Image Denoising with Kernels Based on Natural Image Relations
Valero Laparra, Juan Gutiérrez, Gustavo Camps-Valls, Jesús Malo.
Year: 2010, Volume: 11, Issue: 29, Pages: 873−903
Abstract
A successful class of image denoising methods is based on Bayesian approaches working in
wavelet representations. The performance of these methods improves when relations among the local frequency coefficients are explicitly included. However, in these techniques, 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. In the proposed scheme,
training considers minimizing the Kullback-Leibler divergence (KLD) between the estimated
and actual probability functions (or histograms) of signal and noise in order
to enforce similarity up to the higher (computationally estimable) order.
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.