Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Stochastic Processes”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,135 records · Page 63Linked to original sources
PubMed2005

Spike detection using the continuous wavelet transform.

This paper combines wavelet transforms with basic detection theory to develop a new unsupervised method for robustly detecting and localizing spikes in noisy neural recordings. The method does not require the construction of templates, or the supervised setting of thresholds. We present extensive Monte Carlo simulations, based on actual extracellular recordings, to show that this technique surpasses other commonly used methods in a wide variety of recording conditions. We further demonstrate that falsely detected spikes corresponding to our method resemble actual spikes more than the false positives of other techniques such as amplitude thresholding. Moreover, the simplicity of the method allows for nearly real-time execution.

Action Potentials↗
PubMed2005

Fetal electrocardiogram extraction by sequential source separation in the wavelet domain.

This paper addresses the problem of fetal electrocardiogram extraction using blind source separation (BSS) in the wavelet domain. A new approach is proposed, which is particularly advantageous when the mixing environment is noisy and time-varying, and that is shown, analytically and in simulation, to improve the convergence rate of the natural gradient algorithm. The distribution of the wavelet coefficients of the source signals is then modeled by a generalized Gaussian probability density, whereby in the time-scale domain the problem of selecting appropriate nonlinearities when separating mixtures of both sub- and super-Gaussian signals is mitigated, as shown by experimental results.

Algorithms↗
PubMed2005

Fast wavelet estimation of weak biosignals.

Wavelet-based signal processing has become commonplace in the signal processing community over the past decade and wavelet-based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by thresholding wavelet coefficients in order to separate signal from noise. Substantial work in this area was summarized by Donoho and colleagues at Stanford University, who developed a variety of algorithms for conventional denoising. However, conventional denoising fails for signals with low signal-to-noise ratio (SNR). Electrical signals acquired from the human body, called biosignals, commonly have below 0 dB SNR. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of such signals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) and of auditory middle latency response (AMLR) signals. Experimental results with both simulated data and human subjects demonstrate that the novel wavelet estimator achieves superior performance to that of linear averaging.

Adult↗
PubMed2005

Time-frequency characterization of interdependencies in nonstationary signals: application to epileptic EEG.

For the past decades, numerous works have been dedicated to the development of signal processing methods aimed at measuring the degree of association between electroencephalographic (EEG) signals. This interdependency parameter, which may be defined in various ways, is often used to characterize a functional coupling between different brain structures or regions during either normal or pathological processes. In this paper, we focus on the time-frequency characterization of the interdependency between signals. Particularly, we propose a novel estimator of the linear relationship between nonstationary signals based on the cross correlation of narrow band filtered signals. This estimator is compared to a more classical estimator based on the coherence function. In a simulation framework, results show that it may exhibit better statistical performances (bias and variance or mean square error) when a priori knowledge about time delay between signals is available. On real data (intracerebral EEG signals), results show that this estimator may also enhance the readability of the time-frequency representation of relationship and, thus, can improve the interpretation of nonstationary interdependencies in EEG signals. Finally, we illustrate the importance of characterizing the relationship in both time and frequency domains by comparing with frequency-independent methods (linear and nonlinear).

Algorithms↗
PubMed2005

Adaptive modeling and spectral estimation of nonstationary biomedical signals based on Kalman filtering.

We describe an algorithm to estimate the instantaneous power spectral density (PSD) of nonstationary signals. The algorithm is based on a dual Kalman filter that adaptively generates an estimate of the autoregressive model parameters at each time instant. The algorithm exhibits superior PSD tracking performance in nonstationary signals than classical nonparametric methodologies, and does not assume local stationarity of the data. Furthermore, it provides better time-frequency resolution, and is robust to model mismatches. We demonstrate its usefulness by a sample application involving PSD estimation of intracranial pressure signals (ICP) from patients with traumatic brain injury (TBI).

Computer Simulation↗
PubMed2005

Single-trial dynamical estimation of event-related potentials: a Kalman filter-based approach.

A method for single-trial dynamical estimation of event-related potentials (ERPs) is presented. The method is based on recursive Bayesian mean square estimation and the estimators are obtained with a Kalman filtering procedure. We especially focus on the case that previous trials contain prior information of relevance to the trial being analyzed. The potentials are estimated sequentially using the previous estimates as prior information. The performance of the method is evaluated with simulations and with real P300 responses measured using auditory stimuli. Our approach is shown to have excellent capability of estimating dynamic changes form stimulus to stimulus present in the parameters of the ERPs, even in poor signal-to-noise ratio (SNR) conditions.

Algorithms↗
PubMed2006

Tracking tremor frequency in spike trains using the extended Kalman smoother.

Tremor is one of the most disabling symptoms in patients with many movement disorders including Parkinson's disease (PD) and essential tremor (ET). Neural tremor manifests itself as a quasi-periodic fluctuation of the firing rate. We describe a frequency tracking method based on the extended Kalman smoother (EKS) to estimate the instantaneous tremor frequency (ITF) exhibited in binary spike trains detected from neural recordings. Simulation results demonstrate that the EKS frequency tracker can estimate the ITF accurately, even though the signal of interest is not sinusoidal and the noise is not Gaussian. The EKS frequency tracker can obtain a normalized mean squared error (NMSE) as low as 0.1 and performs much better than the conventional approach based on the Hilbert transform.

Action Potentials↗
PubMed2004

Tone-dependent error diffusion.

We present an enhanced error diffusion halftoning algorithm for which the filter weights and the quantizer thresholds vary depending on input pixel value. The weights and thresholds are optimized based on a human visual system model. Based on an analysis of the edge behavior, a tone dependent threshold is designed to reduce edge effects and start-up delay. We also propose an error diffusion system with parallel scan that uses variable weight locations to reduce worms.

Algorithms↗
PubMed2004

Adaptive alpha-trimmed mean filters under deviations from assumed noise model.

Alpha-trimmed mean filters are widely used for the restoration of signals and images corrupted by additive non-Gaussian noise. They are especially preferred if the underlying noise deviates from Gaussian with the impulsive noise components. The key design issue of these filters is to select its only parameter, alpha, optimally for a given noise type. In image restoration, adaptive filters utilize the flexibility of selecting alpha according to some local noise statistics. In the present paper, we first review the existing adaptive alpha-trimmed mean filter schemes. We then analyze the performance of these filters when the underlying noise distribution deviates from the Gaussian and does not satisfy the assumptions such as symmetry. Specifically, the clipping effect and the mixed noise cases are analyzed. We also present a new adaptive alpha-trimmed filter implementation that detects the nonsymmetry points locally and applies alpha-trimmed mean filter that trims out the outlier pixels such as edges or impulsive noise according to this local decision. Comparisons of the speed and filtering performances under deviations from symmetry and Gaussian assumptions show that the proposed filter is a very good alternative to the existing schemes.

Algorithms↗
PubMed2004

Improved Poisson intensity estimation: denoising application using Poisson data.

Recently, Timmermann and Nowak developed algorithms for estimating the means of independent Poisson random variables. The algorithms are based on a multiscale model where certain random variables are assumed to obey a beta-mixture density function. Timmermann and Nowak simplify the density estimation problem by assuming the beta parameters are known and only one mixture parameter is unknown. They use the observed data and the method of moments to estimate the unknown mixture parameter. Taking a different approach, we generate training data from the observed data and compute maximum likelihood estimates of all of the beta-mixture parameters. To assess the improved performance obtained by the proposed modification, we consider a denoising application using Poisson data.

Algorithms↗
PubMed2004

A new class of chromatic filters for color image processing. Theory and applications.

This paper advances a new framework for chromatic filtering of color images. The chromatic content of a color image is encoded in the CIE u'v' chromaticity coordinates whereas the achromatic content is encoded as CIE Y tristimulus value. Within the u'v' chromaticity diagram, colors are added according to the well-known center of gravity law of additive color mixtures, which is generalized here into a nonlinear filtering scheme for processing the two chromatic signals u' and v'. The achromatic channel Y can be processed with traditional filtering schemes, either linear or nonlinear, depending on the specific task at hand. The most interesting characteristics of the new filtering scheme are: 1) the elimination of color smearing effects along edges between bright and dark areas; 2) the possibility of processing chromatic components in a noniterative fashion through linear convolution operations; and 3) the consequent amenability to computationally efficient implementations with fast Fourier transform. The paper includes several examples with both synthetic and real images where the performance of the new filtering method is compared with that of other color image processing algorithms.

Algorithms↗
PubMed2004

Differentiation of discrete multidimensional signals.

We describe the design of finite-size linear-phase separable kernels for differentiation of discrete multidimensional signals. The problem is formulated as an optimization of the rotation-invariance of the gradient operator, which results in a simultaneous constraint on a set of one-dimensional low-pass prefilter and differentiator filters up to the desired order. We also develop extensions of this formulation to both higher dimensions and higher order directional derivatives. We develop a numerical procedure for optimizing the constraint, and demonstrate its use in constructing a set of example filters. The resulting filters are significantly more accurate than those commonly used in the image and multidimensional signal processing literature.

Algorithms↗
PubMed2004

Efficient blind image restoration using discrete periodic radon transform.

Restoring an image from its convolution with an unknown blur function is a well-known ill-posed problem in image processing. Many approaches have been proposed to solve the problem and they have shown to have good performance in identifying the blur function and restoring the original image. However, in actual implementation, various problems incurred due to the large data size and long computational time of these approaches are undesirable even with the current computing machines. In this paper, an efficient algorithm is proposed for blind image restoration based on the discrete periodic Radon transform (DPRT). With DPRT, the original two-dimensional blind image restoration problem is converted into one-dimensional ones, which greatly reduces the memory size and computational time required. Experimental results show that the resulting approach is faster in almost an order of magnitude as compared with the traditional approach, while the quality of the restored image is similar.

Algorithms↗
PubMed2004

Adaptive two-pass rank order filter to remove impulse noise in highly corrupted images.

In this paper, we present an adaptive two-pass rank order filter to remove impulse noise in highly corrupted images. When the noise ratio is high, rank order filters, such as the median filter for example, can produce unsatisfactory results. Better results can be obtained by applying the filter twice, which we call two-pass filtering. To further improve the performance, we develop an adaptive two-pass rank order filter. Between the passes of filtering, an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise. The adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values. These pixels are then kept unchanged during the second filtering. In combination, the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering. As a final result, the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise. The idea of adaptive two-pass processing can be applied to many rank order filters, such as a center-weighted median filter (CWMF), adaptive CWMF, lower-upper-middle filter, and soft-decision rank-order-mean filter. Results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters.

Algorithms↗
PubMed2004

Wavelet thresholding of multivalued images.

In this paper, a denoising technique for multivalued images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. Specific functions of the wavelet coefficients are defined that exploit interscale and/or interband correlation of the signal. Three functions are studied: the square of the wavelet coefficients, products of coefficients at adjacent scales, and products of coefficients from different bands. For these functions, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal MRI images.

Algorithms↗
PubMed2004

RAGS: Region-aided Geometric Snake.

An enhanced, region-aided, geometric active contour that is more tolerant toward weak edges and noise in images is introduced. The proposed method integrates gradient flow forces with region constraints, composed of image region vector flow forces obtained through the diffusion of the region segmentation map. We refer to this as the Region-aided Geometric Snake or RAGS. The diffused region forces can be generated from any reliable region segmentation technique, greylevel or color. This extra region force gives the snake a global complementary view of the boundary information within the image which, along with the local gradient flow, helps detect fuzzy boundaries and overcome noisy regions. The partial differential equation (PDE) resulting from this integration of image gradient flow and diffused region flow is implemented using a level set approach. We present various examples and also evaluate and compare the performance of RAGS on weak boundaries and noisy images.

Algorithms↗
PubMed2004

Matching shapes with self-intersections: application to leaf classification.

We address the problem of two-dimensional (2-D) shape representation and matching in presence of self-intersection for large image databases. This may occur when part of an object is hidden behind another part and results in a darker section in the gray level image of the object. The boundary contour of the object must include the boundary of this part which is entirely inside the outline of the object. The Curvature Scale Space (CSS) image of a shape is a multiscale organization of its inflection points as it is smoothed. The CSS-based shape representation method has been selected for MPEG-7 standardization. We study the effects of contour self-intersection on the Curvature Scale Space image. When there is no self-intersection, the CSS image contains several arch shape contours, each related to a concavity or a convexity of the shape. Self intersections create contours with minima as well as maxima in the CSS image. An efficient shape representation method has been introduced in this paper which describes a shape using the maxima as well as the minima of its CSS contours. This is a natural generalization of the conventional method which only includes the maxima of the CSS image contours. The conventional matching algorithm has also been modified to accommodate the new information about the minima. The method has been successfully used in a real world application to find, for an unknown leaf, similar classes from a database of classified leaf images representing different varieties of chrysanthemum. For many classes of leaves, self-intersection is inevitable during the scanning of the image. Therefore the original contributions of this paper is the generalization of the Curvature Scale Space representation to the class of 2-D contours with self-intersection, and its application to the classification of Chrysanthemum leaves.

Algorithms↗
PubMed2004

Holographic image representation with reduced aliasing and noise effects.

This paper presents a novel holographic image representation which has a better reconstruction quality after cropping the hologram than any known representation today. Reconstructed images are very close to ideally low-pass filtered versions of the original image, almost without aliasing. We use the same test images which were used by Bruckstein et al. in [1], and show empirically that our method has smaller reconstruction errors, on all of them, than the errors produced by subsampling and Fourier transform methods presented in [1].

Algorithms↗