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Nonlinear extraction of independent components of natural images using radial gaussianization
Lyu, Siwei; Simoncelli, Eero P
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
PMCID:3120963
PMID: 19191599
ISSN: 0899-7667
CID: 143626
Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures
Lyu, Siwei; Simoncelli, Eero P
The local statistical properties of photographic images, when represented in a multi-scale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSMs). Specifically, we model multi-scale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible, and that samples drawn from a FoGSM model have marginal and joint statistics similar to subband coefficients of photographic images. We develop an algorithm for removing additive Gaussian white noise based on the FoGSM model, and demonstrate denoising performance comparable with state-of-the-art methods
PMCID:3718887
PMID: 19229084
ISSN: 0162-8828
CID: 143628
Multiscale Denoising of Photographic Images
Chapter by: Rajashekar, Umesh; Simoncelli, Eero P
in: The essential guide to image processing by Bovik, Alan C. [Eds]
London ; Boston : Academic Press, 2009
pp. 241-261
ISBN: 9780123744579
CID: 370642
Optimal estimation in sensory systems
Chapter by: Simoncelli, Eero P
in: The cognitive neurosciences by Gazzaniga, Michael S [Eds]
Cambridge, Mass. : MIT Press, 2009
pp. 525-538
ISBN: 026201341x
CID: 1721982
Quantifying color image distortions based on adaptive spatio-chromatic signal decompositions
Chapter by: Rajashekar, U.; Zhou Wang; Simoncelli, E.P.
in: Proceedings of the 2009 16th IEEE International Conference on Image Processing (ICIP 2009) by
Piscataway, N.J. : IEEE, 2009
pp. 2213-16
ISBN: 978-1-4244-5653-6
CID: 371632
Sound texture synthesis via filter statistics
Chapter by: McDermott, J.H.; Oxenham, A.J.; Simoncelli, E.P.
in: 2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA) by
[Piscataway, N.J.] : IEEE, 2009
pp. 297-300
ISBN: 978-1-4244-3678-1
CID: 371662
Capturing Visual Image Properties with Probabilistic Models
Chapter by: Simoncelli, Eero P
in: The essential guide to image processing by Bovik, Alan C. [Eds]
London ; Boston : Academic Press, 2009
pp. 205-223
ISBN: 9780123744579
CID: 370632
Image modeling and denoising with orientation-adapted Gaussian scale mixtures
Hammond, David K; Simoncelli, Eero P
We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multiscale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated according to the values of two hidden random variables, thus allowing the model to adapt to the local amplitude and orientation of the signal. A third hidden variable selects between this oriented process and a nonoriented scale mixture of Gaussians process, thus providing adaptability to the local orientedness of the signal. Based on this model, we develop an optimal Bayesian least squares estimator for denoising images and show through simulations that the resulting method exhibits significant improvement over previously published results obtained with Gaussian scale mixtures
PMCID:4144921
PMID: 18972652
ISSN: 1057-7149
CID: 143623
Maximum differentiation (MAD) competition: a methodology for comparing computational models of perceptual quantities
Wang, Zhou; Simoncelli, Eero P
We propose an efficient methodology for comparing computational models of a perceptually discriminable quantity. Rather than comparing model responses to subjective responses on a set of pre-selected stimuli, the stimuli are computer-synthesized so as to optimally distinguish the models. Specifically, given two computational models that take a stimulus as an input and predict a perceptually discriminable quantity, we first synthesize a pair of stimuli that maximize/minimize the response of one model while holding the other fixed. We then repeat this procedure, but with the roles of the two models reversed. Subjective testing on pairs of such synthesized stimuli provides a strong indication of the relative strengths and weaknesses of the two models. Specifically, the model whose extremal stimulus pairs are easier for subjects to discriminate is the better model. Moreover, careful study of the synthesized stimuli may suggest potential ways to improve a model or to combine aspects of multiple models. We demonstrate the methodology for two example perceptual quantities: contrast and image quality
PMCID:4143340
PMID: 18831621
ISSN: 1534-7362
CID: 143621
Spatio-temporal correlations and visual signalling in a complete neuronal population
Pillow, Jonathan W; Shlens, Jonathon; Paninski, Liam; Sher, Alexander; Litke, Alan M; Chichilnisky, E J; Simoncelli, Eero P
Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons
PMCID:2684455
PMID: 18650810
ISSN: 1476-4687
CID: 143618