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237


SPARSE DECOMPOSITION OF TRANSFORMATION-INVARIANT SIGNALS WITH CONTINUOUS BASIS PURSUIT [Meeting Abstract]

Ekanadham, Chaitanya; Tranchina, Daniel; Simoncelli, Eero P; IEEE
Consider the decomposition of a signal into features that undergo transformations drawn from a continuous family. Current methods discretely sample the transformations and apply sparse recovery methods to the resulting finite dictionary. These methods do not exploit the underlying continuous structure, thereby limiting the ability to produce sparse solutions. Instead, we employ interpolation functions which linearly approximate the manifold of scaled and transformed features. Coefficients are interpreted as interpolation weights, and we formulate a convex optimization problem for obtaining them, enforcing both reconstruction accuracy and sparsity. We compare our method, which we call continuous basis pursuit (CBP) with the standard basis pursuit approach on a sparse deconvolution task. CBP yields substantially sparser solutions without sacrificing accuracy, and does so with a smaller dictionary. We conclude that for signals generated by transformation-invariant processes, a representation that explicitly accommodates the transformation(s) can yield sparser and more interpretable decompositions.
ISI:000296062404142
ISSN: 1520-6149
CID: 1681452

Implicit encoding of prior probabilities in optimal neural populations

Chapter by: Ganguli, Deep; Simoncelli, Eero P.
in: Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010 by
[S.l.] : Neural information processing systems foundation, 2010
pp. ?-?
ISBN: 9781617823800
CID: 2873052

Implicit encoding of prior probabilities in optimal neural populations

Ganguli, Deep; Simoncelli, Eero P
Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of neurons and spikes in a population. We model the spikes of each cell as samples from an independent Poisson process with rate governed by an associated tuning curve. For this response model, we approximate the Fisher information in terms of the density and amplitude of the tuning curves, under the assumption that tuning width varies inversely with cell density. We consider a family of objective functions based on the expected value, over the sensory prior, of a functional of the Fisher information. This family includes lower bounds on mutual information and perceptual discriminability as special cases. In all cases, we find a closed form expression for the optimum, in which the density and gain of the cells in the population are power law functions of the stimulus prior. This also implies a power law relationship between the prior and perceptual discriminability. We show preliminary evidence that the theory successfully predicts the relationship between empirically measured stimulus priors, physiologically measured neural response properties (cell density, tuning widths, and firing rates), and psychophysically measured discrimination thresholds.
PMCID:4209846
PMID: 25356064
ISSN: 1049-5258
CID: 1931302

An Empirical Bayesian interpretation and generalization of NL-means

Raphan, Martin; Simoncelli, Eero P
[s.l.] : Courant Institute, 2010
Extent: 8 p.
ISBN: n/a
CID: 379372

Perceptual quality assessment of color images using adaptive signal representation

Rajashekar, U.; Zhou Wang; Simoncelli, E.P.
INSPEC:11214796
ISSN: 0277-786x
CID: 367512

Hierarchical modeling of local image features through L p-nested symmetric distributions

Chapter by: Sinz, Fabian; Simoncelli, Eero P.; Bethge, Matthias
in: Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference by
[S.l.] : Neural information processing systems foundation, 2009
pp. 1696-1704
ISBN: 9781615679119
CID: 2873032

A Bayesian model of conditioned perception

Chapter by: Stocker, Alan A.; Simoncelli, Eero P.
in: Advances in Neural Information Processing Systems 20 - Proceedings of the 2007 Conference by
[S.l.] : Neural information processing systems foundation, 2009
pp. ?-?
ISBN: 9781605603520
CID: 2873022

Hierarchical modeling of local image features through Lp-nested symmetric distributions

Sinz, F; Simoncelli, Eero P; Bethge, M
ORIGINAL:0008279
ISSN: 1049-5258
CID: 371192

Is the homunculus "aware" of sensory adaptation?

Series, Peggy; Stocker, Alan A; Simoncelli, Eero P
Neural activity and perception are both affected by sensory history. The work presented here explores the relationship between the physiological effects of adaptation and their perceptual consequences. Perception is modeled as arising from an encoder-decoder cascade, in which the encoder is defined by the probabilistic response of a population of neurons, and the decoder transforms this population activity into a perceptual estimate. Adaptation is assumed to produce changes in the encoder, and we examine the conditions under which the decoder behavior is consistent with observed perceptual effects in terms of both bias and discriminability. We show that for all decoders, discriminability is bounded from below by the inverse Fisher information. Estimation bias, on the other hand, can arise for a variety of different reasons and can range from zero to substantial. We specifically examine biases that arise when the decoder is fixed, 'unaware' of the changes in the encoding population (as opposed to 'aware' of the adaptation and changing accordingly). We simulate the effects of adaptation on two well-studied sensory attributes, motion direction and contrast, assuming a gain change description of encoder adaptation. Although we cannot uniquely constrain the source of decoder bias, we find for both motion and contrast that an 'unaware' decoder that maximizes the likelihood of the percept given by the preadaptation encoder leads to predictions that are consistent with behavioral data. This model implies that adaptation-induced biases arise as a result of temporary suboptimality of the decoder
PMCID:3134250
PMID: 19686064
ISSN: 0899-7667
CID: 143633

Visual motion aftereffects arise from a cascade of two isomorphic adaptation mechanisms

Stocker, Alan A; Simoncelli, Eero P
Prolonged exposure to a moving stimulus can substantially alter the perceived velocity (both speed and direction) of subsequently presented stimuli. Here, we show that these changes can be parsimoniously explained with a model that combines the effects of two isomorphic adaptation mechanisms, one nondirectional and one directional. Each produces a pattern of velocity biases that serves as an observable 'signature' of the corresponding mechanism. The net effect on perceived velocity is a superposition of these two signatures. By examining human velocity judgments in the context of different adaptor velocities, we are able to separate these two signatures. The model fits the data well, successfully predicts subjects' behavior in an additional experiment using a nondirectional adaptor, and is in agreement with a variety of previous experimental results. As such, the model provides a unifying explanation for the diversity of motion aftereffects
PMCID:3718883
PMID: 19761342
ISSN: 1534-7362
CID: 143636