awsbi {aws} | R Documentation |
Performes two dimensional Adaptive Weigths Smoothing (depreciated version, use aws instead)
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))
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 |
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 |
The function assumes that the data are given on a 2D-grid corresponding to the dimensionality of y. This function is superseded by function aws and will be removed in the next mayor version of the package.
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(0:255,256),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)