Empirical Bayes approach to improve wavelet thresholding for image noise reduction

Wavelet threshold algorithms replace small magnitude wavelet coefficients with zero and keep or shrink the other coefficients. This is basically a local procedure, because wavelet coefficients characterize the local regularity of a function. Although a wavelet transform has decorrelating properties, structures in images, like edges, are never decorrelated completely, and these structures appear in the wavelet coefficients: a classification based on a local criterion-like coefficient magnitude is not the perfect method to distinguish important, uncorrupted coefficients from coefficients dominated by noise. We therefore introduce a geometrical prior model for configurations of important wavelet coefficients and combine this with local characterization of a classical threshold procedure into a Bayesian framework. The local characterization is incorporated into the conditional model, whereas the prior model describes only configurations, not coefficient values. More precisely, local characterization favors configurations with clusters of important coefficients. In this way, we can compute, for each coefficient, the posterior probability of being "sufficiently clean." This article proposes and motivates the particular and original choice of the conditional model. Instead of introducing this Bayesian framework, we could also apply heuristic image processing techniques to find clustered configurations of large coefficients. This article also explains the benefits of the Bayesian approach compared to these simple techniques. The parameter of the prior model is estimated on an empirical basis using a pseudolikelihood criterion.