# Smoothing a Graph Signal This function denoises a graph signal. ```r 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. ## Returns 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. tools:::Rd_expr_doi("https://doi.org/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. tools:::Rd_expr_doi("https://doi.org/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. tools:::Rd_expr_doi("https://doi.org/10.1214/009053604000000030") ## See Also `gextrema`, `ginterpolating`, `sgemd`. ## Examples ```r #### 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) ```

gsmoothing function