haarfisz (version 4.5.4)

hf.bt: hf.bt

Description

Denoises a Gaussian contaminated vector using a version of the wavelet-based ``greedy tree" algorithm by Baraniuk, see references. 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.bt(x, filter.number = 1, family = "DaubExPhase", min.level = 3, noise.level = NULL)

Value

Denoised version of x.

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 NULL; in the latter case it will be estimated using MAD.

Author

Piotr Fryzlewicz

References

Baraniuk, R. G. (1999) Optimal tree approximation with wavelets. Pages 206-214 of Unser, M.A., Aldroubi, A. and Laine, A.F. (eds), Wavelet Applications in Signal and Image Processing VII, Proceedings of SPIE 3813. SPIE. tools:::Rd_expr_doi("10.1117/12.366780")

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

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.bt(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)