A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Adaptive thresholding of wavelet coefficients
Computational Statistics & Data Analysis
Empirical Bayes approach to block wavelet function estimation
Computational Statistics & Data Analysis
Advanced lectures on machine learning
Nonparametric identification of population models via Gaussian processes
Automatica (Journal of IFAC)
Bayes and empirical Bayes semi-blind deconvolution using eigenfunctions of a prior covariance
Automatica (Journal of IFAC)
Wavelet representations of stochastic processes and multiresolutionstochastic models
IEEE Transactions on Signal Processing
Brief Regularization networks for inverse problems: A state-space approach
Automatica (Journal of IFAC)
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
Modeling and estimation of multiresolution stochastic processes
IEEE Transactions on Information Theory - Part 2
Correlation structure of the discrete wavelet coefficients of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
Regularization networks: fast weight calculation via Kalman filtering
IEEE Transactions on Neural Networks
Hi-index | 22.14 |
Many wavelet-based algorithms have been proposed in recent years to solve the problem of function estimation from noisy samples. In particular it has been shown that threshold approaches lead to asymptotically optimal estimation and are extremely effective when dealing with real data. Working under a Bayesian perspective, in this paper we first study optimality of the hard and soft thresholding rules when the function is modelled as a stochastic process with known covariance function. Next, we consider the case where the covariance function is unknown, and propose a novel approach that models the covariance as a certain wavelet combination estimated from data by Bayesian model selection. Simulated data are used to show that the new method outperforms traditional threshold approaches as well as other wavelet-based Bayesian techniques proposed in the literature.