Neural coding

About: Neural coding is a research topic. Over the lifetime, 5086 publications have been published within this topic receiving 219167 citations. The topic is also known as: temporal coding & neural representation.

Independent Component Analysis

Abstract: In this chapter, we discuss a statistical generative model called independent component analysis. It is basically a proper probabilistic formulation of the ideas underpinning sparse coding. It shows how sparse coding can be interpreted as providing a Bayesian prior, and answers some questions which were not properly answered in the sparse coding framework.

Image Super-Resolution Via Sparse Representation

Abstract: This paper presents a new approach to single-image superresolution, based upon sparse signal representation. Research on image statistics suggests that image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary. Inspired by this observation, we seek a sparse representation for each patch of the low-resolution input, and then use the coefficients of this representation to generate the high-resolution output. Theoretical results from compressed sensing suggest that under mild conditions, the sparse representation can be correctly recovered from the downsampled signals. By jointly training two dictionaries for the low- and high-resolution image patches, we can enforce the similarity of sparse representations between the low-resolution and high-resolution image patch pair with respect to their own dictionaries. Therefore, the sparse representation of a low-resolution image patch can be applied with the high-resolution image patch dictionary to generate a high-resolution image patch. The learned dictionary pair is a more compact representation of the patch pairs, compared to previous approaches, which simply sample a large amount of image patch pairs , reducing the computational cost substantially. The effectiveness of such a sparsity prior is demonstrated for both general image super-resolution (SR) and the special case of face hallucination. In both cases, our algorithm generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods. In addition, the local sparse modeling of our approach is naturally robust to noise, and therefore the proposed algorithm can handle SR with noisy inputs in a more unified framework.

Spikes: Exploring the Neural Code

Abstract: Our perception of the world is driven by input from the sensory nerves. This input arrives encoded as sequences of identical spikes. Much of neural computation involves processing these spike trains. What does it mean to say that a certain set of spikes is the right answer to a computational problem? In what sense does a spike train convey information about the sensory world? Spikes begins by providing precise formulations of these and related questions about the representation of sensory signals in neural spike trains. The answers to these questions are then pursued in experiments on sensory neurons.The authors invite the reader to play the role of a hypothetical observer inside the brain who makes decisions based on the incoming spike trains. Rather than asking how a neuron responds to a given stimulus, the authors ask how the brain could make inferences about an unknown stimulus from a given neural response. The flavor of some problems faced by the organism is captured by analyzing the way in which the observer can make a running reconstruction of the sensory stimulus as it evolves in time. These ideas are illustrated by examples from experiments on several biological systems. Intended for neurobiologists with an interest in mathematical analysis of neural data as well as the growing number of physicists and mathematicians interested in information processing by "real" nervous systems, Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory. A quantitative framework is used to pose precise questions about the structure of the neural code. These questions in turn influence both the design and analysis of experiments on sensory neurons.

Efficient sparse coding algorithms

Abstract: Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higher-level features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we present efficient sparse coding algorithms that are based on iteratively solving two convex optimization problems: an L1-regularized least squares problem and an L2-constrained least squares problem. We propose novel algorithms to solve both of these optimization problems. Our algorithms result in a significant speedup for sparse coding, allowing us to learn larger sparse codes than possible with previously described algorithms. We apply these algorithms to natural images and demonstrate that the inferred sparse codes exhibit end-stopping and non-classical receptive field surround suppression and, therefore, may provide a partial explanation for these two phenomena in V1 neurons.