Wavelet Denoising Based on the MAP Estimation Using the BKF Prior With Application to Images and EEG Signals

Abstract

This paper presents a novel nonparametric Bayesian estimator for signal and image denoising in the wavelet domain. This approach uses a prior model of the wavelet coefficients designed to capture the sparseness of the wavelet expansion. A new family of Bessel K Form (BKF) densities are designed to fit the observed histograms, so as to provide a probabilistic model for the marginal densities of the wavelet coefficients. This paper first shows how the BKF prior can characterize images belonging to Besov spaces. Then, a new hyper-parameters estimator based on EM algorithm is designed to estimate the parameters of the BKF density; and, it is compared with a cumulants-based estimator. Exploiting this prior model, another novel contribution is to design a Bayesian denoiser based on the Maximum A Posteriori (MAP) estimation under the 0–1 loss function, for which we formally establish the mathematical properties and derive a closed-form expression. Finally, a comparative study on a digitized database of natural images and biomedical signals shows the effectiveness of this new Bayesian denoiser compared to other classical and Bayesian denoising approaches. Results on biomedical data illustrate the method in the temporal as well as the time-frequency domain.