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PubMed2000

Iterative linear minimum mean-square-error image restoration from partially known blur.

We address the problem of space-invariant image restoration when the blurring operator is not known exactly, a situation that arises regularly in practice. To account for this uncertainty, we model the point-spread function as the sum of a known deterministic component and an unknown random one. Such an approach has been studied before, but the problem of estimating the parameters of the restoration filter to our knowledge has not been addressed systematically. We propose an approach based on a Gaussian statistical assumption and derive an iterative, expectation-maximization algorithm that simultaneously restores the image and estimates the required filter parameters. We obtain two versions of the algorithm based on two different models for the statistics of the image. The computations are performed in the discrete Fourier transform domain; thus they are computationally efficient even for large images. We examine the convergence properties of the resulting estimators and evaluate their performance experimentally.

Algorithms↗

PubMed1977

K+ conduction description from the low frequency impedance and admittance of squid axon.

The form of power spectra of K+ conduction fluctuations in patches of squid axon suggested that K+ conduction kinetics are higher than first order (Fishman, Moore & Poussart, 1975, J. Membrane Biol. 24:305). To obtain an alternative description of ion conduction kinetics consistent with spontaneous fluctuations, the complex impedance and admittance of squid (Loligo pealei) axon were measured at low frequencies (1-1000 Hz) with a four electrode system using white Gaussian noise as a stochastic perturbation. As predicted from the spontaneous noise measurements, a low frequency impedance feature is observed between 1 and 30 Hz which is voltage and temperature dependent, disappears after substantial reduction in [Ki+], and is unaffected by the state of Na+ conduction or active transport. These measurements confirm and constitute strong support for the patch noise measurements and interpretations. The linearized Hodgkin-Huxley (HH) equations do not produce the low frequency feature since first order ion conduction kinetics are assumed. Computation of diffusion polarization effects associated with the axon sheath gives a qualitative account of the low frequency feature, but the potential dependence is opposite to that of the data. Thus, K+ conduction kinetics in the axon are not adequately described by a single first order process. In addition, significant changes in HH parameter values were required to describe the usual impedance (resonance) feature in Loligo pealei axon data.

Animals↗

PubMed2001

Statistical thermodynamics of membrane bending-mediated protein-protein attractions.

Highly wedge-shaped integral membrane proteins, or membrane-adsorbed proteins can induce long-ranged deformations. The strain in the surrounding bilayer creates relatively long-ranged forces that contribute to interactions with nearby proteins. In contrast, to direct short-ranged interactions such as van der Waal's, hydrophobic, or electrostatic interactions, both local membrane Gaussian curvature and protein ellipticity can induce forces acting at distances of up to a few times their typical radii. These forces can be attractive or repulsive, depending on the proteins' shape, height, contact angle with the bilayer, and a pre-existing local membrane curvature. Although interaction energies are not pairwise additive, for sufficiently low protein density, thermodynamic properties depend only upon pair interactions. Here, we compute pair interaction potentials and entropic contributions to the two-dimensional osmotic pressure of a collection of noncircular proteins. For flat membranes, bending rigidities of approximately 100k(B)T, moderate ellipticities, and large contact angle proteins, we find thermally averaged attractive interactions of order k(B)T. These interactions may play an important role in the intermediate stages of protein aggregation. Numerous biological processes where membrane bending-mediated interactions may be relevant are cited, and possible experiments are discussed.

Lipid Bilayers↗

PubMed2007

Output power enhancement of a palmtop terahertz-wave parametric generator.

Broadband terahertz (THz) waves were generated by optical parametric processes based on laser light scattering from the polariton mode of a nonlinear crystal. By using the parametric oscillation of a MgO-doped LiNbO3 crystal pumped by a nanosecond Q-switched Nd:YAG laser, we have realized a broadband, high-energy and compact THz-wave source. We report the development of a THz-wave parametric generator (TPG) using a small pump source with a short pulse width and a top-hat beam profile. These characteristics of the pump beam permit high-intensity pumping especially close to the output surface of the THz wave without thermal damage to the crystal surface. We also calculated the outcoupled THz wave for beams with two different intensity profiles: a top-hat beam (in this experiment) and a Gaussian beam (previously reported). The result shows the mechanism of the output energy and/or power enhancement.

Journal Article↗

PubMed2004

Maximum likelihood estimation of signal amplitude and noise variance from MR data.

In MRI, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian-distributed noise. After applying an inverse Fourier transform, the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This article addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the maximum likelihood method. As a performance criterion, the mean-squared error (MSE) is used.

Algorithms↗

PubMed2002

Effects of restricted diffusion on MR signal formation.

Numerous functional MRI (fMRI) and diffusion MR studies have recently boosted interest in the theory of MR signal formation in biological systems in the presence of mesoscopic magnetic field in homogeneities. Herein we report an exact solution to the problem of free induction decay (FID) and spin echo (SE) signal formation in the presence of a constant field gradient in three models of one-, two-, and three-dimensional restricted diffusion. We demonstrate the transition with increasing diffusion coefficient from the oscillating FID signal behavior in the static dephasing regime to a monotonic exponential behavior in the motional narrowing regime. Quantitative criteria are presented for applicability of the Gaussian approximation for the description of the MR signal. The spatial distribution of signal density and the edge enhancement effect are analyzed. We also demonstrate that the presence of restrictive barriers in a one-compartment model can lead to a quasi-two-compartment behavior of the MR signal. This result suggests a simple rationale for the experimental findings of biexponential echo attenuation curves in MR diffusion experiments with tissue systems.

Diffusion↗

PubMed2003

An algorithm for rapid calculation of a probabilistic functional atlas of subcortical structures from electrophysiological data collected during functional neurosurgery procedures.

The paper introduces an optimal algorithm for rapid calculation of a probabilistic functional atlas (PFA) of subcortical structures from data collected during functional neurosurgery procedures. The PFA is calculated based on combined intraoperative electrophysiology, pre- and intraoperative neuroimaging, and postoperative neurological verification. The algorithm converts the coordinates of the neurologically most effective contacts into probabilistic functional maps taking into account the geometry of a stimulating electrode. The PFA calculation comprises the reconstruction of the contact coordinates from two orthogonal projections, normalizing (warping) the contacts modeled as cylinders, voxelizing the contact models, calculating the atlas, and computing probability. In addition, an analytical representation of the PFA is formulated based on Gaussian modeling. The initial PFA has been calculated from the data collected during the treatment of 274 Parkinson's disease patients, most of them operated bilaterally (487 operated hemispheres). It contains the most popular stereotactic targets, the subthalamic nucleus, globus pallidus internus, and ventral intermedius nucleus. The key application of the algorithm is targeting in stereotactic and functional neurosurgery, and it also can be employed in human and animal brain research.

Algorithms↗

PubMed2002

Fusing speed and phase information for vascular segmentation of phase contrast MR angiograms.

This paper presents a statistical approach to aggregating speed and phase (directional) information for vascular segmentation of phase contrast magnetic resonance angiograms (PC-MRA). Rather than relying on speed information alone, as done by others and in our own work, we demonstrate that including phase information as a priori knowledge in a Markov random field (MRF) model can improve the quality of segmentation. This is particularly true in the region within an aneurysm where there is a heterogeneous intensity pattern and significant vascular signal loss. We propose to use a Maxwell-Gaussian mixture density to model the background signal distribution and combine this with a uniform distribution for modelling vascular signal to give a Maxwell-Gaussian-uniform (MGU) mixture model of image intensity. The MGU model parameters are estimated by the modified expectation-maximisation (EM) algorithm. In addition, it is shown that the Maxwell-Gaussian mixture distribution (a) models the background signal more accurately than a Maxwell distribution, (b) exhibits a better fit to clinical data and (c) gives fewer false positive voxels (misclassified vessel voxels) in segmentation. The new segmentation algorithm is tested on an aneurysm phantom data set and two clinical data sets. The experimental results show that the proposed method can provide a better quality of segmentation when both speed and phase information are utilised.

Algorithms↗

PubMed1998

Robust parameter estimation of intensity distributions for brain magnetic resonance images.

This paper presents two new methods for robust parameter estimation of mixtures in the context of magnetic resonance (MR) data segmentation. The head is constituted of different types of tissue that can be modeled by a finite mixture of multivariate Gaussian distributions. Our goal is to estimate accurately the statistics of desired tissues in presence of other ones of lesser interest. These latter can be considered as outliers and can severely bias the estimates of the former. For this purpose, we introduce a first method, which is an extension of the expectation-maximization (EM) algorithm, that estimates parameters of Gaussian mixtures but incorporates an outlier rejection scheme which allows to compute the properties of the desired tissues in presence of atypical data. The second method is based on genetic algorithms and is well suited for estimating the parameters of mixtures of different kind of distributions. We use this property by adding a uniform distribution to the Gaussian mixture for modeling the outliers. The proposed genetic algorithm can efficiently estimate the parameters of this extended mixture for various initial settings. Also, by changing the minimization criterion, estimates of the parameters can be obtained by histogram fitting which considerably reduces the computational cost. Experiments on synthetic and real MR data show that accurate estimates of the gray and white matters parameters are computed.

Adolescent↗

PubMed2006

Approximate first passage time distribution for barrier crossing in a double well under fractional Gaussian noise.

The distribution of waiting times, f(t), between successive turnovers in the catalytic action of single molecules of the enzyme beta-galactosidase has recently been determined in closed form by Chaudhury and Cherayil [J. Chem. Phys. 125, 024904 (2006)] using a one-dimensional generalized Langevin equation (GLE) formalism in combination with Kramers' flux-over-population approach to barrier crossing dynamics. The present paper provides an alternative derivation of f(t) that eschews this approach, which is strictly applicable only under conditions of local equilibrium. In this alternative derivation, a double well potential is incorporated into the GLE, along with a colored noise term representing protein conformational fluctuations, and the resulting equation transformed approximately to a Smoluchowski-type equation. f(t) is identified with the first passage time distribution for a particle to reach the barrier top starting from an equilibrium distribution of initial points, and is determined from the solution of the above equation using local boundary conditions. The use of such boundary conditions is necessitated by the absence of definite information about the precise nature of the boundary conditions applicable to stochastic processes governed by non-Markovian dynamics. f(t) calculated in this way is found to have the same analytic structure as the distribution calculated by the flux-over-population method.

Journal Article↗

PubMed2003

Probabilistic Monte Carlo based mapping of cerebral connections utilising whole-brain crossing fibre information.

A methodology is presented for estimation of a probability density function of cerebral fibre orientations when one or two fibres are present in a voxel. All data are acquired on a clinical MR scanner, using widely available acquisition techniques. The method models measurements of water diffusion in a single fibre by a Gaussian density function and in multiple fibres by a mixture of Gaussian densities. The effects of noise on complex MR diffusion weighted data are explicitly simluated and parameterised. This information is used for standard and Monte Carlo streamline methods. Deterministic and probabilistic maps of anatomical voxel scale connectivity between brain regions are generated.

Algorithms↗

PubMed2000

Quantitative analysis of cell columns in the cerebral cortex.

We present a quantified imaging method that describes the cell column in mammalian cortex. The minicolumn is an ideal template with which to examine cortical organization because it is a basic unit of function, complete in itself, which interacts with adjacent and distance columns to form more complex levels of organization. The subtle details of columnar anatomy should reflect physiological changes that have occurred in evolution as well as those that might be caused by pathologies in the brain. In this semiautomatic method, images of Nissl-stained tissue are digitized or scanned into a computer imaging system. The software detects the presence of cell columns and describes details of their morphology and of the surrounding space. Columns are detected automatically on the basis of cell-poor and cell-rich areas using a Gaussian distribution. A line is fit to the cell centers by least squares analysis. The line becomes the center of the column from which the precise location of every cell can be measured. On this basis several algorithms describe the distribution of cells from the center line and in relation to the available surrounding space. Other algorithms use cluster analyses to determine the spatial orientation of every column.

Algorithms↗

PubMed2002

Optimal green (red-free) digital imaging of conjunctival vasculature.

AIMS/BACKGROUND: Green illumination is commonly used to image vessels of the retina and conjunctiva. The purpose was to derive the best optical set-up for imaging vessels of the conjunctiva. METHODS: The concept of exposure density was used to predict a digital camera response to imaging vessels on a scleral background. Practical verification was performed to verify vessel contrast because of the difficulties in measuring the spectral components of the imaging system, such as the spectral reflectivity of vessels and sclera. Images of the same conjunctiva were repetitively taken through different coloured filters, using the Nikon FS-2 photo slit-lamp and recorded on different coloured channels of the Kodak DCS 100 digital camera. Gaussian blurred tubular models were fitted to densitometric profiles across three vessels from each image, allowing vessel contrast and width to be objectively measured. These measures were compared using different optical set-ups. RESULTS: Optimal exposure density calculations and vessel contrast was obtained with the xenon light source filtered with Wratten 99 (green) and Wratten 96 (neutral density, 0.2 log units) gelatine absorption filters using the green channel of the digital camera. This image set-up was associated with a 46% (99% CI 43-51%) to 64% (99% CI 58-72%) increase in contrast compared with vessels imaged without filtration, using the combined colour channel of the digital camera. Although differences in vessel widths resulted, absolute differences were marginal. CONCLUSION: With the increased use of digital imaging, and the need for image processing of vascular networks, image optimisation is beneficial. This study verified the optimal set-up for non-invasively imaging vessels of the bulbar conjunctiva.

Blood Vessels↗

PubMed2006

Detecting statistically significant common insertion sites in retroviral insertional mutagenesis screens.

Retroviral insertional mutagenesis screens, which identify genes involved in tumor development in mice, have yielded a substantial number of retroviral integration sites, and this number is expected to grow substantially due to the introduction of high-throughput screening techniques. The data of various retroviral insertional mutagenesis screens are compiled in the publicly available Retroviral Tagged Cancer Gene Database (RTCGD). Integrally analyzing these screens for the presence of common insertion sites (CISs, i.e., regions in the genome that have been hit by viral insertions in multiple independent tumors significantly more than expected by chance) requires an approach that corrects for the increased probability of finding false CISs as the amount of available data increases. Moreover, significance estimates of CISs should be established taking into account both the noise, arising from the random nature of the insertion process, as well as the bias, stemming from preferential insertion sites present in the genome and the data retrieval methodology. We introduce a framework, the kernel convolution (KC) framework, to find CISs in a noisy and biased environment using a predefined significance level while controlling the family-wise error (FWE) (the probability of detecting false CISs). Where previous methods use one, two, or three predetermined fixed scales, our method is capable of operating at any biologically relevant scale. This creates the possibility to analyze the CISs in a scale space by varying the width of the CISs, providing new insights in the behavior of CISs across multiple scales. Our method also features the possibility of including models for background bias. Using simulated data, we evaluate the KC framework using three kernel functions, the Gaussian, triangular, and rectangular kernel function. We applied the Gaussian KC to the data from the combined set of screens in the RTCGD and found that 53% of the CISs do not reach the significance threshold in this combined setting. Still, with the FWE under control, application of our method resulted in the discovery of eight novel CISs, which each have a probability less than 5% of being false detections.

Chromosome Mapping↗

PubMedDate not supplied

Spatial analysis of phosphorus sorption capacity in a semiarid altered wetland.

The observed increase in phosphorus (P) loading into the Jordan River could increase eutrophication processes in Lake Kinneret, the only freshwater lake in Israel, which provides 25% of the country's drinking water. The P may originate from the peat soils of the highly altered Hula Valley's semiarid wetland ecosystem through which the Jordan River runs. The objectives of this research were to ascertain the sorption capacity of these soils and to identify areas with high potential for P release from soils to ground water. We extracted 80 soil samples collected across the valley with ammonium oxalate and determined the ratio of extractable P to Fe and Al, from which we derived the degree of phosphorus saturation (DPS). A relatively low DPS (<15%) was observed in Histosols compared with the high DPS (>30%) observed in many of the hydromorphic organo-mineral soils. We used a sequential Gaussian simulation technique to assess the spatial pattern of the DPS and found that the Histosols have a low probability (<10%) of exceeding the widely used environmental DPS threshold of 25%. The areas characterized by mineral soils, such as hydromorphic Vertisols and various marl redoximorphic soils, have a high probability (>60%) of exceeding the threshold value. The ability to predict the concentrations of dissolved P in ground water based on DPS values was somewhat impaired because of the preferential flow characteristics in this altered wetland.

Adsorption↗

PubMed2001

"Voxel-based morphometry" should not be used with imperfectly registered images.

John Ashburner and Karl Friston (2000) introduced a standardized method of "voxel-based morphometry" (VBM) for comparisons of local concentrations of gray matter between two groups of subjects. Segmented images of gray matter from grossly normalized high-resolution images are smoothed and their group differences analyzed by the now-conventional voxelwise Worsley approach to Gaussian random fields of differences. This comment concerns an unfortunate interaction between the algorithm's spatial normalization and voxelwise comparison steps, whereby several obvious quantitative confounds are injected at the core of the inference engine the authors put forward. Specifically, the statistics of the resulting voxelwise comparisons are uninformative about group differences wherever the spatial normalization algorithm has failed to register on any robustly appearing image gradient. The method of Ashburner and Friston is defensible only far from all image gradients.

Artifacts↗

PubMed1996

The registration of MR images using multiscale robust methods.

Acquisition of MR images involves their registration against some prechosen reference image. Motion artifacts and misregistration can seriously flaw their interpretation and analysis. This article provides a global registration method that is robust in the presence of noise and local distortions between pairs of images. It uses a two-stage approach, comprising an optional Fourier phase-matching method to carry out preregistration, followed by an iterative procedure. The iterative stage uses a prescribed set of registration points, defined on the reference image, at which a robust nonlinear regression is computed from the squared residuals at these points. The method can readily accommodate general linear or even nonlinear, registration transformations on the images. The algorithm was tested by recovering the registration transformation parameters when a 256 x 256 pixel T2*-weighted human brain image was scaled, rotated, and translated by prescribed amounts, and to which different amounts of Gaussian noise had been added. The results show subpixel accuracy of recovery when no noise is present, and graceful degradation of accuracy as noise is added. When 40% noise is added to images undergoing small shifts, the recovery errors are less than 3 pixels. The same tests applied to the Woods algorithm gave slightly inferior accuracy for these images, but failed to converge to the correct parameters in some cases of large-scale-shifted images with 10% added noise.

Algorithms↗

PubMed2001

Dynamic random effects models for times between repeated events.

We consider recurrent event data when the duration or gap times between successive event occurrences are of intrinsic interest. Subject heterogeneity not attributed to observed covariates is usually handled by random effects which result in an exchangeable correlation structure for the gap times of a subject. Recently, efforts have been put into relaxing this restriction to allow non-exchangeable correlation. Here we consider dynamic models where random effects can vary stochastically over the gap times. We extend the traditional Gaussian variance components models and evaluate a previously proposed proportional hazards model through a simulation study and some examples. Besides, semiparametric estimation of the proportional hazards models is considered. Both models are easily used. The Gaussian models are easily interpreted in terms of the variance structure. On the other hand, the proportional hazards models would be more appropriate in the context of survival analysis, particularly in the interpretation of the regression parameters. They can be sensitive to the choice of model for random effects but not to the choice of the baseline hazard function.

Animals↗