WSwavelet: Bayesian Wavelet Denoising with Wendland-Semicircle Slab Mixture

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.

Installation

Install the dependency first:

install.packages("wavethresh")

Then install the package archive:

install.packages("WSwavelet_0.1.0.tar.gz", repos = NULL, type = "source")

Minimal example

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_summary

The 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.

Citation

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