efg’s R Notes: waveslim: dwt.2d

dwt.2d

Perform a separable two-dimensional discrete wavelet transform (DWT) on a matrix of dyadic dimensions (powers of 2).

Xbox image

data(xbox)
xbox.dwt <- dwt.2d(xbox, "haar", 3)
par(mfrow=c(1,1), pty="s")
plot.dwt.2d(xbox.dwt)

par(mfrow=c(2,2), pty="s")
image(1:dim(xbox)[1], 1:dim(xbox)[2], xbox, xlab="", ylab="",
      main="Original Image")
image(1:dim(xbox)[1], 1:dim(xbox)[2], idwt.2d(xbox.dwt), xlab="", ylab="",
      main="Wavelet Reconstruction")
image(1:dim(xbox)[1], 1:dim(xbox)[2], xbox - idwt.2d(xbox.dwt),
      xlab="", ylab="", main="Difference")

Ingrid Daubechies image

The Daubechies wavelets are based on the work of Ingrid Daubechies.

data(dau)
dim(dau)

## [1] 256 256

hist(dau)

par(mfrow=c(1,1), pty="s")
image(dau, col=rainbow(128))

sum(dau^2)

## [1] 1049732962

dau.dwt <- dwt.2d(dau, "d4", 3)
plot.dwt.2d(dau.dwt)

sum(plot.dwt.2d(dau.dwt, plot=FALSE)^2)

## [1] 1049732962

Explanation of above image: How to apply DWT (Discrete Wavelet Transform) to Image?

References

Stephane Mallat. A Wavelet Tour of Signal Processing. Academic Press, 2008.
Martin Vetterli and Jelena Kovacevic. Wavelets and Subband Coding, Prentice Hall 1995.
Ramazan Gen?ay, Faruk Sel?uk, and Brandon Whitcher. An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press, 2001.

packageVersion("waveslim")

## [1] '1.7.5'

efg
2015-01-28 2141