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Results for “Gaussian process”

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PubMed2001

Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability.

We consider detection of a nodule signal profile in noisy images meant to roughly simulate the statistical properties of tomographic image reconstructions in nuclear medicine. The images have two sources of variability arising from quantum noise from the imaging process and anatomical variability in the ensemble of objects being imaged. Both of these sources of variability are simulated by a stationary Gaussian random process. Sample images from this process are generated by filtering white-noise images. Human-observer performance in several signal-known-exactly detection tasks is evaluated through psychophysical studies by using the two-alternative forced-choice method. The tasks considered investigate parameters of the images that influence both the signal profile and pixel-to-pixel correlations in the images. The effect of low-pass filtering is investigated as an approximation to regularization implemented by image-reconstruction algorithms. The relative magnitudes of the quantum and the anatomical variability are investigated as an approximation to the effects of exposure time. Finally, we study the effect of the anatomical correlations in the form of an anatomical slope as an approximation to the effects of different tissue types. Human-observer performance is compared with the performance of a number of model observers computed directly from the ensemble statistics of the images used in the experiments for the purpose of finding predictive models. The model observers investigated include a number of nonprewhitening observers, the Hotelling observer (which is equivalent to the ideal observer for these studies), and six implementations of channelized-Hotelling observers. The human observers demonstrate large effects across the experimental parameters investigated. In the regularization study, performance exhibits a mild peak at intermediate levels of regularization before degrading at higher levels. The exposure-time study shows that human observers are able to detect ever more subtle lesions at increased exposure times. The anatomical slope study shows that human-observer performance degrades as anatomical variability extends into higher spatial frequencies. Of the observers tested, the channelized-Hotelling observers best capture the features of the human data.

Artifacts↗

PubMed2001

Simulation of jet-noise excitation in an acoustic progressive wave tube facility.

Acoustic excitation produced by jet-engine effluxes was simulated in a progressive wave tube (APWT) facility with a computer-based control system. The APWT siren is driven by a signal generated numerically in a PC and then converted into analog form. Characteristics of the acoustic pressure measured by a microphone are analyzed in digital form and compared with those prescribed for simulation. Divergence is compensated by immediate modification of the driving signal and this action is repeated in the form of iterative process until the test specification is attained. Typical power spectral density (PSD) shapes with maxima at low and high frequencies were simulated. A "tailoring" approach has been also achieved when a test specification was determined directly from field measurements for the particular aircraft under consideration. Since acoustic pressure signals of high level differ from the Gaussian random process model, particularly in terms of asymmetric probability density function, a method has been developed to make the driving signal also non-Gaussian by simulating skewness and kurtosis parameters of the APWT acoustic excitation simultaneously with PSD control. Experimental results with Gaussian and non-Gaussian characteristics obtained for various PSD specifications including sharp and narrow peaks are presented in the paper.

Journal Article↗

PubMed2006

Multistage graph-based segmentation of thoracoscopic images.

This paper presents a graph-based segmentation method using multiple criteria in successive stages to segment thoracoscopic images acquired during a diskectomy procedure commonly used for thoracoscopic anterior release and fusion for scoliosis treatment. Starting with image pre-processing, including Gaussian smoothing, brightness and contrast enhancement, and histogram thresholding, a standard graph-based method is applied to produce a coarse segmentation of thoracoscopic images. Next, regions are further merged in a multistage graph-based process based on features like grey-level similarity, region size and common edge length. Experimental results show that our approach achieves good spatial coherence, accurate edge location and appropriate segmentation of the regions of interest from a sequence of thoracoscopic images.

Algorithms↗

PubMed1993

Characterization of the dynamic stress response of manual and powered wheelchair frames.

Two wheelchairs, one manual, one electrically powered, were instrumented with strain gages and operated over various laboratory terrains. Both wheelchairs were folding models with cross tubes pinned together at the center. The wheelchairs were operated on a constant speed treadmill with no bump, and with 0.953 cm (0.375 in) and 1.6 cm (0.625 in) dowels simulating bumps. The wheelchairs were also rolled off a 10.8 cm (4.25 in) platform to simulate a curb drop. The von Mises stresses were computed from the recorded strains, and statistical hypothesis tests were performed to determine whether the stresses were consistent with a stationary, narrow-band Gaussian random process. Such a stress history has been used in random fatigue analyses. Summary data for two strain gage locations on each wheelchair, for the four different test terrains, suggest that the von Mises stress can be considered stationary, but neither narrow-banded, nor Gaussian distributed.

Humans↗

PubMed2003

Anomalous transport of particle tracers in multidimensional cellular flows.

Advection of tracers is studied numerically in time-dependent, two-dimensional cellular flows and a time-independent, three-dimensional cellular flow field. Tracers in these flows follow trajectories that are either periodic or chaotic and mimic correlated Lévy flights. The probability density function of displacements for particles in the ordered regions of the flow follows a classical Gaussian dispersion process. The particle trajectories in the chaotic regions of the flow exhibit anomalous diffusion and the probability density function of displacements is well modeled by a time-fractional diffusion equation of order alpha. The overall process of particle dispersion is found to be controlled mainly by the chaotic regions within the flow field. From the perspective of Lagrangian dynamics our results indicate that the advection of particles in flow fields prone to exhibit chaotic advection is a combination of both classical, i.e., Gaussian, behavior and anomalous, i.e., non-Gaussian, diffusion.

Journal Article↗

PubMed1997

Non-Gaussian statistical property of the ultrasonic Doppler signal downstream of a severe stenosis.

The Doppler signal is generally considered as a Gaussian random process. However, to date very little experimental validation of this model has been available. Recently, the K model was proposed to describe the statistical properties of ultrasonic radio frequency signals and their envelopes. The coefficient of kurtosis, which has been shown to be related to the parameters of the K model, was used in the literature as an index to assess the deviations from the Gaussian statistical property of ultrasonic signals obtained from simulations, phantoms and tissues. In the present study, an in vitro flow loop model was used to evaluate the effect of a severe stenosis on the coefficient of kurtosis. Our results showed non-Gaussian statistical properties of the Doppler signal in the jet of the stenosis.

Constriction, Pathologic↗

PubMedDate not supplied

The effect of digital unsharp-mask filtering on the signal-to-noise ratio in computed radiography.

The effect of image processing in computed radiography (CR) has been analyzed in many ROC studies. The results have not shown great diagnostic improvements, except in some special occasions. The theoretical effect of image enhancement on the signal-to-noise ratio in CR images has so far not been assessed. Concerning the previous results, the changes induced in the signal-to-noise ratio by digital image processing are certainly of interest. We calculated the signal-to-noise ratio in various conditions according to the principles of the Rose model, using the computerized image data of storage phosphor radiography. Seventy-seven computed radiographs processed by Gaussian unsharp-mask filtering using different kernel widths were analyzed. The signal-to-noise ratio was reduced in all images by more than 40% when the smallest kernels were used, and increased slowly towards the original value with greater kernel sizes. In no conditions did the ratio exceed the original one. The results show that although edges and signal contrast can be enhanced by unsharp-mask filtering, this happens at the cost of increased noise. This might at least in part explain why image processing does not significantly improve the diagnostic information content of a computed radiograph.

Filtration↗

PubMed2006

A Bayesian semi-parametric model for colorectal cancer incidences.

A Bayesian semi-parametric model is proposed to capture the interaction among demographic effects (age and gender), spatial effects (county) and temporal effects of colorectal cancer incidences simultaneously. In particular, an extension of multivariate conditionally autoregressive (CAR) processes to a partially informative Gaussian demographic spatial temporal CAR (DSTCAR) process for a spatial-temporal setting is proposed. The precision matrix of the Gaussian DSTCAR process is the Kronecker product of several components. The spatial component is modelled with a CAR prior. A pth order intrinsic autoregressive prior (IAR(p)) is implemented for the temporal component to estimate a smoothed and non-parametric temporal trend. The demographic component is modelled with a Wishart prior. Data analysis shows significant spatial correlation only exists in the age group of 50-59. Males and females in their 50s and 60s show fairly strong correlation. The hypothesis testing based on Bayes factor suggests that gender correlation cannot be ignored in this model.

Adult↗

PubMed2005

Lévy-Student distributions for halos in accelerator beams.

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of stochastic mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Schrödinger-like (SL) equation. The space charge effects have been introduced in recent papers by coupling this S-L equation with the Maxwell equations. We analyze the space-charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self-consistent solutions are related to the (external and space-charge) potentials both when we suppose that the external field is harmonic (constant focusing), and when we a priori prescribe the shape of the stationary solution. We then proceed to discuss a few other ideas by introducing generalized Student distributions, namely, non-Gaussian, Lévy infinitely divisible (but not stable) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Lévy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws and in the case (b) the discontinuities of the Lévy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.

Journal Article↗

PubMed2002

Time-dependent structure in the discharge rate of human motor units.

OBJECTIVES: The aim of this study was to examine the influence of visual and motor processes on the deterministic and stochastic structure of force output and motor unit discharge variability. METHODS: Young adult subjects produced continuous, isometric force at 3, 6, 12, and 24% of their maximal voluntary contraction at low and high visual gain levels through abduction of the index finger. Force and fine-wire intramuscular electromyography were recorded. RESULTS: There was a linear increase in discharge irregularity with increases in the mean motor unit discharge rate (8-30 Hz). Recurrence analysis showed that the percentage of deterministic structure in discharge variability remained high, but decreased linearly with increased motor unit discharge rate. Surrogate analyses confirmed that the motor unit discharge variability was inconsistent with an uncorrelated and linearly correlated Gaussian noise process. Spectral analysis revealed that both the force output and the mean time-varying motor unit discharge time series had a dominant frequency of 0-2 Hz. Visual feedback gain did not affect the individual motor unit discharge patterns. CONCLUSIONS: The motor unit discharge rate has deterministic time-dependent structure. The motor unit discharge rate is modulated at multiple time scales likely by pre- and post-synaptic induced fluctuations from spinal level pathways impinging on the motor neuron.

Action Potentials↗

PubMed2005

A stochastic model for studying the laminar structure of cortex from MRI.

The human cerebral cortex is a laminar structure about 3 mm thick, and is easily visualized with current magnetic resonance (MR) technology. The thickness of the cortex varies locally by region, and is likely to be influenced by such factors as development, disease and aging. Thus, accurate measurements of local cortical thickness are likely to be of interest to other researchers. We develop a parametric stochastic model relating the laminar structure of local regions of the cerebral cortex to MR image data. Parameters of the model include local thickness, and statistics describing white, gray and cerebrospinal fluid (CSF) image intensity values as a function of the normal distance from the center of a voxel to a local coordinate system anchored at the gray/white matter interface. Our fundamental data object, the intensity-distance histogram (IDH), is a two-dimensional (2-D) generalization of the conventional 1-D image intensity histogram, which indexes voxels not only by their intensity value, but also by their normal distance to the gray/white interface. We model the IDH empirically as a marked Poisson process with marking process a Gaussian random field model of image intensity indexed against normal distance. In this paper, we relate the parameters of the IDH model to the local geometry of the cortex. A maximum-likelihood framework estimates the parameters of the model from the data. Here, we show estimates of these parameters for 10 volumes in the posterior cingulate, and 6 volumes in the anterior and posterior banks of the central sulcus. The accuracy of the estimates is quantified via Cramer-Rao bounds. We believe that this relatively crude model can be extended in a straightforward fashion to other biologically and theoretically interesting problems such as segmentation, surface area estimation, and estimating the thickness distribution in a variety of biologically relevant contexts.

Algorithms↗

PubMed2002

High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity.

Magnetic resonance (MR) diffusion tensor imaging (DTI) can resolve the white matter fiber orientation within a voxel provided that the fibers are strongly aligned. However, a given voxel may contain a distribution of fiber orientations due to, for example, intravoxel fiber crossing. The present study sought to test whether a geodesic, high b-value diffusion gradient sampling scheme could resolve multiple fiber orientations within a single voxel. In regions of fiber crossing the diffusion signal exhibited multiple local maxima/minima as a function of diffusion gradient orientation, indicating the presence of multiple intravoxel fiber orientations. The multimodality of the observed diffusion signal precluded the standard tensor reconstruction, so instead the diffusion signal was modeled as arising from a discrete mixture of Gaussian diffusion processes in slow exchange, and the underlying mixture of tensors was solved for using a gradient descent scheme. The multitensor reconstruction resolved multiple intravoxel fiber populations corresponding to known fiber anatomy. Ma

Anisotropy↗

PubMed2004

Characterizing non-Gaussian diffusion by using generalized diffusion tensors.

Diffusion tensor imaging (DTI) is known to have a limited capability of resolving multiple fiber orientations within one voxel. This is mainly because the probability density function (PDF) for random spin displacement is non-Gaussian in the confining environment of biological tissues and, thus, the modeling of self-diffusion by a second-order tensor breaks down. The statistical property of a non-Gaussian diffusion process is characterized via the higher-order tensor (HOT) coefficients by reconstructing the PDF of the random spin displacement. Those HOT coefficients can be determined by combining a series of complex diffusion-weighted measurements. The signal equation for an MR diffusion experiment was investigated theoretically by generalizing Fick's law to a higher-order partial differential equation (PDE) obtained via Kramers-Moyal expansion. A relationship has been derived between the HOT coefficients of the PDE and the higher-order cumulants of the random spin displacement. Monte-Carlo simulations of diffusion in a restricted environment with different geometrical shapes were performed, and the strengths and weaknesses of both HOT and established diffusion analysis techniques were investigated. The generalized diffusion tensor formalism is capable of accurately resolving the underlying spin displacement for complex geometrical structures, of which neither conventional DTI nor diffusion-weighted imaging at high angular resolution (HARD) is capable. The HOT method helps illuminate some of the restrictions that are characteristic of these other methods. Furthermore, a direct relationship between HOT and q-space is also established.

Anisotropy↗

PubMed2005

Analysis of interval-censored longitudinal data with application to onco-haematology.

The analysis of repeated measurements on a biomarker, either alone or jointly with the analysis of time to the event of interest, is an area of active research. Nevertheless, we are not yet able to deal in complete generality with these complex data, which frequently consist of error-prone, sparse and intermittent values. In many cancer studies, they arise in the framework of clinical trials and thus their relationship with prognosis is a primary focus. In such a setting, the Cox model is regarded as the standard technique for analysis. The aim of this work is to illustrate an alternative approach to the analysis of studies in which the biomarker values are complicated by interval censoring and an event occurs when the biomarker itself passes a certain threshold. We propose a linear mixed model with a Gaussian stochastic process that allows for interval-censored data and can be used both to track the biomarker trajectory and to estimate the probability of event occurrence. It is developed within the classic approach to longitudinal data analysis that was previously adapted for left-censored data, only. We apply this method to a study on the minimal residual disease (MRD) in childhood leukaemia. MRD is an interval-censored measurement of residual leukaemic cells that was scheduled at 9 time-points during treatment. The aim is to investigate the relationship between MRD and the disease process. Relapse, the event of interest, may conveniently be represented as MRD over a pre-defined threshold. Our focus is on modelling the probability of relapse conditional on MRD observed prior to it. Results show that the approach is promising as it allows proper description of the data, while maintaining flexibility of modelling, feasibility of computations and interpretability of results.

Biomarkers↗

PubMed1998

Spin Echo Attenuation of Restricted Diffusion as a Discord of Spin Phase Structure

By using the particle probability density we analyze the spin echo attenuation of particles, diffusing in a bounded region. It provides a means to expand a nonuniform spin phase distribution into a series of waves that characterize the geometry and boundary conditions of confinement. Random motion disrupts the initial phase structure created by applied gradients and consequently discords its structure waves. By assuming the spin phase fluctuation and/or the randomness of spin phase distribution in the subensemble as a Gaussian stochastic process, we derive a new analytical expression for the echo attenuation related to the particle velocity correlation. For a diffusion in porous structure we get the expression featuring the same "diffusive diffraction" patterns as those being found and explained by P. T. Callaghan and A. Coy ("Principles of Nuclear Magnetic Resonance Microscopy," Oxford Univ. Press, Oxford (1991); J. Chem. Phys. 101, 4599-4609 (1994)) with the use of propagator theory. With the new approach we cast a new light on the phenomena and derive analitically how the diffusive diffractions appear when the sequence of finite or even modulated gradients are applied. The method takes into account the non-Markovian character of restricted diffusion, and therefore the echo dependence on the diffusion lengths and on the strength of applied gradient differs from the results of authors assuming the Markovian diffusion either by dealing with the diffusion propagators or by the computer simulation of Fick's diffusion. Copyright 1998 Academic Press.

Journal Article↗

PubMed1979

The response of a spatially distributed neuron to white noise current injection.

The depolarization of passive nerve cylinder or dendritic tree in the equivalent cylinder representation is assumed to satisfy the cable equation. We consider in detail the effects of white noise current injection at a given location for the case of sealed end boundary conditions and for an initial resting state. The depolarization at a point is a Gaussian random process but is not Markovian. Expression (infinite series) are obtained for the expectation, variance, spatial and temporal covariances of the depolarization. We examine the steady state expectation and variance and investigate how these are approached in time over the whole neuronal surface. We consider the relative contributions of various terms in the series for the expectation and variance of the depolarization at x = 0 (soma, trigger zone, recording electrode) for various positions of the input process. It is found that different numbers of terms must be taken to obtain a reasonable approximation depending on whether the stimulus is at proximal, central or distal parts of the dendritic tree. We consider briefly the interspike time problem and see in an approximate way how spatial effects are important in determining the mean time between impulses.

Action Potentials↗

PubMed1985

A maximum entropy criterion of filtering and coding for stationary autoregressive signals: its physical interpretations and suggestions for its application to neural information transmission.

The operations of encoding and decoding in communication agree with filtering operations of convolution and deconvolution for Gaussian signal processing. In an analogy with power transmission in thermodynamics, an autoregressive model of information transmission is proposed for representing a continuous communication system which requires a pair of an internal noise source and a signal source to encode or decode a message. In this model transinformation (informational entropy) equals the increase in stationary nonequilibrium organization formed through the amplification of white noise by a positive feedback system. The channel capacity is finite due to the existence of inherent noise in the system. The maximum entropy criterion in information dynamics corresponds to the 2nd law of thermodynamics. If the process is stationary, the communication system is invertible, and has the maximum efficiency of transformation. The total variation in informational entropy is zero in the cycle of the invertible system, while in the noninvertible system the entropy of decoding is less than that of encoding. A noisy autoregressive coding which maximizes transinformation is optimum, but is also ideal.

Animals↗

PubMed1993

Cardiac Doppler blood-flow signal analysis. Part 1. Evaluation of the normality and stationarity of the temporal signal.

The normality (Gaussian property) and stationarity of the cardiac Doppler blood-flow signal were evaluated on short-time segments distributed over the cardiac cycle. The basic approaches used to perform statistical tests on the nonstationary and quasiperiodic cardiac Doppler signal are presented. The results obtained from the data of ten patients having a normal aortic valve and ten patients having a stenotic valve indicate that a complex Gaussian random process is an acceptable approximation for the clinical cardiac Doppler signal. For segments of 10 ms or less, 82 per cent of them were accepted to be stationary with a significance level of 0.05, whereas for durations greater than 40 ms, the percentage of stationary segments was less than 75 per cent. It was concluded that the 10 ms window generally used in practice is a good choice for Doppler spectrogram estimation, but a shorter time interval would be preferable.

Aortic Valve↗