WSwavelet-package.RdBayesian wavelet denoising with a resolution-adaptive spike-and-slab prior. The continuous slab is a mixture of a compactly supported Wendland-type density and the semicircle density. The package provides Gaussian and Laplace working-likelihood versions, empirical-Bayes fitting of resolution-specific slab weights, robust noise-scale estimation, posterior-mean coefficient shrinkage, inverse-DWT reconstruction, and diagnostic tools.
The primary user-facing function is
wswavelet. It requires a finite numeric
vector whose length is a dyadic integer, such as 128 or 1024. The function
applies an orthogonal discrete wavelet transform using
wavethresh, retains the scaling coefficients, shrinks detail
coefficients, and reconstructs the denoised signal.
The prior for a detail coefficient at level \(j\) is $$ \theta_{j,k} \sim \pi_j\delta_0 + (1-\pi_j)\{\omega_j g_W(\theta;\beta_j) +(1-\omega_j)g_S(\theta;\beta_j)\}. $$ Here \(\pi_j\) is the spike probability, \(\omega_j\) is the conditional Wendland weight among nonzero coefficients, and \(\beta_j\) is the common support scale.
See wswavelet for the empirical-Bayes
fitting details and level_posterior for the coefficient-level
posterior calculation.
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>