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PubMed2005

Statistical validation of mutual information calculations: comparison of alternative numerical algorithms.

Given two time series X and Y , their mutual information, I (X,Y) = I (Y,X) , is the average number of bits of X that can be predicted by measuring Y and vice versa. In the analysis of observational data, calculation of mutual information occurs in three contexts: identification of nonlinear correlation, determination of an optimal sampling interval, particularly when embedding data, and in the investigation of causal relationships with directed mutual information. In this contribution a minimum description length argument is used to determine the optimal number of elements to use when characterizing the distributions of X and Y . However, even when using partitions of the X and Y axis indicated by minimum description length, mutual information calculations performed with a uniform partition of the XY plane can give misleading results. This motivated the construction of an algorithm for calculating mutual information that uses an adaptive partition. This algorithm also incorporates an explicit test of the statistical independence of X and Y in a calculation that returns an assessment of the corresponding null hypothesis. The previously published Fraser-Swinney algorithm for calculating mutual information includes a sophisticated procedure for local adaptive control of the partitioning process. When the Fraser and Swinney algorithm and the algorithm constructed here are compared, they give very similar numerical results (less than 4% difference in a typical application). Detailed comparisons are possible when X and Y are correlated jointly Gaussian distributed because an analytic expression for I (X,Y) can be derived for that case. Based on these tests, three conclusions can be drawn. First, the algorithm constructed here has an advantage over the Fraser-Swinney algorithm in providing an explicit calculation of the probability of the null hypothesis that X and Y are independent. Second, the Fraser-Swinney algorithm is marginally the more accurate of the two algorithms when large data sets are used. With smaller data sets, however, the Fraser-Swinney algorithm reports structures that disappear when more data are available. Third, the algorithm constructed here requires about 0.5% of the computation time required by the Fraser-Swinney algorithm.

Journal Article↗

PubMed2005

An optimal nonlinear extension of linear filters based on distributed arithmetic.

Distributed arithmetic (DA)-based implementation of linear filters relies on the linear nature of this operation and has been suggested as a multiplication free solution. In this work, we introduce a nonlinear extension of linear filters optimizing under mean-square error criterion the memory function [(MF) multivariate Boolean function with not only binary output] which is in the core of DA based implementation. Such an extension will improve the filtering of noise which may contain non-Gaussian components without increasing the complexity of implementation. Experiments on real images have shown the superiority of the proposed filters over the optimal linear filters. Different versions of these filters are also considered for an impulsive noise removal, faster processing, and filtering using large input data windows.

Algorithms↗

PubMed2006

Quadratic weighted median filters for edge enhancement of noisy images.

Quadratic Volterra filters are effective in image sharpening applications. The linear combination of polynomial terms, however, yields poor performance in noisy environments. Weighted median (WM) filters, in contrast, are well known for their outlier suppression and detail preservation properties. The WM sample selection methodology is naturally extended to the quadratic sample case, yielding a filter structure referred to as quadratic weighted median (QWM) that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise. Through statistical analysis of higher order samples, it is shown that, although the parent Gaussian distribution is light tailed, the higher order terms exhibit heavy-tailed distributions. The optimal combination of terms contributing to a quadratic system, i.e., cross and square, is approached from a maximum likelihood perspective which yields the WM processing of these terms. The proposed QWM filter structure is analyzed through determination of the output variance and breakdown probability. The studies show that the QWM exhibits lower variance and breakdown probability indicating the robustness of the proposed structure. The performance of the QWM filter is tested on constant regions, edges and real images, and compared to its weighted-sum dual, the quadratic Volterra filter. The simulation results show that the proposed method simultaneously suppresses the noise and enhances image details. Compared with the quadratic Volterra sharpener, the QWM filter exhibits superior qualitative and quantitative performance in noisy image sharpening.

Algorithms↗

PubMed2003

Automated segmentation of acetabulum and femoral head from 3-D CT images.

This paper describes several new methods and software for automatic segmentation of the pelvis and the femur, based on clinically obtained multislice computed tomography (CT) data. The hip joint is composed of the acetabulum, cavity of the pelvic bone, and the femoral head. In vivo CT data sets of 60 actual patients were used in the study. The 120 (60 x 2) hip joints in the data sets were divided into four groups according to several key features for segmentation. Conventional techniques for classification of bony tissues were first employed to distinguish the pelvis and the femur from other CT tissue images in the hip joint. Automatic techniques were developed to extract the boundary between the acetabulum and the femoral head. An automatic method was built up to manage the segmentation task according to image intensity of bone tissues, size, center, shape of the femoral heads, and other characters. The processing scheme consisted of the following five steps: 1) preprocessing, including resampling 3-D CT data by a modified Sinc interpolation to create isotropic volume and to avoid Gibbs ringing, and smoothing the resulting images by a 3-D Gaussian filter; 2) detecting bone tissues from CT images by conventional techniques including histogram-based thresholding and binary morphological operations; 3) estimating initial boundary of the femoral head and the joint space between the acetabulum and the femoral head by a new approach utilizing the constraints of the greater trochanter and the shapes of the femoral head; 4) enhancing the joint space by a Hessian filter; and 5) refining the rough boundary obtained in step 3) by a moving disk technique and the filtered images obtained in step 4). The above method was implemented in a Microsoft Windows software package and the resulting software is freely available on the Internet. The feasibility of this method was tested on the data sets of 60 clinical cases (5000 CT images).

Acetabulum↗

PubMed2003

Variational mixture of Bayesian independent component analyzers.

There has been growing interest in subspace data modeling over the past few years. Methods such as principal component analysis, factor analysis, and independent component analysis have gained in popularity and have found many applications in image modeling, signal processing, and data compression, to name just a few. As applications and computing power grow, more and more sophisticated analyses and meaningful representations are sought. Mixture modeling methods have been proposed for principal and factor analyzers that exploit local gaussian features in the subspace manifolds. Meaningful representations may be lost, however, if these local features are nongaussian or discontinuous. In this article, we propose extending the gaussian analyzers mixture model to an independent component analyzers mixture model. We employ recent developments in variational Bayesian inference and structure determination to construct a novel approach for modeling nongaussian, discontinuous manifolds. We automatically determine the local dimensionality of each manifold and use variational inference to calculate the optimum number of ICA components needed in our mixture model. We demonstrate our framework on complex synthetic data and illustrate its application to real data by decomposing functional magnetic resonance images into meaningful-and medically useful-features.

Bayes Theorem↗

PubMed2004

Tools and strategies for processing diffusion-ordered 2D NMR spectroscopy (DOSY) of a broad, featureless resonance: an application to methylaluminoxane (MAO).

UNLABELLED: DOSY has been extremely successful in many studies of molecular weight distributions, especially when the components are separable along the chemical shift axis. However, an unresolved NMR resonance yields the familiar problem of overlapping exponential decays. In a study of methylaluminoxane (MAO), a set of data processing and simulation tools were developed: read Bruker data files (Matlab); preliminary non-linear least-squares fit with f-test (Matlab); movie generation of the fits (Matlab); conversion of diffusion coefficients to molecular masses through molecular volumes (Gaussian-98); and simulation of DOSY data sets for various molecular mass distributions (Mathematica). These tools are presented here and briefly compared with other DOSY analysis methods. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00216-003-2457-1. The following Matlab and Mathematica files are made available: Plot_Raw_DOSY.m, Fit_Two_Component.m (which calls One_Gaussian_LEASTSQ.m, Two_Gaussian_LEASTSQ.m, and pFTest.m), and DOSY_theory.nb. Note: Matlab v5.2 optimization toolbox, as supplied, lacked a confidence interval subroutine; upon our request, confint.m was provided to the authors by Mathworks, Inc. Newer versions of Matlab have a similar program already included in the optimization.

Journal Article↗

PubMed1999

Canonical phase-space approach to the noisy Burgers equation.

Presenting a general phase-space approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short-time regime we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer-replica model and asymmetric exclusion model results.

Journal Article↗

PubMed2006

A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

Electronic Data Processing↗

PubMed2004

Comparison of TCA and ICA techniques in fMRI data processing.

PURPOSE: To make a quantitative comparison of temporal cluster analysis (TCA) and independent component analysis (ICA) techniques in detecting brain activation by using simulated data and in vivo event-related functional MRI (fMRI) experiments. MATERIALS AND METHODS: A single-slice MRI image was replicated 150 times to simulate an fMRI time series. An event-related brain activation pattern with five different levels of intensity and Gaussian noise was superimposed on these images. Maximum contrast-to-noise ratio (CNR) of the signal change ranged from 1.0 to 2.0 by 0.25 increments. In vivo visual stimulation fMRI experiments were performed on a 1.9 T magnet. Six human volunteers participated in this study. All imaging data were analyzed using both TCA and ICA methods. RESULTS: Both simulated and in vivo data have shown that no statistically significant difference exists in the activation areas detected by both ICA and TCA techniques when CNR of fMRI signal is larger than 1.75. CONCLUSION: TCA and ICA techniques are comparable in generating functional brain maps in event-related fMRI experiments. Although ICA has richer features in exploring the spatial and temporal information of the functional images, the TCA method has advantages in its computational efficiency, repeatability, and readiness to average data from group subjects

Brain Mapping↗

PubMed1999

Experimental and clinical validation of arterial diameter waveform and intimal media thickness obtained from B-mode ultrasound image processing.

A new automated computerized system (IôTEC) that assesses concomitantly the instantaneous temporal arterial diameter and intimal media thickness (IMT) obtained from B-mode ultrasound (US) images was validated by sonomicrometry in sheep, by an echo-tracking system in humans, and by a Lucite phantom in vitro. Differences between methods for diameter measurements did not vary in any systematic way, with no significant differences in the lower frequency range. Ultrasonic measurements of the true phantom gap sizes showed high correlation (r2 = 0.98,p < 0.001) with no systematic errors. Carotid and femoral arteries in humans were strongly related between IôTEC and echo-tracking device (r2 = 0.94 carotid; R2 = 0.88 femoral, p < 0.001), with a Gaussian distribution of the errors. This new method showed high intra- and interobserver repeatability of arterial diameter and IMT, allowing consistent characterization of arterial dynamics in humans.

Animals↗

PubMed2000

Universal distributions for growth processes in 1+1 dimensions and random matrices

We develop a scaling theory for Kardar-Parisi-Zhang growth in one dimension by a detailed study of the polynuclear growth model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential.

Journal Article↗

PubMed1991

Can the analytic techniques of nonlinear dynamics distinguish periodic, random and chaotic signals?

Recent advances in the mathematical discipline of nonlinear dynamics have led to its use in the analysis of many biologic processes. But the ability of the tools of nonlinear dynamic analysis to identify chaotic behavior has not been determined. We analyzed a series of signals--periodic, chaotic and random--with five tools of nonlinear dynamics. Periodic signals were sine, square, triangular, sawtooth, modulated sine waves and quasiperiodic, generated at multiple amplitudes and frequencies. Chaotic signals were generated by solving sets of nonlinear equations including the logistic map, Duffing's equation, Lorenz equations and the Silnikov attractor. Random signals were both discontinuous and continuous. Gaussian noise was added to some signals at magnitudes of 1, 2, 5, 10 and 20% of the signal's amplitude. Each signal was then subjected to tools of nonlinear dynamics (phase plane plot, return map, Poincaré section, correlation dimension and spectral analysis) to determine the relative ability of each to characterize the underlying system as periodic, chaotic or random. In the absence of noise, phase plane plots and return maps were the most sensitive detectors of chaotic and periodic processes. Spectral analysis could determine if a process was periodic or quasiperiodic, but could not distinguish between chaotic and random signals. Correlation dimension was useful to determine the overall complexity of a signal, but could not be used in isolation to identify a chaotic process. Noise at any level effaced the structure of the phase plane plot. Return maps were relatively immune to noise at levels of up to 5%. Spectral analysis and correlation dimension were insensitive to noise. Accordingly, we recommend that unknown signals be subjected to all of the techniques to increase the accuracy of identification of the underlying process. Based on these data, we conclude that no single test is sufficiently sensitive or specific to categorize an unknown signal as chaotic.

Fourier Analysis↗

PubMed2000

Inverse covariation of spectral density and correlation dimension in cyclic EEG dynamics of the human brain.

The responsiveness or excitability of the central nervous system (CNS) to external or internal stimuli is systematically altered corresponding to transient changes of the EEG background activity, mainly in the alpha range. We hypothesise that a transient alpha power increase is due to an underlying increase in synchronisation or coupling strength between various neuronal elements or cortical networks. Consequently, the 'network' of the CNS may be more ordered and, hence, less complex in the case of high spectral density, and vice versa. The goals of the present paper are (1) to prove the inverse covariation between spectral density and correlation dimension for a set of human EEG data, (2) to falsify the null hypothesis that the observed relationship is a random one, and (3) to propose a neuronal approach which may explain the observed correlations. A sliding computation of the spectral density and correlation dimension [Grassberger P, Procaccia I (1983) Physica D 9:189-208] of mid-occipital EEG recordings derived from eight awake subjects with eyes closed was performed. The similarity between the two time courses was quantified by similarity measures and descriptive correlation coefficients. The temporal pattern of dimensional complexity showed an inverse relationship with simultaneously computed spectral power changes most pronounced in the alpha range. The group means of similarity measures and correlation coefficients were compared with the corresponding means of a sample set established by 20 Gaussian random signals. Statistically significant differences were obtained at the 0.1% level, rejecting the null hypothesis that the observed relationship is a random one. The results support the idea that the dynamics of the EEG signals investigated reflect a chaotic deterministic process with state transitions from 'high-dimensional' to 'low-dimensional' non-linear dynamics, and vice versa. Adequate neuronal models and approaches to interpret the disclosed transients and the inverse covariation between spectral density and dimensional complexity are proposed, giving additional insight into the integrative functioning of the CNS with respect to the strategy of information processing.

Brain↗

PubMed1997

Evolution of delta activity within the nonREM sleep episode: a biphasic hypothesis.

The time course of delta activity within nonREM (NREM) episodes is measured for 24 healthy subjects with normal REM latencies. The first two NREM episodes in particular, show two very clearly separated peaks for about 35% of the subjects. Another 25% show two less well separated peaks. These double peak patterns are also prevalent in the literature, but there has been a tendency to dismiss them as a skipped REM effect. They are, however, still evident even when the data are averaged over the 24 subjects, indicating a systematic phenomenon. These averaged data are well fitted by an analytic function given by the sum of two consecutive overlapping Gaussian curves. The well-behaved residuals also, are an indication that a biphasic model of this kind is statistically appropriate. The model proposed is simple, with parameters related to physiological phenomena, and it suggests that there may be an underlying process with delta waves emanating from two separate signal sources. Recent neurophysiological findings suggest that delta oscillations are generated both in the thalamus and in the cortex and show that excessive synchronization of slow oscillations may lead to seizures. Hence the speculation that the biphasic process may emanate from cortical and thalamic sources and be protective in the sense that it permits smaller delta amplitudes at each source while retaining the integral delta energy necessary to satisfy sleep pressure. It is significant that the two peaks are most evident in the first two NREM episodes where delta power is high.

Adult↗

PubMed2004

Chain conformation in two-dimensional dense state.

In an effort to provide evidence concerning the conformation of many chains in strict two-dimensional (2D) dense state, we synthesized polymer chains of diameter of nanometers through an anionic polymerization process. The conformational characteristics of the long chain molecules in films of thickness h corresponding to the chain diameter a were directly obtained from atomic force microscopy observations. In 2D dispersed state, the conformations of the long chain molecules were typical Gaussian. However, in 2D dense state the long chain molecules were strongly interpenetrated. Their conformations were largely perturbed by the presence of neighbor chains and were not Gaussian. This result was in contradiction with the segregated globule model predicted by de Gennes. The central reason is that 2D space cannot be filled to normal density with 2D Gaussian globules; either the area must be greatly increased with consequently large voids, or the globule conformation must be expanded by allowing chains to interpenetrate each other.

Journal Article↗

PubMed2006

Conditioning pulse trains in cochlear implants: effects on loudness growth.

HYPOTHESIS: The addition of a high-rate (5 kpps) conditioning pulse train to the input signal of cochlear implants will result in shallower loudness growth across the dynamic range of cochlear implant patients. BACKGROUND: High-rate conditioning pulse trains have been shown to increase the dynamic range of sinusoidal stimuli for cochlear implant recipients in a manner consistent with stochastic resonance. This study further characterizes the effects of conditioning stimuli on loudness by examining the loudness growth functions for sinusoidal stimuli both with and without conditioning. METHODS: Seven post-lingually deafened adults using the Clarion CII cochlear implant participated in this study. The loudness growth functions of each subject were characterized using sinusoidal stimuli, both with and without the presence of a high-rate conditioner. Loudness was measured using magnitude estimation. RESULTS: The loudness growth functions of all seven subjects demonstrate an increase in dynamic range for sinusoidal stimuli with the addition of the conditioning pulse train. Shallower loudness growth is seen across the dynamic range with the addition of a conditioner. This result was shown for loudness growth fitted to exponential, power, and cumulative gaussian functions. CONCLUSION: The addition of high-rate conditioning pulse trains to sinusoidal stimuli presented to cochlear implant recipients results in larger dynamic ranges, with more gradual increases in loudness growth across the dynamic range. This suggests that signal-processing strategies incorporating conditioning may be clinically useful, requiring less compression of the input signal and leading to less distortion perceived by cochlear implant patients.

Adult↗

PubMed2002

Non-Markovian random processes and traveling fronts in a reaction-transport system with memory and long-range interactions.

The problem of finding the propagation rate for traveling waves in reaction-transport systems with memory and long-range interactions has been considered. Our approach makes use of the generalized master equation with logistic growth, hyperbolic scaling, and Hamilton-Jacobi theory. We consider the case when the waiting-time distribution for the underlying microscopic random walk is modeled by the family of gamma distributions, which in turn leads to non-Markovian random processes and corresponding memory effects on mesoscopic scales. We derive formulas that enable us to determine the front propagation rate and understand how the memory and long-range interactions influence the propagation rate for traveling fronts. Several examples involving the Gaussian and discrete distributions for jump densities are presented.

Journal Article↗

PubMed2002

[Synthesis of binocular disparity with motion parallax in depth slant perception: statistical efficiency approach].

Statistical efficiency approach is used in order to investigate sampling properties of both binocular disparity and motion parallax processes in depth slant perception and to examine the independent decisions model (Mulligan & Shaw, 1980) consisting of these processes. We carried out two experiments in which each cue was displayed solely (i.e., single condition) and both cues were displayed simultaneously (i.e., multiple condition). A two-alternative forced-choice (2AFC) task was used under the situation where a Gaussian noise was added to the stimulus value of depth slant. Statistical efficiencies were calculated in each experiment. The results showed that sampling size from binocular disparity was at least comparable or larger by a factor of 2.5-3.5 with that from motion parallax and that efficiencies of the multiple condition considerably exceeded those of the single condition. This suggests invalidity of the independent decisions model.

Cues↗