rob.dwt(x, ..., span=5, cutoff1=2.5, cutoff2=3.75, max.resid.level=3)
dwt
. See
dwt
for details.
n.levels-1
is used.
rob.dwt
, inheriting from the class
dwt, wp
and
crystal.list
. Each element represents a wavelet crystal as a vector of
wavelet coefficients at different resolutions.
All the information for the robust wavelet transform is stored in
dictionary
.
The robust smoother-cleaner wavelet transform is a fast wavelet decomposition which is robust towards outliers. Smoother-cleaner wavelets behave like the classical discrete wavelet transform for Gaussian signals, but prevent outliers and outlier patches from leaking into the wavelet coefficients at coarse levels. The basic idea of robust smoother/cleaner wavelets is that the smooth coefficients are preprocessed with a fast and robust smoother/cleaner. The details and algorithm are given in the S+WAVELETS User's Manual, in the section "Robust Smoother-Cleaner Wavelets".
Bruce, A., Donaho, D. Gao, H., and Martin, D. (1994). "Denoising and Robust Non-Linear Wavelet Analysis," SPIE Proceedings, Wavelet Aplications, Vol 2242, pp. 325-36.
xx <- make.signal("blocks") yy <- xx + rcauchy(length(xx)) # add Cauchy noise par(mfrow=c(2,2)) plot(xx, type="l", xlab="Blocks", ylab="") plot(yy, type="l", xlab="Blocks with Cauchy Noise", ylab="") rw <- rob.dwt(yy, wavelet="d2", span=5) zz <- reconstruct(rw) plot(zz, type="l", xlab="Cleaned Noisy Blocks", ylab="") ss <- wavesmooth(zz, wavelet="d2") plot(ss, type="l", xlab="Smoothed Blocks", ylab="")