fields (version 1.3-1)

Wtransform.image: Quadratic W wavelet transform for an image

Description

Finds the forward or inverse discrete wavelet transform using the quadratic W basis.

Usage

Wtransform.image(x, inv=FALSE, transpose=FALSE, cut.min=8)

Value

A matrix the same size as x.

References

Nychka,D. Wikle,C. , Royle, J.A. (1999) Large spatial prediction problems and nonstationary random fields

Details

The wavelet transform can be thought as matrix multiplication A %*% vec(x) where vec(x) is the matrix x stacked by columns. The inverse transform is inv(A) %*% vec(x) and transpose is t(A) %*% vec( x)

See Also

plot.coef, WQS, WQSi, Wtransform.D

Examples

# Wtransform of John Lennon image
data(lennon)
look<- Wtransform.image( lennon)
# 
### take a look: 
# image.plot( look)
#threshhold 
thr<-  quantile( abs( look), .95)
temp<- look
temp[abs(look)< thr] <- 0
look2<- Wtransform.image( temp, inv=TRUE)
# 
### take a look: 
# image( look2) # 95 \% compressed image

 
# a diagonal detail basis function 
temp<- matrix(0, nrow=32, ncol=32) 
temp[12,12]<- 1 
look<- Wtransform.image( temp , inv=TRUE)
persp( look) 
image( look)
title("diagonal detail W-wavlet")