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PubMedDate not supplied

Role of statistical symmetries in sensory coding: an optimal scale invariant code for vision.

The visual system is the most studied sensory pathway, which is partly because visual stimuli have rather intuitive properties. There are reasons to think that the underlying principle ruling coding, however, is the same for vision and any other type of sensory signal, namely the code has to satisfy some notion of optimality--understood as minimum redundancy or as maximum transmitted information. Given the huge variability of natural stimuli, it would seem that attaining an optimal code is almost impossible; however, regularities and symmetries in the stimuli can be used to simplify the task: symmetries allow predicting one part of a stimulus from another, that is, they imply a structured type of redundancy. Optimal coding can only be achieved once the intrinsic symmetries of natural scenes are understood and used to the best performance of the neural encoder. In this paper, we review the concepts of optimal coding and discuss the known redundancies and symmetries that visual scenes have. We discuss in depth the only approach which implements the three of them known so far: translational invariance, scale invariance and multiscaling. Not surprisingly, the resulting code possesses features observed in real visual systems in mammals.

Animals↗
PubMed2005

Direct or indirect? Graphical models for neural oscillators.

Univariate and bivariate time series analysis techniques have enabled new insights into neural processes. However, these techniques are not feasible to distinguish direct and indirect interrelations in multivariate systems. To this aim multivariate times series techniques are presented and investigated by means of simulated as well as physiological time series. Pitfalls and limitations of these techniques are discussed.

Algorithms↗
PubMed2005

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity.

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

Cerebral Cortex↗
PubMed2005

Neural pattern dynamics in an oscillator model of the thalamo-reticular system.

One of development issues for information processing with synchronous oscillations in the brain is how new information is coded and how a comparison with already existing information is performed. In the present work we study a simple neural network model of the thalamo-reticular system based on the Wilson-Cowan model of neuronal oscillatory behavior. Our results show that both cortical control over the thalamus and external sensory input are essential in coordinating and generating spatio-temporal patterns of synchronous activity. A main finding of the numerical simulations is that the network connectivity and the intrinsic oscillatory properties of the neurons result in distinct collective behaviors within the network. By varying the connectivity schemes comparable with lesionated or damaged brain regions our results are in good agreement with in vivo experimental results. Suppressing the sensory input results in temporal oscillatory activity in the beta and gamma range and a strong spatial dependence of the network activity.

Algorithms↗
PubMed2005

Feature detection using spikes: the greedy approach.

A goal of low-level neural processes is to build an efficient code extracting the relevant information from the sensory input. It is believed that this is implemented in cortical areas by elementary inferential computations dynamically extracting the most likely parameters corresponding to the sensory signal. We explore here a neuro-mimetic feed-forward model of the primary visual area (VI) solving this problem in the case where the signal may be described by a robust linear generative model. This model uses an over-complete dictionary of primitives which provides a distributed probabilistic representation of input features. Relying on an efficiency criterion, we derive an algorithm as an approximate solution which uses incremental greedy inference processes. This algorithm is similar to 'Matching Pursuit' and mimics the parallel architecture of neural computations. We propose here a simple implementation using a network of spiking integrate-and-fire neurons which communicate using lateral interactions. Numerical simulations show that this Sparse Spike Coding strategy provides an efficient model for representing visual data from a set of natural images. Even though it is simplistic, this transformation of spatial data into a spatio-temporal pattern of binary events provides an accurate description of some complex neural patterns observed in the spiking activity of biological neural networks.

Action Potentials↗
PubMed2004

Probabilistic pathway representation of cognitive information.

We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of the brain's functioning as a complex physical system, i.e., mapping of physical and chemical processes in the brain on mathematical spaces. The project is about mapping of purely mental processes on mathematical spaces. We present various arguments--philosophic, mathematical, information, and neurophysiological--in favor of the p-adic model of mental space. p-adic spaces have structures of hierarchic trees and in our model such a tree hierarchy is considered as an image of neuronal hierarchy. Hierarchic neural pathways are considered as fundamental units of information processing. As neural pathways can go through the whole body, the mental space is produced by the whole neural system. Finally, we develop the probabilistic neural pathway model in that mental states are represented by probability distributions on mental space.

Cognition↗
PubMed2006

A mathematical framework for inferring connectivity in probabilistic neuronal networks.

We describe an approach for determining causal connections among nodes of a probabilistic network even when many nodes remain unobservable. The unobservable nodes introduce ambiguity into the estimate of the causal structure. However, in some experimental contexts, such as those commonly used in neuroscience, this ambiguity is present even without unobservable nodes. The analysis is presented in terms of a point process model of a neuronal network, though the approach can be generalized to other contexts. The analysis depends on the existence of a model that captures the relationship between nodal activity and a set of measurable external variables. The mathematical framework is sufficiently general to allow a large class of such models. The results are modestly robust to deviations from model assumptions, though additional validation methods are needed to assess the success of the results.

Algorithms↗
PubMed2004

Gaussian mixture models of ECoG signal features for improved detection of epileptic seizures.

PURPOSE: To investigate the potential for improving the performance of the Osorio-Frei seizure detection algorithm (OFA) by incorporating multiple FIR filters operating in parallel and Gaussian mixture models (GMM) for ECoG features distributions, thus creating "hybrid" system. METHODS: The "hybrid" algorithm decomposes the signal into four subbands, using wavelets, after which relevant features are extracted for each subband. Following these steps, multivariate GMM are developed for seizure and non-seizure states, using training segments. State classification is based on thresholding of the likelihood ratio of seizure vs. non-seizure data. Multiple comparisons are performed between this "hybrid" and a modified version of the OFA suitable for this purpose, using as indices false positives (FP), false negatives (FN) and speed of detection. RESULTS: GMM improved speed of detection over the modified OFA at negligible FP levels. The average detection delay from expert visually placed electrographic onset over all seizures was reduced from 4.8 s for modified OFA to 1.8 s for GMM (p < 0.002) Individualized training by subject proved superior to group-based training. CONCLUSIONS: This work introduces multi-feature extraction from ECoG signals together with use of Gaussian mixtures to model them, as tools to improve automated seizure detection. At the clinical level, this approach appears to increase warning time and with it the window during which safety measures and seizure blockage may be implemented, at an affordable computational cost and with negligible FP rate.

Algorithms↗
PubMed2005

Classification of motor commands using a modified self-organising feature map.

In this paper, a control system for an advanced prosthesis is proposed and has been investigated in two different biological systems: (1) the spinal withdrawal reflex system of a rat and (2) voluntary movements in two human males: one normal subject and one subject with a traumatic hand amputation. The small-animal system was used as a model system to test different processing methods for the prosthetic control system. The best methods were then validated in the human set-up. The recorded EMGs were classified using different ANN algorithms, and it was found that a modified self-organising feature map (SOFM) composed of a combination of a Kohonen network and the conscience mechanism algorithm (KNC) was superior in performance to the reference networks (e.g. multi-layer perceptrons) as regards training time, low memory consumption, and simplicity in finding optimal training parameters and architecture. The KNC network classified both experimental set-ups with high accuracy, including five movements for the animal set-up and seven for the human set-up.

Adult↗
PubMed2005

Fast simulated annealing algorithm for BAEP time delay estimation using a reduced order dynamic model.

The extraction of Brainstem Auditory Evoked Potentials (BAEPs), from the EEG background, is of high clinical interest. The present paper can be considered as a continuation of our previous work related to the BAEP estimation in endocochlear pathologies. In our previous published work, we proposed a technique for time delay estimation on the basis of the BAEPs in response to successive stimulations. Put in a different manner, our objective was the estimation of the dynamics of the cochlea that is responsible for the delayed responses. The estimation technique was based on optimization of a non-linear criterion by means of Simulated Annealing Time Delay Estimation (SATDE) algorithm. However, it is well known that such heuristic algorithms are time consuming and largely depend on the number of parameters to be estimated. The present paper demonstrates that modeling the non-stationarity of responses considerably decreases the convergence time to the global minimum. The newly proposed method in this paper, called Fast Simulated Annealing Time Delay Estimation (FSATDE) algorithm, has been validated on both simulated and real signals.

Algorithms↗
PubMed2006

Automatic correction of artifact from single-trial event-related potentials by blind source separation using second order statistics only.

Event-related potentials (ERP) are in general masked by various kinds of artifacts. To attenuate the effects of artifacts, various schemes have been introduced, such as epoch rejection, electro-oculogram (EOG) regression and independent component analysis (ICA). However, none of the existing techniques can automatically remove various kinds of artifacts from a single ERP epoch. EOG regression cannot handle artifacts other than ocular ones. ICA incorporating higher order statistics (HOS) normally requires data with large number of time samples in order that the solution is robust. In this paper we blindly separate the multi-channel ERP into source components by estimating the correlation matrices of the data. Since only second order statistics (SOS) is involved, the process performs well at the single epoch level. Automatic artifact identification is performed in the source domain by introducing objective criteria for various artifacts. Criteria are based on time domain signal amplitude for blink and spurious peak artifact, scalp distribution of signal power for eye movement artifact and power distribution of frequency components for muscle artifact. The correction procedure can be completed by removing the identified artifactual sources from the raw multi-channel ERP.

Algorithms↗
PubMed2006

Deformable registration of brain tumor images via a statistical model of tumor-induced deformation.

An approach to the deformable registration of three-dimensional brain tumor images to a normal brain atlas is presented. The approach involves the integration of three components: a biomechanical model of tumor mass-effect, a statistical approach to estimate the model's parameters, and a deformable image registration method. Statistical properties of the sought deformation map from the atlas to the image of a tumor patient are first obtained through tumor mass-effect simulations on normal brain images. This map is decomposed into the sum of two components in orthogonal subspaces, one representing inter-individual differences in brain shape, and the other representing tumor-induced deformation. For a new tumor case, a partial observation of the sought deformation map is obtained via deformable image registration and is decomposed into the aforementioned spaces in order to estimate the mass-effect model parameters. Using this estimate, a simulation of tumor mass-effect is performed on the atlas image in order to generate an image that is similar to tumor patient's image, thereby facilitating the atlas registration process. Results for a real tumor case and a number of simulated tumor cases indicate significant reduction in the registration error due to the presented approach as compared to the direct use of deformable image registration.

Algorithms↗
PubMed2006

Statistical representation of high-dimensional deformation fields with application to statistically constrained 3D warping.

This paper proposes a 3D statistical model aiming at effectively capturing statistics of high-dimensional deformation fields and then uses this prior knowledge to constrain 3D image warping. The conventional statistical shape model methods, such as the active shape model (ASM), have been very successful in modeling shape variability. However, their accuracy and effectiveness typically drop dramatically in high-dimensionality problems involving relatively small training datasets, which is customary in 3D and 4D medical imaging applications. The proposed statistical model of deformation (SMD) uses wavelet-based decompositions coupled with PCA in each wavelet band, in order to more accurately estimate the pdf of high-dimensional deformation fields, when a relatively small number of training samples are available. SMD is further used as statistical prior to regularize the deformation field in an SMD-constrained deformable registration framework. As a result, more robust registration results are obtained relative to using generic smoothness constraints on deformation fields, such as Laplacian-based regularization. In experiments, we first illustrate the performance of SMD in representing the variability of deformation fields and then evaluate the performance of the SMD-constrained registration, via comparing a hierarchical volumetric image registration algorithm, HAMMER, with its SMD-constrained version, referred to as SMD+HAMMER. This SMD-constrained deformable registration framework can potentially incorporate various registration algorithms to improve robustness and stability via statistical shape constraints.

Algorithms↗
PubMed2006

3D curve inference for diffusion MRI regularization and fibre tractography.

We develop a differential geometric framework for regularizing diffusion MRI data. The key idea is to model white matter fibres as 3D space curves and to then extend Parent and Zucker's 2D curve inference approach [Parent, P., Zucker, S., 1989. Trace inference, curvature consistency, and curve detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 823-839] by using a notion of co-helicity to indicate compatibility between fibre orientations at each voxel with those in a local neighborhood. We argue that this provides several advantages over earlier regularization methods. We validate the approach quantitatively on a biological phantom and on synthetic data, and qualitatively on data acquired in vivo from a human brain. We also demonstrate the use of the technique to improve the performance of a fibre tracking algorithm.

Algorithms↗
PubMed2006

Adaptive Markov modeling for mutual-information-based, unsupervised MRI brain-tissue classification.

This paper presents a novel method for brain-tissue classification in magnetic resonance (MR) images that relies on a very general, adaptive statistical model of image neighborhoods. The method models MR-tissue intensities as derived from stationary random fields. It models the associated Markov statistics nonparametrically via a data-driven strategy. This paper describes the essential theoretical aspects underpinning adaptive, nonparametric Markov modeling and the theory behind the consistency of such a model. This general formulation enables the method to easily adapt to various kinds of MR images and the associated acquisition artifacts. It implicitly accounts for the intensity nonuniformity and performs reasonably well on T1-weighted MR data without nonuniformity correction. The method minimizes an information-theoretic metric on the probability density functions associated with image neighborhoods to produce an optimal classification. It automatically tunes its important internal parameters based on the information content of the data. Combined with an atlas-based initialization, it is completely automatic. Experiments on real, simulated, and multimodal data demonstrate the advantages of the method over the current state-of-the-art.

Algorithms↗
PubMed2006

Fiber tract-oriented statistics for quantitative diffusion tensor MRI analysis.

Quantitative diffusion tensor imaging (DTI) has become the major imaging modality to study properties of white matter and the geometry of fiber tracts of the human brain. Clinical studies mostly focus on regional statistics of fractional anisotropy (FA) and mean diffusivity (MD) derived from tensors. Existing analysis techniques do not sufficiently take into account that the measurements are tensors, and thus require proper interpolation and statistics of tensors, and that regions of interest are fiber tracts with complex spatial geometry. We propose a new framework for quantitative tract-oriented DTI analysis that systematically includes tensor interpolation and averaging, using nonlinear Riemannian symmetric space. A new measure of tensor anisotropy, called geodesic anisotropy (GA) is applied and compared with FA. As a result, tracts of interest are represented by the geometry of the medial spine attributed with tensor statistics (average and variance) calculated within cross-sections. Feasibility of our approach is demonstrated on various fiber tracts of a single data set. A validation study, based on six repeated scans of the same subject, assesses the reproducibility of this new DTI data analysis framework.

Algorithms↗
PubMed2006

Hidden Markov multiple event sequence models: A paradigm for the spatio-temporal analysis of fMRI data.

This paper presents a novel, completely unsupervised fMRI brain mapping method that addresses the three problems of hemodynamic response function (HRF) variability, hemodynamic event timing, and fMRI response non-linearity. Spatial and temporal information are directly taken into account into the core of the activation detection process. In practice, activation detection at voxel v is formulated in terms of temporal alignment between sequences of hemodynamic response onsets (HROs) detected in the fMRI signal at v and in the spatial neighborhood of v, and the input sequence of stimuli or stimulus onsets. Event-related and epoch paradigms are considered. The multiple event sequence alignment problem is solved within the probabilistic framework of hidden Markov multiple event sequence models (HMMESMs), a new class of hidden Markov models. Results obtained on real and synthetic data significantly outperform those obtained with the popular statistical parametric mapping (SPM2) method without requiring any prior definition of the expected activation patterns, the HMMESM mapping approach being completely unsupervised.

Adolescent↗
PubMed2004

The emergence of consciousness.

Consciousness is the primary aspect of our lives. The true nature of consciousness (its subjectivity and intentionality) has resisted scientific explanation for centuries. This has important implications for scientific understanding and progress, as well as for the study and treatment of medical disorders, most of which involve some element of consciousness. In this paper, a basic nonlinear emergent mechanism (responsible for a large number of natural phenomena) is described. This mechanism produces nonlinear explicit states that have all the same properties as consciousness and hence the two may be identical. This mechanism might be applied to explain the generation of human consciousness. There is an intimate relation between consciousness and voluntary (by choice, free will) new or novel intentional (goal-directed) action-any action or action sequence (whether muscular movement, ocular movement, speech, thought, emotion) created anew by choice to achieve some goal. Consciousness always accompanies the production of such action (conscious action). Thus, a physical mechanism utilizing the basic type of nonlinear emergence (positive feedback between release and dissipation events, inhibition, formation of an explicit state, effects produced in other systems) was suggested for the production of voluntary new or novel intentional action from perception. This mechanism agrees with a large amount of research data for the production of such action. The nonlinear explicit states produced by the nonlinear mechanism from perception appear to have identical properties to human consciousness. Hence consciousness is natural, material, and functional; not something mysterious, nonmaterial, and epiphenomenal as has often been portrayed. It has evolved in humans for the creation of adaptive action. This means that consciousness can be explained and studied scientifically and medical disorders involving consciousness treatable by basic clinical treatment (psychiatric, medicinal, psychological). This theory also provides possibilities for the explanation of many puzzling questions: What brain structures are involved in producing consciousness. How these effects may be produced, manipulated, or complemented. That other animals may be conscious. That machines may be built to be conscious. That certain natural systems may have a degree of consciousness. That paranormal phenomena may be explained via these principles.

Adaptation, Physiological↗