A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
High-order contrasts for independent component analysis
Neural Computation
The multiinformation function as a tool for measuring stachastic dependence
Learning in graphical models
Kernel PCA and de-noising in feature spaces
Proceedings of the 1998 conference on Advances in neural information processing systems II
A statistic for testing the null hypothesis of elliptical symmetry
Journal of Multivariate Analysis
Universal Analytical Forms for Modeling Image Probabilities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dependence, correlation and Gaussianity in independent component analysis
The Journal of Machine Learning Research
Energy-based models for sparse overcomplete representations
The Journal of Machine Learning Research
ICA using spacings estimates of entropy
The Journal of Machine Learning Research
Topographic Independent Component Analysis
Neural Computation
Learning Overcomplete Representations
Neural Computation
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Towards a theory of early visual processing
Neural Computation
Modeling Multiscale Subbands of Photographic Images with Fields of Gaussian Scale Mixtures
IEEE Transactions on Pattern Analysis and Machine Intelligence
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
IEEE Transactions on Signal Processing
Image compression via joint statistical characterization in the wavelet domain
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Nonlinear image representation for efficient perceptual coding
IEEE Transactions on Image Processing
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
PCA Gaussianization for image processing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Lp-Nested Symmetric Distributions
The Journal of Machine Learning Research
Complex-valued independent component analysis of natural images
ICANN'11 Proceedings of the 21st international conference on Artificial neural networks - Volume Part II
Cross-talk induces bifurcations in nonlinear models of synaptic plasticity
Neural Computation
What is the limit of redundancy reduction with divisive normalization?
Neural Computation
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We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent. A widely studied linear solution, known as independent component analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent nongaussian sources. Here, we examine a complementary case, in which the source is nongaussian and elliptically symmetric. In this case, no invertible linear transform suffices to decompose the signal into independent components, but we show that a simple nonlinear transformation, which we call radial gaussianization (RG), is able to remove all dependencies. We then examine this methodology in the context of natural image statistics. We first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ICA. Finally, we show that the RG transformation may be closely approximated by divisive normalization, which has been used to model the nonlinear response properties of visual neurons.