gasper (version 1.1.6)

analysis: Compute the Analysis Operator for a Graph Signal

Description

analysis computes the transform coefficients of a given graph signal using the provided frame coefficients.

Usage

analysis(y, tf)

Value

coef Numeric vector or matrix of transform coefficients of the graph signal.

Arguments

y

Numeric vector or matrix representing the graph signal to analyze.

tf

Numeric matrix of frame coefficients.

Details

The analysis operator uses the frame coefficients to transform a given graph signal into its representation in the transform domain. It is defined by the linear map \(T_{\mathfrak F} : \mathbb R^V \rightarrow \mathbb R^I\). Given a function \(f \in \mathbb R^V\), the analysis operation is defined as: $$T_{\mathfrak F}f=(\langle f,r_i \rangle)_{i \in I}$$ where \(r_i\) are the frame vectors.

The transform is computed as: $$coef = tf . y$$

See Also

synthesis, tight_frame

Examples

if (FALSE) {
# 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)
}