A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical performance of block thresholded wavelet estimators
Statistics and Computing
Empirical Bayes approach to block wavelet function estimation
Computational Statistics & Data Analysis
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
IEEE Transactions on Signal Processing
The discrete multiple wavelet transform and thresholding methods
IEEE Transactions on Signal Processing
Wavelet-based statistical signal processing using hidden Markovmodels
IEEE Transactions on Signal Processing
Wavelet analysis and synthesis of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
IEEE Transactions on Image Processing
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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.