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Contextually adaptive signal representation using conditional principal component analysis
Chapter by: Figueras i Ventura, R.M.; Rajashekar, U.; Zhou Wang; Simoncelli, Eero P
in: ICASSP 2008. IEEE International Conference on Acoustic, Speech and Signal Processes by
Piscataway, NJ IEEE Service Center, 2008
pp. 877-880
ISBN: 978-1-4244-1483-3
CID: 371672
Image denoising using mixtures of Gaussian scale mixtures
Chapter by: Guerrero-Colon, J.A.; Simoncelli, Eero P; Portilla, J
in: 2008 15th IEEE International Conference on Image Processing - ICIP 2008 by
Piscataway NJ : IEEE, 2008
pp. 565-568
ISBN: 978-1-4244-1765-0
CID: 377112
Nonlinear extraction of 'Independent Components' of elliptically symmetric densities using radial Gaussianization
Lyu, Siwei; Simoncelli, Eero P
[s.l.] : Courant Institute, 2008
Extent: 34 p.
ISBN: n/a
CID: 379362
Nonlinear Image Representation Using Divisive Normalization
Lyu, Siwei; Simoncelli, Eero P
In this paper, we describe a nonlinear image representation based on divisive normalization that is designed to match the statistical properties of photographic images, as well as the perceptual sensitivity of biological visual systems. We decompose an image using a multi-scale oriented representation, and use Student's t as a model of the dependencies within local clusters of coefficients. We then show that normalization of each coefficient by the square root of a linear combination of the amplitudes of the coefficients in the cluster reduces statistical dependencies. We further show that the resulting divisive normalization transform is invertible and provide an efficient iterative inversion algorithm. Finally, we probe the statistical and perceptual advantages of this image representation by examining its robustness to added noise, and using it to enhance image contrast.
PMCID:4207373
PMID: 25346590
ISSN: 1063-6919
CID: 1931322
Reducing statistical dependencies in natural signals using radial Gaussianization
Lyu, Siwei; Simoncelli, Eero P
We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but elliptically symmetric. Such a source cannot be decomposed into independent components using a linear transform, but we show that a simple nonlinear transformation, which we call radial Gaussianization (RG), is able to remove all dependencies. We apply this methodology to natural signals, demonstrating that the joint distributions of nearby bandpass filter responses, for both sounds and images, are closer to being elliptically symmetric than linearly transformed factorial sources. Consistent with this, we demonstrate that the reduction in dependency achieved by applying RG to either pairs or blocks of bandpass filter responses is significantly greater than that achieved by PCA or ICA.
PMCID:4199336
PMID: 25328365
ISSN: 1049-5258
CID: 1931312
Learning to be Bayesian without supervision
Chapter by: Raphan, Martin; Simoncelli, Eero P.
in: Advances in Neural Information Processing Systems by
[S.l.] : Neural information processing systems foundation, 2007
pp. 1145-1152
ISBN: 9780262195683
CID: 2873002
Statistical modeling of images with fields of Gaussian scale mixtures
Chapter by: Lyu, Siwei; Simoncelli, Eero P.
in: Advances in Neural Information Processing Systems by
[S.l.] : Neural information processing systems foundation, 2007
pp. 945-952
ISBN: 9780262195683
CID: 2873012
Statistically and perceptually motivated nonlinear image representation
Siwei Lyu; Simoncelli, E.P.
INSPEC:10070575
ISSN: 0277-786x
CID: 367542
Empirical Bayes Least Squares Estimation without an Explicit Prior
Raphan, Martin; Simoncelli, Eero P
[s.l.] : Courant Institute, 2007
Extent: 17 p.
ISBN: n/a
CID: 379352
Statistically driven sparse image approximation
Chapter by: Figueras i Ventura, R.M.; Simoncelli, Eero P
in: Proceedings 2007 IEEE International Conference on Image Processing, ICIP 2007 by
Piscataway, NJ IEEE Service Center, 2007
pp. 461-464
ISBN: 978-1-4244-1436-9
CID: 371682