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WSwavelet implements resolution-adaptive Bayesian wavelet denoising with a spike-and-slab prior. The continuous slab is a mixture of a compactly supported Wendland-type density and the semicircle density. The package supports Gaussian errors as the primary likelihood and a Laplace working-likelihood sensitivity option.
The main function is wswavelet(). It performs an orthogonal discrete wavelet transform, estimates the noise scale robustly, constructs resolution-specific support scales and spike probabilities, fits the Wendland mixture weight by empirical Bayes, shrinks detail coefficients by posterior means, and reconstructs the signal.
Install the dependency first:
install.packages("wavethresh")Then install the package archive:
install.packages("WSwavelet_0.1.0.tar.gz", repos = NULL, type = "source")library(WSwavelet)
set.seed(1)
n <- 128
x <- seq(0, 1, length.out = n)
y <- sin(6 * pi * x) + rnorm(n, sd = 0.5)
fit <- wswavelet(
y,
likelihood = "gaussian",
filter.number = 6L,
quadrature_n = 24L
)
fit$estimate
fit$level_summaryThe input length must be a finite dyadic integer, such as 64, 128, or 256. The scaling coefficients are retained, and the detail coefficients are replaced by their posterior-mean estimates.
Sanyal, N. (2026). Resolution-Adaptive Compact-Support Priors for Bayesian Wavelet Denoising: A Wendland-Semicircle Slab Mixture for Low-SNR Signal Recovery. Axioms, 15(9), 678. DOI:10.3390/axioms15090678
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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