5 research outputs found
Image Denoising with Kernels based on Natural Image Relations
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
Iterative Gaussianization: from ICA to Random Rotations
Most signal processing problems involve the challenging task of
multidimensional probability density function (PDF) estimation. In this work,
we propose a solution to this problem by using a family of Rotation-based
Iterative Gaussianization (RBIG) transforms. The general framework consists of
the sequential application of a univariate marginal Gaussianization transform
followed by an orthonormal transform. The proposed procedure looks for
differentiable transforms to a known PDF so that the unknown PDF can be
estimated at any point of the original domain. In particular, we aim at a zero
mean unit covariance Gaussian for convenience. RBIG is formally similar to
classical iterative Projection Pursuit (PP) algorithms. However, we show that,
unlike in PP methods, the particular class of rotations used has no special
qualitative relevance in this context, since looking for interestingness is not
a critical issue for PDF estimation. The key difference is that our approach
focuses on the univariate part (marginal Gaussianization) of the problem rather
than on the multivariate part (rotation). This difference implies that one may
select the most convenient rotation suited to each practical application. The
differentiability, invertibility and convergence of RBIG are theoretically and
experimentally analyzed. Relation to other methods, such as Radial
Gaussianization (RG), one-class support vector domain description (SVDD), and
deep neural networks (DNN) is also pointed out. The practical performance of
RBIG is successfully illustrated in a number of multidimensional problems such
as image synthesis, classification, denoising, and multi-information
estimation
Spatio-Chromatic Information available from different Neural Layers via Gaussianization
How much visual information about the retinal images can be extracted from
the different layers of the visual pathway?. Separate subsystems (e.g. opponent
channels, spatial filters, nonlinearities of the texture sensors) have been
suggested to be organized for optimal information transmission. However, the
efficiency of these different layers has not been measured when they operate
together on colorimetrically calibrated natural images and using multivariate
information-theoretic units over the joint spatio-chromatic array of responses.
In this work we present a statistical tool to address this question in an
appropriate (multivariate) way. Specifically, we propose an empirical estimate
of the information transmitted by the system based on a recent Gaussianization
technique that reduces the challenging multivariate PDF estimation problem to a
set of simpler univariate estimations. Total correlation measured using the
proposed estimator is consistent with predictions based on the analytical
Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If
the noise at certain representation is proportional to the dynamic range of the
response, and one assumes sensors of equivalent noise level, transmitted
information shows the following trends: (1) progressively deeper
representations are better in terms of the amount of information about the
input, (2) the transmitted information up to the cortical representation
follows the PDF of natural scenes over the chromatic and achromatic dimensions
of the stimulus space, (3) the contribution of spatial transforms to capture
visual information is substantially bigger than the contribution of chromatic
transforms, and (4) nonlinearities of the responses contribute substantially to
the transmitted information but less than the linear transforms
Image Denoising with Kernels Based on Natural Image Relations
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-parametri
Submitted 9/08; Published Image Denoising with Kernels Based on Natural Image Relations
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-parametri