  A successful class of image denoising methods is based on Bayesian approaches
working in wavelet representations. However, analytical estimates can be
obtained only for particular combinations of analytical models of signal and
noise, thus precluding its straightforward extension to deal with other
arbitrary noise sources. In this paper, we propose an alternative non-explicit
way to take into account the relations among natural image wavelet coefficients
for denoising: we use support vector regression (SVR) in the wavelet domain to
enforce these relations in the estimated signal. Since relations among the
coefficients are specific to the signal, the regularization property of SVR is
exploited to remove the noise, which does not share this feature. The specific
signal relations are encoded in an anisotropic kernel obtained from mutual
information measures computed on a representative image database. Training
considers minimizing the Kullback-Leibler divergence (KLD) between the
estimated and actual probability functions of signal and noise in order to
enforce similarity. Due to its non-parametric nature, the method can eventually
cope with different noise sources without the need of an explicit
re-formulation, as it is strictly necessary under parametric Bayesian
formalisms. Results under several noise levels and noise sources show that: (1)
the proposed method outperforms conventional wavelet methods that assume
coefficient independence, (2) it is similar to state-of-the-art methods that do
explicitly include these relations when the noise source is Gaussian, and (3)
it gives better numerical and visual performance when more complex, realistic
noise sources are considered. Therefore, the proposed machine learning approach
can be seen as a more flexible (model-free) alternative to the explicit
description of wavelet coefficient relations for image denoising.
