est_riskshrink_thresh: Estimate the RiskShrink Hard Thresholding Level

In SynchWave: Synchrosqueezed Wavelet Transform

Estimate the RiskShrink Hard Thresholding Level

Description

This function estimates the RiskShrink hard thresholding level.

This code is translated from MATLAB Synchrosqueezing Toolbox, version 1.1 developed by Eugene Brevdo (http://www.math.princeton.edu/~ebrevdo/).

Usage

est_riskshrink_thresh(Wx, nv)

Arguments

Wx	wavelet transform of a signal, see cwt_fw
nv	number of voices

Details

This function implements Defn. 1 of Sec. 2.4 in [1], using the suggested noise estimator from the discussion "Estimating the noise level" in that same section.

Value

the RiskShrink hard threshold estimate

References

[1] Donoho, D. L. and Johnstone, I. M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425–455.

See Also

cwt_fw, cwt_iw.

Examples

tt <- seq(0, 10, , 1024)
nv <- 32
f0 <- (1+0.6*cos(2*tt))*cos(4*pi*tt+1.2*tt^2)
sigma <- 0.5
f <- f0 + sigma*rnorm(length(tt))

# Continuous wavelet transform
opt <- list(type = "bump")
cwtfit <- cwt_fw(f, opt$type, nv, tt[2]-tt[1], opt)

# Hard thresholing
thresh <- est_riskshrink_thresh(cwtfit$Wx, nv)
cwtfit$Wx[which(abs(cwtfit$Wx) < thresh)] <- 0.0

SynchWave documentation built on May 7, 2022, 5:05 p.m.