Λ-neighborhood wavelet shrinkage

We propose a wavelet-based denoising methodology based on total energy of a neighboring pair of coefficients plus their “parental” coefficient. The model is based on a Bayesian hierarchical model using a contaminated exponential prior on the total mean energy in a neighborhood of wavelet coefficients. The hyperparameters in the model are estimated by the empirical Bayes method, and the posterior mean, median and Bayes factor are obtained and used in the estimation of the total mean energy. Shrinkage of the neighboring coefficients are based on the ratio of the estimated and the observed energy. It is shown that the methodology is comparable and often superior to several existing and established wavelet denoising methods that utilize neighboring information, which is demonstrated by extensive simulations on a standard battery of test functions. An application to real-word data set from inductance plethysmography is also considered.