hf.tiu {haarfisz}

hf.tiu

Description

Denoises a Gaussian contaminated vector using translation-invariant hard wavelet thresholding with the universal threshold. Note: this function does not actually do any Haar-Fisz transform, it is a homogeneous variance Gaussian denoising function, which is used by the haarfisz package.

Usage

hf.tiu(x, filter.number = 1, family = "DaubExPhase", min.level = 3, noise.level = 1) 

Arguments

x

The noisy vector, its length must be a power of 2.

filter.number

The filter number of the analysing wavelet. Can be set to 1, 2, ..., 10 for family == "DaubExPhase", or to 4, 5, ..., 10 for family == "DaubLeAsymm".

family

The family of wavelet bases from which the wavelet filter.number is chosen. Can be set to "DaubExPhase" or "DaubLeAsymm".

min.level

The minimum level thresholded.

noise.level

Standard deviation of the noise, can be set to a positive number or to an estimate (a function of x).

Details

Uses threshold, wd and AvBasis

Value

Denoised version of x.

Author(s)

Piotr Fryzlewicz

References

Fryzlewicz, P. and Nason, G.P. (2004) A Haar-Fisz algorithm for Poisson intensity estimation. Journal of Computational and Graphical Statistics, 13, 621-638. doi:10.1198/106186004X2697

See Also

threshold, wd, AvBasis

Examples

#
# Generate simple sinusoidal test signal
#
test.sig <- sin(seq(from=0, to=6*pi, length=128))
#
# Invent simulated noisy signal
#
test.dat <- test.sig + rnorm(128, sd=0.2)
#
# Denoise using hf.bt
#
test.est <- hf.tiu(test.dat)
#
# Now plot the results: the truth, the noisy signal, the estimate
#
ts.plot(test.dat)
lines(test.est, col=2)
lines(test.sig, col=3, lty=2)