analysis: Compute the Analysis Operator for a Graph Signal

In gasper: Graph Signal Processing

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)

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

Value

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

See Also

synthesis, tight_frame

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)

## End(Not run)

gasper documentation built on May 29, 2024, 8:32 a.m.