awstri {aws} | R Documentation |
Performes three-dimensional Adaptive Weigths Smoothing (depreciated version, use aws instead)
awstri(y, lambda=3, gamma=1.3, eta =4, s2hat = NULL, kstar = length(radii), rmax=max(radii), weight = c(1,1,1), radii = c((1:4)/2,2.3,(5:12)/2,7:9,10.5,12,13.5), control="dyadic"
y |
array of observed values |
lambda |
main smoothing parameter (should be approximately 3) |
gamma |
allow for increase of variances during iteration by factor gamma
(!!gamma >=1 ) |
eta |
main control parameter (should be approximately 4) |
s2hat |
initial variance estimate (if available, can be either a number (homogeneous case), a matrix of same dimension as y (inhomogeneous variance) or NULL (a homogeneous variance estimate will be generated in this case) |
kstar |
maximal number of iterations to perform, actual number may be smaller depending on parameters radii and rmax |
weight |
weights used for distances, determining elliptical neighborhoods |
radii |
radii of circular neighbourhoods used |
rmax |
maximal radius of neighborhood to be used, may change kstar |
control |
the control step is performed in either a dyadic sceme ("dyadic") or using all previous estimates (otherwise) |
A list with components
yhat |
estimates of the regression function (matrix corresponding to the y's) |
shat |
estimated standard deviations of yhat (conditional on the chosen weights) |
args |
Main arguments supplied to awstri |
The function assumes that the data are given on a 3D-grid corresponding to the dimensionality of y. This function is superseded by function aws and will be removed in the next mayor version of the package.
Joerg Polzehl polzehl@wias-berlin.de
Polzehl, J. and Spokoiny, V. (2000). Adaptive Weights Smoothing with applications to image restoration, J.R.Statist.Soc. B, 62, Part 2, pp.335-354
xy <- rbind(rep(0:30,31),rep(0:30,rep(31,31))) w3 <- array(0,c(31,31,31)) w3[4:28,4:28,4:28] <- 1 dim(w3) <- c(961,31) w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=144,16] <- 0 for(i in 1:12) { r2 <- 144-i*i w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=r2,16+c(-i,i)] <- 0 } dim(w3) <- c(31,31,31) w3[10:22,10:22,10:22] <- 1 dim(w3) <- c(961,31) w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=36,16] <- 0 for(i in 1:6) { r2 <- 36-i*i w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=r2,16+c(-i,i)] <- 0 } dim(w3) <- c(31,31,31) sigma <- .4 y <- w3+rnorm(w3,0,sigma) # increase rmax for better results yhat <- awstri(y,rmax=2) rm(y,yhat,w3,xy)