awsbi {aws}R Documentation

Two-dimensional Adaptive Weights Smoothing

Description

Performes two dimensional Adaptive Weigths Smoothing (depreciated version, use aws instead)

Usage

awsbi(y, lambda=3, gamma=1.3, eta =4, s2hat = NULL, kstar = length(radii),
             rmax=max(radii), radii = c((1:8)/2,4.4,5.,(6:10),(6:10)*2), 
             graph = FALSE, u0 = NULL, control="dyadic", demomode=FALSE, 
             colors=gray((0:255)/255))

Arguments

y matrix 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
radii radii of circular neighbourhoods used
rmax maximal radius of neighborhood to be used, may change kstar
graph logical, if TRUE progress (for each iteration) is illustrated grahically, if FALSE the program runs until the final estimate is obtained (much faster !!!)
u0 allows for submission of "true" values for illustration and test purposes; only if graph=TRUE, MSE and MAE are reported for each iteration step
control the control step is performed in either a dyadic sceme ("dyadic") or using all previous estimates (otherwise)
demomode if TRUE the function will wait for user input after each iteration; only if graph=TRUE
colors color sceme to be used for images

Value

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)
nu maximal number of design points in neighborhood used
args main arguments supplied to awsbi

Note

The function assumes that the data are given on a 2D-grid corresponding to the dimensionality of y. This function is superseded by function aws and will be removed in the next mayor version of the package.

Author(s)

Joerg Polzehl polzehl@wias-berlin.de

References

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, awsuni,awstri

Examples

xy<-rbind(rep(0:255,256),rep(0:255,rep(256,256)))
indw<-c(1:12,29:48,73:100,133:168,209:256)
w0<-matrix(rep(0,256*256),ncol=256)
w0[indw,]<-1
w0[,indw]<-!w0[,indw]
w0<-w0-.5
w0[((xy[1,]-129)^2+(xy[2,]-129)^2)<=10000&((xy[1,]-129)^2+(xy[2,]-129)^2)>=4900]<- 0
w0[abs(xy[1,]-xy[2,])<=20&((xy[1,]-129)^2+(xy[2,]-129)^2)<4900]<- 0
w0[((xy[1,]-225)^2+2*(xy[2,]-30)^2)-(xy[1,]-225)*(xy[2,]-30)<=625]<- 0
w0[((xy[1,]-225)^2+2*(xy[2,]-30)^2)-(xy[1,]-225)*(xy[2,]-30)<=625&xy[2,]>27&xy[2,]<31]<- -.5
w0[((xy[1,]-225)^2+2*(xy[2,]-30)^2)-(xy[1,]-225)*(xy[2,]-30)<=625&xy[1,]>223&xy[1,]<227]<- .5
w0[((xy[2,]-225)^2+2*(xy[1,]-30)^2)+(xy[2,]-225)*(xy[1,]-30)<=625]<- 0
w0[((xy[2,]-225)^2+2*(xy[1,]-30)^2)+(xy[2,]-225)*(xy[1,]-30)<=625&xy[1,]>27&xy[1,]<31]<- -.5
w0[((xy[2,]-225)^2+2*(xy[1,]-30)^2)+(xy[2,]-225)*(xy[1,]-30)<=625&xy[2,]>223&xy[2,]<227]<- .5
w0[((xy[2,]-225)^2+(xy[1,]-225)^2)+1*(xy[2,]-225)*(xy[1,]-225)<=400]<- 0
w0[((xy[2,]-30)^2+(xy[1,]-30)^2)<=256]<-0
sigma<-.25
y<-w0+rnorm(w0,0,sigma)
#  increase rmax for better results
yhat<-awsbi(y,rmax=3)
par(mfrow=c(1,3))
image(y,col=gray((0:255)/255))
title("Noisy image")
image(yhat$yhat,zlim=range(y),col=gray((0:255)/255))
title("AWS reconstruction")
image(w0,zlim=range(y),col=gray((0:255)/255))
title("Original image")
rm(y,w0,yhat,xy)

[Package aws version 1.3-0 Index]