tight_frame: Tight-Frame Computation

In gasper: Graph Signal Processing

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 zetav function but other frame filters can be passed.
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 k_{\text{max}} using \lambda_{\text{max}} and b 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)

gasper documentation built on Oct. 27, 2023, 1:07 a.m.