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PubMed2006

Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform.

An affine mapping mathematical expression of the double-random-phase encryption technique has been deduced utilizing the matrix form of discrete fractional Fourier transforms. This expression clearly describes the encryption laws of the double-random-phase encoding techniques based on both the fractional Fourier transform and the ordinary Fourier transform. The encryption process may be regarded as a substantial optical realization of the affine cryptosystem. It has been illustrated that the encryption process converts the original image into a white Gaussian noise with a zero-mean value. Also, the decryption process converts the data deviations of the encrypted image into white Gaussian noises, regardless of the type of data deviations. These noises superimpose on the decrypted image and degrade the signal-to-noise ratio. Numerical simulations have been implemented for the different types of noises introduced into the encrypted image, such as the white noise with uniform distribution probability, the white noise with Gaussian distribution probability, colored noise, and the partial occlusion of the encrypted image.

Journal Article↗

PubMed2005

Local spectrum analysis of field propagation in an anisotropic medium. Part I. Time-harmonic fields.

The phase-space beam summation is a general analytical framework for local analysis and modeling of radiation from extended source distributions. In this formulation, the field is expressed as a superposition of beam propagators that emanate from all points in the source domain and in all directions. In this Part I of a two-part investigation, the theory is extended to include propagation in anisotropic medium characterized by a generic wave-number profile for time-harmonic fields; in a companion paper [J. Opt. Soc. Am. A 22, 1208 (2005)], the theory is extended to time-dependent fields. The propagation characteristics of the beam propagators in a homogeneous anisotropic medium are considered. With use of Gaussian windows for the local processing of either ordinary or extraordinary electromagnetic field distributions, the field is represented by a phase-space spectral distribution in which the propagating elements are Gaussian beams that are formulated by using Gaussian plane-wave spectral distributions over the extended source plane. By applying saddle-point asymptotics, we extract the Gaussian beam phenomenology in the anisotropic environment. The resulting field is parameterized in terms of the spatial evolution of the beam curvature, beam width, etc., which are mapped to local geometrical properties of the generic wave-number profile. The general results are applied to the special case of uniaxial crystal, and it is found that the asymptotics for the Gaussian beam propagators, as well as the physical phenomenology attached, perform remarkably well.

Journal Article↗

PubMed2003

Statistical models of shape for the analysis of protein spots in two-dimensional electrophoresis gel images.

In image analysis of two-dimensional electrophoresis gels, individual spots need to be identified and quantified. Two classes of algorithms are commonly applied to this task. Parametric methods rely on a model, making strong assumptions about spot appearance, but are often insufficiently flexible to adequately represent all spots that may be present in a gel. Nonparametric methods make no assumptions about spot appearance and consequently impose few constraints on spot detection, allowing more flexibility but reducing robustness when image data is complex. We describe a parametric representation of spot shape that is both general enough to represent unusual spots, and specific enough to introduce constraints on the interpretation of complex images. Our method uses a model of shape based on the statistics of an annotated training set. The model allows new spot shapes, belonging to the same statistical distribution as the training set, to be generated. To represent spot appearance we use the statistically derived shape convolved with a Gaussian kernel, simulating the diffusion process in spot formation. We show that the statistical model of spot appearance and shape is able to fit to image data more closely than the commonly used spot parameterizations based solely on Gaussian and diffusion models. We show that improvements in model fitting are gained without degrading the specificity of the representation.

Computer Simulation↗

PubMed1997

Gaussian neural networks for glass bottles inspection: a learning procedure.

In glass bottle inspection, the defects detection is of first importance. For online system detection, high speed and robust detection of faults are highly required. Neural networks have recently, and successfully, been applied to fault detection in many manufacturing processes. In this study, a Gaussian neural network, an extension of the RBF network, trained through a competitive algorithm, has been chosen for fault detection. Four parameters extracted from images of the bottles are used as inputs of the network. The number of Gaussian units is adjusted by an informational criterion. Experimental results show that the performance of this network are better than classical parametric and non parametric classifiers.

Algorithms↗

PubMed2005

Non-Gaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process.

The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context in Nowak, [Nature (London) 428, 646 (2004)] defines a promising standard model of evolutionary game theory in finite populations for which analytical results are accessible. In this paper, we derive the stationary distribution of the Moran process population dynamics for arbitrary 2 x 2 games for the finite-size case. We show that a nonvanishing background fitness can be transformed to the vanishing case by rescaling the payoff matrix. In contrast to the common approach to mimic finite-size fluctuations by Gaussian distributed noise, the finite-size fluctuations can deviate significantly from a Gaussian distribution.

Adaptation, Physiological↗

PubMed1995

Fractal analysis of interstitial lung abnormalities in chest radiography.

A computerized method for analyzing interstitial lung abnormalities seen on chest radiographs was investigated. The method includes two main steps: (a) extraction of linear opacities on chest radiographs and (b) calculation of the fractal dimension. Extraction of linear opacities uses the processes of four-directional Laplacian-Gaussian filtering, binarization, and linear opacity judgment. The fractal dimensions in the processed images are then calculated by using the box-counting algorithm. The accuracy of the computerized method in differentiating between normal and abnormal lung tissue was tested on digitized chest radiographs (0.175 mm pixel, 10-bit) of 100 randomly selected patients. One hundred regions of interest (ROIs) from radiographs of 50 patients with interstitial lung abnormalities and 100 ROIs from radiographs of 50 patients with normal lungs were analyzed. The fractal dimensions obtained from the ROIs in lungs with interstitial abnormalities were significantly higher compared with those from ROIs in normal lungs (mean, 1.67 +/- 0.10 vs 1.44 +/- 0.12, respectively; P < .001). This result indicates that fractal analysis is useful in distinguishing interstitial lung abnormalities from normal lung tissue on chest radiographs.

Adult↗

PubMed2004

Self-similar processes and flicker noise from a fluctuating nanopore in a lipid membrane.

Stochastic properties of a fluctuating nanopore generated and sustained by an electric field in a lipid bilayer membrane are studied. It is shown that the process of voltage fluctuations, in the current clamp experiment, is a stochastic fractal with long memory, which is the main reason for its nonstationarity. The aging process contributes to the nonstationarity if molecular interactions in the membrane are weak. An attempt to classify the process reveals a non-Gaussian distribution with long tails, which contradicts the hypothesis of fractional Brownian motion, showing that stable motion may be possible. The self-similarity index, estimated by three different methods, depends on current value and membrane sensitivity to electric field in a well defined and explicable manner. The stochastic analysis provided for calculated conductance of nanopore revealed the process close to 1/f noise, the result observed only for the pores not exceeding 1 nm in diameter, induced in membranes with strong molecular interactions. Our results show that such a pore is the simplest biological system needed for flicker noise to occur, and the complexity of highly regulated protein channel is not a necessary factor. A case of noise 1/f(2), observed for a pore with impeded dynamics, suggests a process without memory in such a situation. A physical interpretation is presented for some of the results.

Cell Membrane Permeability↗

PubMed1998

Relative coordination reconsidered: a stochastic account.

Von Holst (1939/1973) parsed intersegmental coordination into relative and absolute to distinguish moderate and extreme forms. Kelso and DeGuzman (1992) discussed an interpretation of relative coordination in terms of the chaotic phenomenon of intermittency. The data of concern (DeGuzman &amp Kelso, 1991) do not, however, exclude a stochastic interpretation, which is detailed here following earlier suggestions. The key difference is modeling relative coordination by stochastic variability about weak attractors rather than by deterministic variability about remnants of attractors ("ghost attractors"). The intermittency interpretation is not robust in the presence of noise and, therefore, is not well disposed to account for uncertainty in detailing a model of behavioral data or its parameters. In contrast, the stochastic interpretation is based upon an approximation of unknown underlying processes in the form of Gaussian white noise. A stochastic method for estimating model parameters from a stationary probability distribution and a mean first passage time is illustrated using experimental and simulated data.

Humans↗

PubMed2003

Estimating a state-space model from point process observations.

A widely used signal processing paradigm is the state-space model. The state-space model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a state-space model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectation-maximization (EM) algorithm to estimate the unobservable state-space process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the state-space covariance algorithm to compute the complete data log likelihood efficiently. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.

Action Potentials↗

PubMed2003

Dynamical model and nonextensive statistical mechanics of a market index on large time windows.

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e., the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log returns for such a financial market index, for small and large time windows, and both for small and large log returns. These turbulent market volatility (of normalized log returns) distributions can be sufficiently well fitted with a chi(2) distribution. The transition between the small time scale model of nonextensive, intermittent process, and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at ca. a 200 day time lag. The intermittency exponent kappa in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, thereby giving weight to the model. The large value of kappa points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating "no restoring force." A comparison is made between normalized log returns and mere price increments.

Journal Article↗

PubMed2002

Additive noise, Weibull functions and the approximation of psychometric functions.

The Weibull function is frequently chosen to define psychometric functions. Tyler and Chen (Vis. Res. 40 (2000) 3121) criticised the high-threshold postulate implied by the Weibull function and argued that this function implies the assumption of multiplicative noise. It will be shown in this paper that in fact the Weibull function is compatible with the assumption of additive noise, and that the Weibull function may be generalised to the case of detection not being high threshold. The derivations rest, however, on a representation of sensory activity lacking a satisfying degree of generality. Therefore, a more general representation of sensory activity in terms of stochastic processes will be suggested, with detection being defined as a level-crossing process, containing the original representation as a special case. Two classes of stochastic processes will be considered: one where the noise is assumed to be additive, stationary Gaussian, and another resulting from cascaded Poisson processes, representing a form of multiplicative noise. While Weibull functions turn out to approximate well psychometric functions generated by both types of stochastic processes, it also becomes obvious that there is no simple interpretation of the parameters of the fitted Weibull functions. Moreover, corresponding to Tyler and Chen's discussion of the role of multiplicative noise particular sources of this type of noise will be considered and shown to be compatible with the Weibull. It is indicated how multiplicative noise may be defined in general; however, it will be argued that in the light of certain empirical data the role of this type of noise may be negligible in most detection tasks.

Contrast Sensitivity↗

PubMed2001

An anisotropic diffusion method for denoising dynamic susceptibility contrast-enhanced magnetic resonance images.

The purpose of this study was to present an application of a novel denoising technique for improving the accuracy of cerebral blood flow (CBF) images generated from dynamic susceptibility contrast-enhanced magnetic resonance imaging (DSC-MRI). The method presented in this study was based on anisotropic diffusion (AD). The usefulness of this method was firstly investigated using computer simulations. We applied this method to patient data acquired using a 1.5 T MR system. After a bolus injection of Gd-DTPA, we obtained 40-50 dynamic images with a 1.32-2.08 s time resolution in 4-6 slices. The dynamic images were processed using the AD method, and then the CBF images were generated using pixel-by-pixel deconvolution analysis. For comparison, the CBF images were also generated with or without processing the dynamic images using a median or Gaussian filter. In simulation studies, the standard deviation of the CBF values obtained after processing by the AD method was smaller than that of the CBF values obtained without any processing, while the mean value agreed well with the true CBF value. Although the median and Gaussian filters also reduced image noise, the mean CBF values were considerably underestimated compared with the true values. Clinical studies also suggested that the AD method was capable of reducing the image noise while preserving the quantitative accuracy of CBF images. In conclusion, the AD method appears useful for denoising DSC-MRI, which will make the CBF images generated from DSC-MRI more reliable.

Aged↗

PubMed1985

A central spectrum model for the perception of coloration in filtered Gaussian noise.

In this paper we describe a monaural auditory signal-processing model for the perception of coloration. The model gives a central spectrum display of a stationary input signal. The central spectrum level for a nerve fiber tuned to a given frequency is computed as a combination of the average firing rate and the firing synchronized to the center frequency of the nerve. The model incorporates a critical-band filter bank, steady-state representations of the average and synchronized firing rates, and temporal integration. The central spectrum model, when used to process simulated data, accurately predicts the perception of coloration in filtered Gaussian noise.

Auditory Perception↗

PubMed1996

Contributions of frequency distribution analysis to the understanding of coronary restenosis. A reappraisal of the gaussian curve.

BACKGROUND: Clinical restenosis after balloon angioplasty can be categorized by use of dichotomous terms based on the presence or absence of recurrent myocardial ischemia. In contrast, recent investigations have concluded that late luminal renarrowing, documented through angiographic imaging, occurs to a variable extent in nearly all stenoses. This process has been characterized by a gaussian or normal frequency distribution, with restenosis simply representing an extreme form of this delayed remodeling. In the current study, frequency distribution analysis was used to examine the process of coronary restenosis in a large cohort of patients at risk. METHODS AND RESULTS: Quantitative coronary angiographic analysis was applied to 9279 cineangiograms obtained in 3093 patients before and immediately after angioplasty and after 6-month follow-up. Late loss, defined as the change in minimum lumen diameter of the target stenosis from postdilation to follow-up, did not statistically conform to a normal distribution (P<.0001 by both chi2 statistic and Kolmogorov-Smirnov test), even after the exclusion of the 236 stenoses that displayed total occlusions at follow-up angiography. Examination of deviation from a normal curve revealed an excessively high frequency of stenoses that experienced either little change (0.0+/-0.3 mm) or marked change (1.0 to 2.0 mm) in late loss, with a low frequency of stenoses with intermediate values (0.3 to 1.0 mm). Similarly, although the distribution of percent diameter stenosis of the target lesion was statistically normal immediately after dilation, this gaussian distribution disappeared during the follow-up period. Other angiographic indexes of restenosis also failed to approximate a normal curve. In an attempt to improve the goodness of fit, a probabilistic model of late loss was created on the basis of deconvolution of the observed data distribution. Two theoretical, discrete populations of stenoses were identified, one with and one without overall late luminal narrowing. Unlike the gaussian distribution, this model provided a good representation of the observed data (P=NS for lack of fit). CONCLUSIONS: The frequency distributions of angiographic indexes of restenosis often superficially resemble a gaussian curve, an appearance that is artifactually enhanced by the measurement imprecision of current quantitative techniques. Nevertheless, standard indexes of coronary restenosis fail to conform statistically to a normal distribution. The pattern of deviations observed supports the possible existence of discrete subpopulations of lesions, each with a different propensity toward the development of restenosis after coronary intervention.

Adult↗

PubMed1975

On the separation of semiperiodic superimposed point processes: application to electromyographic signals.

A method for the separation of semiperiodic (Gaussian probability distribution of intervals with moderate coefficient of variation) superimposed point processes, to be implemented on a digital computer is described. The efficiency of the filter used for the extraction of the underlying event sequences from the pooled array has been investigated by simulation. Approximately 80 percent of the events belonging to the underlying sequence to be extracted were recovered (with the addition of "impurity events"), still preserving the mean rate and coefficient of variation of the original indicidual sequence concerned. The program was used on an example of an actual electromyographic recording (comprised of a number of motor units discharging simultaneously), resolving the number of motor units involved, their mean rates, and the coefficient of variation of the individual action potential sequences.

Action Potentials↗

PubMed2006

Analysis of heartbeat dynamics by point process adaptive filtering.

Heartbeats are a point process yet, most of the current analysis methods do not model this important characteristic of these data. We describe human heartbeat time series as a history dependent inverse Gaussian model. We present a point process adaptive filter algorithm to estimate the model's time-varying parameters, and use it to compute new measures of heart rate variability. We apply our algorithm to analyze simulated heartbeat data and actual heartbeat data from a tilt table experiment and from healthy subjects and subjects with congestive heart failure during sleep. Our results suggest a new approach for characterizing heartbeat dynamics.

Algorithms↗

PubMed2004

Decreasing motion artifacts in calcium-dependent fluorescence transients from the perfused mouse heart using frequency filtering.

A strategy has been developed for the removal of motion artifact and noise in calcium-dependent fluorescence transients from the perfused mouse heart using frequency filtering. An analytical model indicates that the spectral removal of motion artifacts is independent of the phase shift of the motion waveform in the frequency domain, and thus to the time shift (or delay) of motion in the time domain. This is based on the "shift theorem" of Fourier analysis, which avoids erroneous correction of motion artifact when using the motion signal obtained using reflectance from the heart. Several major steps are adopted to implement this model for elimination of motion as well as detection noise from the fluorescence transient signals from the calcium-sensitive probe Rhod-2. These include (1) extracting the fluorescence calcium transient signal from the raw data by using power spectrum density (PSD) in the frequency domain by subtracting the motion recorded using the reflectance of excitation light, (2) digitally filtering out the random noise using multiple bandpass filters centralized at harmonic frequencies of the transients, and (3) extracting high frequency noise with a Gaussian Kernel filter method. The processed signal of transients acquired with excessive motion artifact is comparable to transients acquired with minimal motion obtained by immobilizing the heart against the detection window, demonstrating the usefulness of this technique.

Animals↗

PubMed2005

Estimation of odor emission rate from landfill areas using the sniffing team method.

The monitoring of the odor annoyance generated by a landfill area is difficult, since it is a multi-area-sources problem, with a discontinuous odor emission. This paper proposes an adaptation of the method of sniffing team campaigns to the particular case of fresh waste odors. The method is based on the field determination of odor perception points, followed by data processing with a bi-Gaussian-type model, adapted to handle the odors. In a first step, field observers delineate the region in which odor impact is experienced and then the emission rate is manipulated in a dispersion model until the predicted size of the impact zone matches that observed in the field. In a second step the adjusted emission rate is entered into the model to calculate the percentiles corresponding to the average annoyance zone. The originality of the proposed method is the introduction of all observation points and of all recorded meteorological data into the model. The paper discusses the method limitations and the errors induced on the results, i.e. the odor emission rate and the percentile lines (or iso-concentration lines) which are used to describe the odor concentrations on a map of the surroundings of the plant. The proposed method proves to be reliable for diffuse sources, such as landfill areas. The obtained results are coherent with other results found in the literature with other techniques.

Air Movements↗