gsmoothing {GSD}

Smoothing a Graph Signal

Description

This function denoises a graph signal.

Usage

gsmoothing(ad_mat, signal)

Arguments

ad_mat

an weighted adjacency matrix.

signal

a graph signal.

Details

This function denoises a graph signal utilizing the graph Fourier transform and empirical Bayes thresholding.

Value

a denoised signal.

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

Johnstone, I. and Silverman, B.~W. (2004). Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. The Annals of Statistics, 32, 594–1649. doi:10.1214/009053604000000030

See Also

gextrema, ginterpolating, 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) 

# smoothing upper, lower and mean envelope
suenvelope <- gsmoothing(A, uenvelope)
slenvelope <- gsmoothing(A, lenvelope) 

smenvelope <- (suenvelope + slenvelope) / 2

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

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