
Examples
## Not run:
# Extract the adjacency matrix from the grid1 and compute the Laplacian
L <- laplacian_mat(grid1$sA)
# Compute the spectral decomposition of L
decomp <- eigensort(L)
# Generate the tight frame coefficients using the tight_frame function
tf <- tight_frame(decomp$evalues, decomp$evectors)
## End(Not run)