The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex

Edge and Line Feature Extraction Based on Covariance Models

age segmentation based on contour extraction usually involves three stages of image operations: feature extraction, edge detection and edge linking. This paper is devoted to the first stage: a method to design feature extractors used to detect edges from noisy and/or blurred images. The method relies on a model that describes the existence of image discontinuities (e.g. edges) in terms of covariance functions. The feature extractor transforms the input image into a “log-likelihood ratio” image. Such an image is a good starting point of the edge detection stage since it represents a balanced trade-off between signal-to-noise ratio and the ability to resolve detailed structures. For 1-D signals, the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called “average risk measure”. The results are compared with the performances of 1-D edge detectors known from literature. Generalizations to 2-D operators are given. Applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors. Finally it is shown that the covariance model can be coupled to a MRF-model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

Consensus image method for unknown noise removal

Noise removal has been, and it is nowadays, an important task in computer vision. Usually, it is a previous task preceding other tasks, as segmentation or reconstruction. However, for most existing denoising algorithms the noise model has to be known in advance. In this paper, we introduce a new approach based on consensus to deal with unknown noise models. To do this, different filtered images are obtained, then combined using multifuzzy sets and averaging aggregation functions. The final decision is made by using a penalty function to deliver the compromised image. Results show that this approach is consistent and provides a good compromise between filters.This work is supported by the European Commission under Contract No. 238819 (MIBISOC Marie Curie ITN). H. Bustince was supported by Project TIN 2010-15055 of the Spanish Ministry of Science