ginterpolating {GSD}

Interpolation of a Graph Signal

Description

This function interpolates a graph signal utilizing the Laplacian matrix.

Usage

ginterpolating(ad_mat, signal, vertices)

Arguments

ad_mat

an weighted adjacency matrix.

signal

a graph signal.

vertices

specifies vertices for the observed signal. A signal on vertices and Laplacian matrix is used for interpolating a signal outside vertices.

Details

This function interpolates a graph signal utilizing the Laplacian matrix.

Value

a signal with interpolated points.

References

Ortega, A., Frossard, P., Kovačević, J., Moura, J. M. F., and Vandergheynst, P. (2018). Graph signal processing: overview, challenges, and applications. Proceedings of the IEEE 106, 808–828. doi:10.1109/JPROC.2018.2820126

Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., and Vandergheynst, P. (2013). The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Processing Magazine, 30(3), 83–98. doi:10.1109/MSP.2012.2235192

Tremblay, N., Borgnat, P., and Flandrin, P. (2014). Graph empirical mode decomposition. 22nd European Signal Processing Conference (EUSIPCO), 2350–2354.

Zeng, J., Cheung, G., and Ortega, A. (2017). Bipartite approximation for graph wavelet signal decomposition. IEEE Transactions on Signal Processing, 65(20), 5466–5480. doi:10.1109/TSP.2017.2733489

See Also

gextrema, gsmoothing, sgemd.

Examples

#### example : composite of two components having different frequencies

## define vertex coordinate
x <- y <- seq(0, 1, length=30)
xy <- expand.grid(x=x, y=y)

## weighted adjacency matrix by Gaussian kernel 
## for connecting vertices within distance 0.04
A <- adjmatrix(xy, method = "dist", 0.04) 

## signal
# high-frequency component
signal1 <- rep(sin(12.5*pi*x - 1.25*pi), 30)

# low-frequency component
signal2 <- rep(sin(5*pi*x - 0.5*pi), 30)

# composite signal
signal0 <- signal1 + signal2

# noisy signal with SNR(signal-to-noise ratio)=5
signal <- signal0 + rnorm(900, 0, sqrt(var(signal0) / 5)) 

# graph with signal
gsig <- gsignal(vertex = cbind(xy, signal), edge = A, edgetype = "matrix")

# local extrema using graph object
extremaout <- gextrema(as_adjacency_matrix(gsig, attr="weight"), V(gsig)$z)
maxima <- extremaout$maxima_list; minima <- extremaout$minima_list

# Interpolation of upper, lower and mean envelope
uenvelope <- ginterpolating(as_adjacency_matrix(gsig, attr="weight"), 
    V(gsig)$z, maxima)
lenvelope <- ginterpolating(as_adjacency_matrix(gsig, attr="weight"), 
    V(gsig)$z, minima) 
menvelope <- (uenvelope + lenvelope) / 2

# display a graph signal
gplot(gsig, size=3, legend=FALSE) 

# display mean envelope
gplot(gsig, menvelope, size=3, legend=FALSE)