awstri {aws}R Documentation

Three-dimensional Adaptive Weights Smoothing


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The function assumes that the data are given on a 3D-grid corresponding to the dimensionality of y. This function is superseded by function aws and will be removed in the next mayor version of the package.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, J. and Spokoiny, V. (2000). Adaptive Weights Smoothing with applications to image restoration, J.R.Statist.Soc. B, 62, Part 2, pp.335-354

See Also

aws, awsbi,awsuni


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)

[Package aws version 1.3-0 Index]