synthesis {gasper} | R Documentation |
Compute the Synthesis Operator for Transform Coefficients
Description
synthesis
computes the graph signal synthesis from its transform coefficients using the provided frame coefficients.
Usage
synthesis(coeff, tf)
Arguments
coeff |
Numeric vector/matrix. Transformed coefficients of the graph signal. |
tf |
Numeric matrix. Frame coefficients. |
Details
The synthesis
operator uses the frame coefficients to retrieve the graph signal from its representation in the transform domain. It is the adjoint of the analysis operator and is defined by the linear map
. For a vector of coefficients
, the synthesis operation is defined as:
The synthesis is computed as:
Value
y
Numeric vector/matrix. Synthesized graph signal.
See Also
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)
# Create a random graph signal.
f <- rnorm(nrow(L))
# Compute the transform coefficients using the analysis operator
coef <- analysis(f, tf)
# Retrieve the graph signal using the synthesis operator
f_rec <- synthesis(coef, tf)
## End(Not run)
[Package gasper version 1.1.6 Index]