the distribution of maxima of approximately gaussian random fields motivated by the problem of testing for the existence of a signal of known parametric structure and unknown location as explained below against a noisy background we obtain for the maximum of a centered smooth random field an approximation for the tail of the distribution for the motivating class of problems this gives approximately the significance level of the maximum score test the method is based on an application of a likelihood ratio identity followed by approximations of local fields numerical examples illustrate the accuracy of the approximations

multi stage robust chinese remainder theorem it is well known that the traditional chinese remainder theorem crt is not robust in the sense that a small error in a remainder may cause a large reconstruction error a robust crt was recently proposed for a special case when the greatest common divisor gcd of all the moduli is more than 1 and the remaining integers factorized by the gcd are co prime it basically says that the reconstruction error is upper bounded by the remainder error level tau if tau is smaller than a quarter of the gcd of all the moduli in this paper we consider the robust reconstruction problem for a general set of moduli we first present a necessary and sufficient condition on the remainder errors with a general set of moduli and also a corresponding robust reconstruction method this can be thought of as a single stage robust crt we then propose a two stage robust crt by grouping the moduli into several groups as follows first the single stage robust crt is applied to each group then with these robust reconstructions from all the groups the single stage robust crt is applied again across the groups this is easily generalized to multi stage robust crt with this two stage robust crt the robust reconstruction holds even when the remainder error level tau is above the quarter of the gcd of all the moduli and an algorithm on how to group a set of moduli for a better reconstruction robustness is proposed in some special cases

spatial normalization of diffusion tensor mri using multiple channels diffusion tensor mri dt mri can provide important in vivo information for the detection of brain abnormalities in diseases characterized by compromised neural connectivity to quantify diffusion tensor abnormalities based on voxel based statistical analysis spatial normalization is required to minimize the anatomical variability between studied brain structures in this article we used a multiple input channel registration algorithm based on a demons algorithm and evaluated the spatial normalization of diffusion tensor image in terms of the input information used for registration registration was performed on 16 dt mri data sets using different combinations of the channels including a channel of t2 weighted intensity a channel of the fractional anisotropy a channel of the difference of the first and second eigenvalues two channels of the fractional anisotropy and the trace of tensor three channels of the eigenvalues of the tensor and the six channel tensor components to evaluate the registration of tensor data we defined two similarity measures i e the endpoint divergence and the mean square error which we applied to the fiber bundles of target images and registered images at the same seed points in white matter segmentation we also evaluated the tensor registration by examining the voxel by voxel alignment of tensors in a sample of 15 normalized dt mris in all evaluations nonlinear warping using six independent tensor components as input channels showed the best performance in effectively normalizing the tract morphology and tensor orientation we also present a nonlinear method for creating a group diffusion tensor atlas using the average tensor field and the average deformation field which we believe is a better approach than a strict linear one for representing both tensor distribution and morphological distribution of the population

unified framework for anisotropic interpolation and smoothing of diffusion tensor images to enhance the performance of diffusion tensor imaging dti based fiber tractography this study proposes a unified framework for anisotropic interpolation and smoothing of dti data the critical component of this framework is an anisotropic sigmoid interpolation kernel which is adaptively modulated by the local image intensity gradient profile the adaptive modulation of the sigmoid kernel permits image smoothing in homogeneous regions and meanwhile guarantees preservation of structural boundaries the unified scheme thus allows piece wise smooth continuous and boundary preservation interpolation of dti data so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure the new interpolation method is compared with conventional interpolation methods on the basis of fiber tracking from synthetic and in vivo dti data which demonstrates the effectiveness of this unified framework

some asymptotic results of gaussian random fields with varying mean functions and the associated processes in this paper we derive tail approximations of integrals of exponential functions of gaussian random elds with varying mean functions and approximations of the associated point processes this study is motivated naturally by multiple applications such as hypothesis testing for spatial models study of the distribution of bayesian marginal likelihood and bayes factor and nancial applications

laplace transform of product of generalized marcum q bessel i and power functions with applications integral transforms of special functions often occur in different research and practical areas analyzing the kappa mu fading distribution also known as the generalized rician distribution we find out that the assessment of a few different performance metrics involves the evaluation of an improper integral expressed as the laplace transform of product of marcum q bessel i and power functions we evaluate this integral in a closed form and apply the derived results to assess the probability of detection of unknown signals over kappa mu fading channels as well as to evaluate the outage probability under interference limited kappa mu fading scenarios with kappa mu faded co channel interference

selecting wavelengths for least squares range estimation we consider the problem of estimating the distance or range between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations traditional estimators developed for optical interferometry include the beat wavelength and excess fractions methods more recently estimators based on the chinese remainder theorem crt and least squares have appeared recent research suggests the least squares estimator to be the most accurate in many cases the accuracy of all of these range estimators depends upon the wavelengths chosen this leads to the problem of selecting wavelengths that maximize accuracy procedures for selecting wavelengths for the beat wavelength and excess fractions methods have previously been described but procedures for the crt and least squares estimators are yet to be developed in this paper we develop an algorithm to automatically select wavelengths for use with the least square range estimator the algorithm minimizes an optimization criterion connected with the mean square error interesting properties of a particular class of lattices simplify the criterion allowing minimization by depth first search monte carlo simulations indicate that wavelengths that minimize the criterion can result in considerably more accurate range estimates than wavelengths selected by ad hoc means

a fourier approach to nonparametric deconvolution of a density estimate we consider the problem of constructing a nonparametric estimate of a probability density function h from independent random samples of observations from densities a and f when a represents the convolution of h and f our approach is based on truncated fourier inversion in which the truncation point plays the role of a smoothing parameter we derive the asymptotic mean integrated squared error of the estimate and use this formula to suggest a simple practical method for choosing the truncation point from the data strikingly when the smoothing parameter is chosen in this way then in many circumstances the estimator behaves to first order as though the true f were known

dynamic range of the detectable parameters for polynomial phase signals using multiple lag diversities in high order ambiguity functions two lag diversities in the high order ambiguity functions for single component polynomial phase signals pps was explored by zhou and wang see ieee signal processing lett vol 4 p 240 42 1997 and signal processing vol 65 no 2 p 1452 55 1998 the lag diversity enlarges the dynamic range of the detectable parameters for pps in this paper we first find a connection between the above multiple lag diversity problem and the multiple undersampling problem in the frequency detection using discrete fourier transform dft using the connection and some results on the multiple undersampling problem we recently obtained we prove that the dynamic range obtained by zhou and wang is already the maximal one for the detectable parameters for single component pps furthermore the dynamic range for the detectable parameters for multicomponent pps is given when multiple lag diversities are used we show that the maximal dynamic range is reached when the number of the lags in the high order ambiguity function haf is at least twice of the number of the single components in a multicomponent pps more lags than twice the number of single components do not increase the dynamic range

nonparametric ridge estimation we study the problem of estimating the ridges of a density function ridge estimation is an extension of mode finding and is useful for understanding the structure of a density it can also be used to find hidden structure in point cloud data we show that under mild regularity conditions the ridges of the kernel density estimator consistently estimate the ridges of the true density when the data are noisy measurements of a manifold we show that the ridges are close and topologically similar to the hidden manifold to find the estimated ridges in practice we adapt the modified mean shift algorithm proposed by ozertem and erdogmus j mach learn res 12 2011 1249 1286 some numerical experiments verify that the algorithm is accurate

an empirical bayes approach to directional data and efficient computation on the sphere this paper proposes a consistent nonparametric empirical bayes estimator of the prior density for directional data the methodology is to use fourier analysis on s 2 to adapt euclidean techniques to this non euclidean environment general consistency results are obtained in addition a discussion of efficient numerical computation of fourier transforms on s 2 is given and their applications to the methods suggested in this paper are sketched

regression models for identifying noise sources in magnetic resonance images stochastic noise susceptibility artifacts magnetic field and radiofrequency inhomogeneities and other noise components in magnetic resonance images mris can introduce serious bias into any measurements made with those images we formally introduce three regression models including a rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities including diffusion weighted imaging dwi and functional mri fmri estimation algorithms are introduced to maximize the likelihood function of the three regression models we also develop a diagnostic procedure for systematically exploring mr images to identify noise components other than simple stochastic noise and to detect discrepancies between the fitted regression models and mri data the diagnostic procedure includes goodness of fit statistics measures of influence and tools for graphical display the goodness of fit statistics can assess the key assumptions of the three r

tracking and localizing moving targets in the presence of phase measurement ambiguities when tracking a target using phase only signal returns range ambiguities due to the modulo 2 in measured signal phases are a major issue standard approaches to such problems would typically involve the use of diophantine equations in this paper a simpler and robust solution is examined which uses look up tables defined between the phase measurement and target location spaces to determine the phase measurement mapping we show first that when the target motion is significant between data sampling intervals the location ambiguity can be resolved over time via known target in cluster tracking techniques this method determines the optimal allocation of location with respect to phase measurements relative to the quantization of look up table values second when the target is undergoing micromotions jitter which results in the same collection of candidate locations from phase measurements over time the location ambiguity can be resolved using a novel phase distribution discrimination method in this method a probability density function of the ambiguous phase only measurement is derived that takes both sensor noise and target motion distributions into account based on directional statistics optimal locations are inferred from such distributions examples are given to demonstrate the effectiveness of these proposed methods

fiber tracking from dti using linear state space models detectability of the pyramidal tract abstract diffusiontensor imaging dti is an emerging and promising tool to provide information about the course of white matter fiber tracts in the human brain based on specific acquisition schemes diffusion tensor data resemble local fiber orientations allowing for a reconstruction of the fiber bundles current techniques to calculate fascicles range from simple heuristic tracking solutions to bayesian and differential equations approaches most methods are based only on local diffusion information often resulting in bending or kinking fiber paths in voxels with reduced diffusion properties in this article we present a new tracking approach based on linear state space models encompassing an inherent smoothness criterion to avoid too wiggly tracked fiber bundles the new technique will be described formally and tested on simulated and real data the performance tests are focused on the pyramidal tract where we employed a test retest study and a group comparison in healthy subjects anatomical course was confirmed in a patient with selective degeneration of the pyramidal tract the potential of the presented technique for improved neurosurgical planning is demonstrated by visualization of a tumor induced displacement of the motor pathways the paper closes with a thorough discussion of perspectives and limitations of the new tracking approach

dti segmentation via the combined analysis of connectivity maps and tensor distances we describe a novel approach to extract the neural tracts of interest from a diffusion tensor image dti compared to standard streamline tractography existing probabilistic methods are able to capture fiber paths that deviate from the main tensor diffusion directions at the same time tensor clustering methods are able to more precisely delimit the border of the bundle to the best of our knowledge we propose the first algorithm which combines the advantages supplied by probabilistic and tensor clustering approaches the algorithm includes a post processing step to limit partial volume related segmentation errors we extensively test the accuracy of our algorithm on different configurations of a dti software phantom for which we systematically vary the image noise the number of gradients the geometry of the fiber paths and the angle between adjacent and crossing fiber bundles the reproducibility of the algorithm is supported by the segmentation of the corticospinal tract of nine patients additional segmentations of the corticospinal tract the arcuate fasciculus and the optic radiations are in accordance with anatomical knowledge the required user interaction is comparable to that of streamline tractography which allows for an uncomplicated integration of the algorithm into the clinical routine

polynomial phase estimation by least squares phase unwrapping estimating the coefficients of a noisy polynomial phase signal is important in fields including radar biology and radio communications one approach attempts to perform polynomial regression on the phase of the signal this is complicated by the fact that the phase is wrapped modulo 2 and must be unwrapped before regression can be performed in this paper we consider an estimator that performs phase unwrapping in a least squares manner we call this the least squares unwrapping lsu estimator the lsu estimator can be computed in a reasonable amount of time for data sets of moderate size using existing general purpose algorithms from algebraic number theory under mild conditions on the distribution of the noise we describe the asymptotic properties of this estimator showing that it is strongly consistent and asymptotically normally distributed a key feature is that the lsu estimator is accurate over a far wider range of parameters than many popular existing estimators monte carlo simulations support our theoretical results and demonstrate the excellent statistical performance of the lsu estimator when compared with existing state of the art estimators

on the path density of a gradient field we consider the problem of reliably finding filaments in point clouds realistic data sets often have numerous filaments of various sizes and shapes statistical techniques exist for finding one or a few filaments but these methods do not handle noisy data sets with many filaments other methods can be found in the astronomy literature but they do not have rigorous statistical guarantees we propose the following method starting at each data point we construct the steepest ascent path along a kernel density estimator we locate filaments by finding regions where these paths are highly concentrated formally we define the density of these paths and we construct a consistent estimator of this path density

deconvolution density estimation on so n this paper develops nonparametric deconvolution density estimation over so n the group of n x n orthogonal matrices of determinant 1 the methodology is to use the group and manifold structures to adapt the euclidean deconvolution techniques to this lie group environment this is achieved by employing the theory of group representations explicit to so n general consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions application to empirical bayes prior estimation and inference is also discussed

euler characteristics for gaussian fields on manifolds we are interested in the geometric properties of real valued gaussian random fields defined on manifolds our manifolds m are of class c3 and the random fields f are smooth our interest in these fields focuses on their excursion sets f 1 u and their geometric properties specifically we derive the expected euler characteristic ee f 1 u of an excursion set of a smooth gaussian random field part of the motivation for this comes from the fact that ee f 1 u relates global properties of m to a geometry related to the covariance structure of f of further interest is the relation between the expected euler characteristic of an excursion set above a level u and pp supp mf p u our proofs rely on results from random fields on rrn as well as differential and riemannian geometry

a diffusion tensor imaging tractography algorithm based on navier stokes fluid mechanics we introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging dti volumes we customize the navier stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the dti image volume we then estimate the most likely connection paths between points in the dti volume using a metric derived from the fluid velocity vector field we validate our algorithm using digital dti phantoms based on a helical shape our method segmented the structure of the phantom with less distortion than was produced using implementations of heat based partial differential equation pde and streamline based methods in addition our method was able to successfully segment divergent and crossing fiber geometries closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts to assess the performance of our algorithm on anatomical data we applied our method to dti volumes from normal human subjects our method produced paths that were consistent with both known anatomy and directionally encoded color images of the dti dataset

error correction in polynomial remainder codes with non pairwise coprime moduli and robust chinese remainder theorem for polynomials this paper investigates polynomial remainder codes with non pairwise coprime moduli we first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small namely the robust chinese remainder theorem crt for polynomials it basically says that a polynomial can be reconstructed from its erroneous residues such that the degree of the reconstruction error is upper bounded by tau whenever the degrees of all residue errors are upper bounded by tau where a sufficient condition for tau and a reconstruction algorithm are obtained by relaxing the constraint that all residue errors have small degrees another robust reconstruction is then presented when there are multiple unrestricted errors and an arbitrary number of errors with small degrees in the residues we finally obtain a stronger residue error correction capability in the sense that apart from the number of errors that can be corrected in the previous existing result some errors with small degrees can be also corrected in the residues with this newly obtained result improvements in uncorrected error probability and burst error correction capability in data transmission are illustrated

minimax estimation for mixtures of wishart distributions the space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference many books and papers have been written on this subject and more recently there has been considerable interest in high dimensional random matrices with particular emphasis on the distribution of certain eigenvalues with the availability of modern data acquisition capabilities smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in euclidean spaces accordingly we present a fourier method of minimax wishart mixture density estimation on the space of positive definite symmetric matrices

a novel tensor distribution model for the diffusion weighted mr signal diffusion mri is a non invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo the directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications in this paper we present a novel statistical model for diffusion weighted mr signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors an interesting observation is that this continuous mixture and the mr signal attenuation are related through the laplace transform of a probability distribution over symmetric positive definite matrices we then show that when the mixing distribution is a wishart distribution the resulting closed form of the laplace transform leads to a rigaut type asymptotic fractal expression which has been phenomenologically used in the past to explain the mr signal decay but never with a rigorous mathematical justification until now our model not only includes the traditional diffusion tensor model as a special instance in the limiting case but also can be adjusted to describe complex tissue structure involving multiple fiber populations using this new model in conjunction with a spherical deconvolution approach we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel by voxel basis experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms

testing for a signal with unknown location and scale in a stationary gaussian random field we suppose that our observations can be decomposed into a fixed signal plus random noise where the noise is modelled as a particular stationary gaussian random field in n dimensional euclidean space the signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude and we are primarily interested in a test to detect such a signal there are many examples where the signal scale or width is assumed known and the test is based on maximising a gaussian random field over all locations in a subset of n dimensional euclidean space the novel feature of this work is that the width of the signal is also unknown and the test is based on maximising a gaussian random field in n 1 dimensions n dimensions for the location plus one dimension for the width two convergent approaches are used to approximate the null distribution one based on the method of knowles and siegmund which uses a version of weyl s tube formula for manifolds with boundaries and the other based on some recent work by worsley which uses the hadwiger characteristic of excursion sets as introduced by adler finally we compare the power of our method with one based on a fixed but perhaps incorrect signal width

on the calculation of the generalized q function via parl s method corresp parl has previously given error bounds suitable for calculating marcum s q function however it is shown that additional terms in the error bound are necessary for accurate calculations of the generalized q function q m alpha beta the values of m alpha and beta that result in successful algorithm completion are examined numerical results are presented for calculations of the noncentral chi square distribution and the probability of detection for a classical multiobservation detection problem

spatial shrinkage estimation of diffusion tensors on diffusion weighted imaging data diffusion tensor imaging dti based on the diffusion weighted imaging dwi data acquired from magnetic resonance experiments has been widely used to analyze the physical structure of white matter fibers in the human brain in vivo the raw dwi data however carry noise this contaminates the diffusion tensor dt estimates and introduces systematic bias into the induced eigenvalues these bias components affect the effectiveness of fiber tracking algorithms in this article we propose a two stage spatial shrinkage estimation spske procedure to accommodate the spatial information carried in dwi data in dt estimation and to reduce the bias components in the corresponding derived eigenvalues to this end in the framework of the heteroscedastic linear model spske incorporates l 1 type penalization and the locally weighted least square function the theoretical properties of spske are explored the effectiveness of spske is further illustrated by simulation and real data examples supplementary materi

statistical inverse estimation in hilbert scales the recovery of signals from indirect measurements blurred by random noise is considered under the assumption that prior knowledge regarding the smoothness of the signal is avialable for greater flexibility the general problem is embedded in an abstract hilbert scale in the applications sobolev scales are used for the construction of estimators we employ preconditioning along with regularized operator inversion in the appropriate inner product where the operator is bounded but not necessarily compact a lower bound to certain minimax rates is included and it is shown that in generic examples the proposed estimators attain the asymptotic minimax rate examples include errors in variables deconvolution and indirect nonparametric regression special instances of the latter are estimation of the source term in a differential equation and the estimation of the initial state in the heat equation

exact and robust reconstructions of integer vectors based on multidimensional chinese remainder theorem md crt the robust chinese remainder theorem crt has been recently proposed for robustly reconstructing a large nonnegative integer from erroneous remainders it has found many applications in signal processing including phase unwrapping and frequency estimation under sub nyquist sampling motivated by the applications in multidimensional md signal processing in this article we propose the md crt and robust md crt for integer vectors specifically by rephrasing the abstract crt for rings in number theoretic terms we first derive the md crt for integer vectors with respect to a general set of integer matrix moduli which provides an algorithm to uniquely reconstruct an integer vector from its remainders if it is in the fundamental parallelepiped of the lattice generated by a least common right multiple of all the moduli for some special forms of moduli we present explicit reconstruction formulae moreover we derive the robust md crt for integer vectors when the remaining integer matrices of all the moduli left divided by their greatest common left divisor gcld are pairwise commutative and coprime two different reconstruction algorithms are proposed and accordingly two different conditions on the remainder error bound for the reconstruction robustness are obtained which are related to a quarter of the minimum distance of the lattice generated by the gcld of all the moduli or the smith normal form of the gcld

optimum statistical estimates in conditions of ambiguity an ambiguity problem arises if a distance is measured by observing phase shift of signals when the range of the measured distance is greater than the wavelength of the signals used this ambiguity generally can be resolved by pumping extra information into the system a classical estimation problem is the obtained at the expense of reduced autonomy of the estimator due to the demand for external information not inherent to the system the interval lambda of the unambiguous estimates can be considerably extended using observations of several different wavelengths lambda sub i this yields lambda as the least common multiple of all lambda sub i a method of developing optimum estimation rules for this case is introduced optimum estimation rules for some typical cases with gaussian observation errors are also developed

a robust generalized chinese remainder theorem for two integers a generalized chinese remainder theorem crt for multiple integers from residue sets has been studied recently where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known a robust crt has also been proposed lately to robustly reconstruct a single integer from its erroneous remainders in this paper we consider the reconstruction problem of two integers from their residue sets where the remainders not only are out of order but also may have errors we prove that two integers can be robustly reconstructed if their remainder errors are less than m 8 where m is the greatest common divisor of all the moduli we also propose an efficient reconstruction algorithm finally we present some simulations to verify the efficiency of the proposed algorithm this paper is motivated from and has applications in the determination of multiple frequencies from multiple undersampled waveforms

applications of invariant differential operators to multivariate distribution theory the invariant differential operators are applied to derive partial differential equations for the zonal polynomials to calculate generalized binomial coefficients and certain multivariate integrals and to deduce a characterization of ep functions kushner lebow and meisner j multivariate anal 11 1981 pp 418 433

diffusion based spatial priors for functional magnetic resonance images we recently outlined a bayesian scheme for analyzing fmri data using diffusion based spatial priors harrison l m penny w ashburner j trujillo barreto n friston k j 2007 diffusion based spatial priors for imaging neuroimage 38 677 695 the current paper continues this theme applying it to a single subject functional magnetic resonance imaging fmri study of the auditory system we show that spatial priors on functional activations based on diffusion can be formulated in terms of the eigenmodes of a graph laplacian this allows one to discard eigenmodes with small eigenvalues to provide a computationally efficient scheme furthermore this formulation shows that diffusion based priors are a generalization of conventional laplacian priors penny w d trujillo barreto n j friston k j 2005 bayesian fmri time series analysis with spatial priors neuroimage 24 350 362 finally we show how diffusion based priors are a special case of gaussian process models that can be inverted using classical covariance component estimation techniques like restricted maximum likelihood patterson h d thompson r 1974 maximum likelihood estimation of components of variance paper presented at 8th international biometrics conference constanta romania the convention in spm is to smooth data with a fixed isotropic gaussian kernel before inverting a mass univariate statistical model this entails the strong assumption that data are generated smoothly throughout the brain however there is no way to determine if this assumption is supported by the data because data are smoothed before statistical modeling in contrast if a spatial prior is used smoothness is estimated given non smoothed data explicit spatial priors enable formal model comparison of different prior assumptions e g that data are generated from a stationary i e fixed throughout the brain or non stationary spatial process indeed for the auditory data we provide strong evidence for a non stationary process which concurs with a qualitative comparison of predicted activations at the boundary of functionally selective regions

a non iterative multiple residue digit error detection and correction algorithm in rrns error detection and correction code based on redundant residue number system rrns has a unique advantage that arithmetical processing errors can also be corrected existing algorithms for multiple residue digit error correction in rrns require either large modulo operations to decode the magnitude of the residue digits or variable number of iterative computations to identify the locations of erroneous residue digits this paper presents an efficient syndrome based multiple residue digit error detection and correction algorithm in rrns the received residue digits are divided into three groups from which seven error location categories are defined for all combinations of residue digit errors of any legitimate moduli set their error magnitudes are abstracted into three syndromes which are used to identify the exact error location category and retrieve the residue digit errors concurrently from six lookup tables in no more than three cycles the syndromes can be computed in parallel by small modulo subtractors and their uniqueness criteria are proved to be easily fulfilled the redundant residue space due to the uniqueness criteria can also be relaxed by increasing the number of syndrome computations and lookup tables used for the error decoding according to the number of information moduli

filtered multitensor tractography we describe a technique that uses tractography to drive the local fiber model estimation existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit we formulate fiber tracking as recursive estimation at each step of tracing the fiber the current estimate is guided by those previous to do this we perform tractography within a filter framework and use a discrete mixture of gaussian tensors to model the signal starting from a seed point each fiber is traced to its termination using an unscented kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction despite the presence of noise and uncertainty this provides a causal estimate of the local structure at each point along the fiber using two and three fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings in vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization

estimation of integral curves from high angular resolution diffusion imaging hardi data we develop statistical methodology for a popular brain imaging technique hardi based on the high order tensor model by ozarslan and mareci 10 we investigate how uncertainty in the imaging procedure propagates through all levels of the model signals tensor fields vector fields and fibers we construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids the procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis the theoretical results are illustrated on simulated and real datasets this work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by carmichael and sakhanenko 3 to several fibers per voxel it is also a pioneering statistical work on tractography from hardi data it avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods our method is computationally cheap and it provides well founded mathematical and statistical framework where diverse functionals on fibers directions and tensors can be studied in a systematic and rigorous way

a sharpened dynamic range of a generalized chinese remainder theorem for multiple integers a generalized chinese remainder theorem crt for multiple integers from residue sets has been studied recently where the remainders in a residue set are not ordered in this correspondence we first propose a majority method and then based on the proposed majority method we present a sharpened dynamic range of multiple integers that can be uniquely determined from their residue sets

fast fault tolerant digital convolution using a polynomial residue number system a fault tolerant convolution algorithm that is an extension of residue number system fault tolerance schemes applied to polynomial rings is described the algorithm is suitable for implementation on multiprocessor systems and is able to concurrently mask processor failures a fast algorithm based on long division for detecting and correcting multiple processor failures is presented moduli polynomials that yield an efficient and robust fast fourier transform fft based algorithm are selected for this implementation a single fault detection and correction is studied and a generalized likelihood ratio test is applied to optimally detect system failures in the presence of computational noise the coding scheme is capable of protecting over 90 of the computation involved in convolution parts not covered by the scheme are assumed to be protected via triple modular redundancy this hybrid approach can detect and correct any single system failure with as little as 70 overhead compared with 200 needed for a system fully protected via modular redundancy

integral curves of noisy vector fields and statistical problems in diffusion tensor imaging nonparametric kernel estimation and hypotheses testing let v be a vector field in a bounded open set g d suppose that v is observed with a random noise at random points x i i 1 n that are independent and uniformly distributed in g the problem is to estimate the integral curve of the differential equation dx t dt q x 0 x 0 g starting at a given point x 0 x 0 g and to develop statistical tests for the hypothesis that the integral curve reaches a specified set r c g we develop an estimation procedure based on a nadaraya watson type kernel regression estimator show the asymptotic normality of the estimated integral curve and derive differential and integral equations for the mean and covariance function of the limit gaussian process this provides a method of tracking not only the integral curve but also the covariance matrix of its estimate we also study the asymptotic distribution of the squared minimal distance from the integral curve to a smooth enough surface r c g building upon this we develop testing procedures for the hypothesis that the integral curve reaches r the problems of this nature are of interest in diffusion tensor imaging a brain imaging technique based on measuring the diffusion tensor at discrete locations in the cerebral white matter where the diffusion of water molecules is typically anisotropic the diffusion tensor data is used to estimate the dominant orientations of the diffusion and to track white matter fibers from the initial location following these orientations our approach brings more rigorous statistical tools to the analysis of this problem providing in particular hypothesis testing procedures that might be useful in the study of axonal connectivity of the white matter

statistical analysis of diffusion tensors in diffusion weighted magnetic resonance imaging data diffusion tensor imaging has been widely used to reconstruct the structure and orientation of fibers in biological tissues particularly in the white matter of the brain because it can track the effective diffusion of water along those fibers the raw diffusion weighted images from which diffusion tensors are estimated however inherently contain noise noise in the images produces uncertainty in the estimation of the tensors which are 3 3 positive definite matrices and of their derived quantities including eigenvalues eigenvectors and the fiber pathways that are reconstructed based on those tensor elements the aim of this article is to provide a comprehensive theoretical framework of statistical inference for quantifying the effects of noise on diffusion tensors on their eigenvalues and eigenvectors and on their morphological classification we propose a semiparametric model to account for noise in diffusion weighted images we then develop a one step weighted least squares estimate of the t

chi 2 random fields in space and time this paper introduces some 2 random functions which are not homogeneous stationary in general but contain the stationary case as a special case and whose correlation structures are nonparametric and flexible so that many parametric forms can be specified the mean square differentiability of such 2 random function is discussed we also make the comparison of two 2 random functions through their finite dimensional laplace transforms

a robust chinese remainder theorem with its applications in frequency estimation from undersampled waveforms the chinese remainder theorem crt allows to reconstruct a large integer from its remainders modulo several moduli in this paper we propose a robust reconstruction algorithm called robust crt when the remainders have errors we show that using the proposed robust crt the reconstruction error is upper bounded by the maximal remainder error range named remainder error bound if the remainder error bound is less than one quarter of the greatest common divisor gcd of all the moduli we then apply the robust crt to estimate frequencies when the signal waveforms are undersampled multiple times it shows that with the robust crt the sampling frequencies can be significantly reduced

manifold estimation and singular deconvolution under hausdorff loss we find lower and upper bounds for the risk of estimating a manifold in hausdorff distance under several models we also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure

deterministic and probabilistic tractography based on complex fibre orientation distributions we propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function odf estimated from high angular resolution diffusion imaging hardi we show that in order to perform accurate probabilistic tractography one needs to use a fibre odf estimation and not the diffusion odf we use a new fibre odf estimation obtained from a sharpening deconvolution transform sdt of the diffusion odf reconstructed from q ball imaging qbi this sdt provides new insight into the relationship between the hardi signal the diffusion odf and the fibre odf we demonstrate that the sdt agrees with classical spherical deconvolution and improves the angular resolution of qbi another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre odf an extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions finally as an application of our new probabilistic tracking we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects most current diffusion tensor imaging dti based methods neglect these fibres which might lead to incorrect interpretations of brain functions

a closed form robust chinese remainder theorem and its performance analysis chinese remainder theorem crt reconstructs an integer from its multiple remainders that is well known not robust in the sense that a small error in a remainder may cause a large error in the reconstruction a robust crt has been recently proposed when all the moduli have a common factor and the robust crt is a searching based algorithm and no closed from is given in this paper a closed form robust crt is proposed and a necessary and sufficient condition on the remainder errors for the closed form robust crt to hold is obtained furthermore its performance analysis is given it is shown that the reason for the robustness is from the remainder differential process in both searching based and our proposed closed form robust crt algorithms which does no exist in the traditional crt we also propose an improved version of the closed form robust crt finally we compare the performances of the traditional crt the searching based robust crt and our proposed closed form robust crt and its improved version algorithms in terms of both theoretical analysis and numerical simulations the results demonstrate that the proposed closed form robust crt its improved version has the best performance has the same performance but much simpler form than the searching based robust crt

theoretical analysis of nonparametric filament estimation this paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density f points on the filament are considered as local extrema of the density when traversing the support of f along the integral curve driven by the vector field of second eigenvectors of the hessian of f we parametrize points on the filaments by such integral curves and thus both the estimation of integral curves and of filaments will be considered via a plug in method using kernel density estimation we establish rates of convergence and asymptotic distribution results for the estimation of both the integral curves and the filaments the main theoretical result establishes the asymptotic distribution of the uniform deviation of the estimated filament from its theoretical counterpart this result utilizes the extreme value behavior of non stationary gaussian processes indexed by manifolds m h h in 0 1 as h to 0

multivariate analysis and jacobi ensembles largest eigenvalue tracy widom limits and rates of convergence abstract let a and b be independent central wishart matrices in p variables with common covariance and having m and n degrees of freedom respectively the distribution of the largest eigenvalue of a b 1 b has numerous applications in multivariate statistics but is difficult to calculate exactly suppose that m and n grow in proportion to p we show that after centering and scaling the distribution is approximated to second order o p 2 3 by the tracy widom law the results are obtained for both complex and then real valued data by using methods of random matrix theory to study the largest eigenvalue of the jacobi unitary and orthogonal ensembles asymptotic approximations of jacobi polynomials near the largest zero play a central role

optimal estimates of two common remainders for a robust generalized chinese remainder theorem estimation of multiple common remainders from a sequence of erroneous residue sets is an important step for the robust generalized chinese remainder theorem crt this paper considers the problem of how to estimate the two common remainders from their residue sets modulo a set of moduli to measure the errors properly under the modular operation we introduce two type circular distances based on these circular distances two estimation methods are proposed by properly grouping the erroneous remainders into two ordered clusters both of the two methods perform better with lower computational complexities than the existing methods in this paper theoretical analysis as well as analytical results for the two proposed methods are obtained for the first method the two optimal estimates are proved to be in a finite set with no more than l candidates where l is the number of the given moduli the second method have closed forms simulation results show that the two proposed methods have nearly the same performance these optimal estimates can improve the performance of the robust generalized crt significantly

uniform in bandwidth consistency of kernel type function estimators we introduce a general method to prove uniform in bandwidth consistency of kernel type function estimators examples include the kernel density estimator the nadaraya watson regression estimator and the conditional empirical process our results may be useful to establish uniform consistency of data driven bandwidth kernel type function estimators

wishart distributions for decomposable graphs when considering a graphical gaussian model n g markov with respect to a decomposable graph g the parameter space of interest for the precision parameter is the cone p g of positive definite matrices with fixed zeros corresponding to the missing edges of g the parameter space for the scale parameter of n g is the cone q g dual to p g of incomplete matrices with submatrices corresponding to the cliques of g being positive definite in this paper we construct on the cones q g and p g two families of wishart distributions namely the type i and type ii wisharts they can be viewed as generalizations of the hyper wishart and the inverse of the hyper inverse wishart as defined by dawid and lauritzen ann statist 21 1993 1272 1317 we show that the type i and ii wisharts have properties similar to those of the hyper and hyper inverse wishart indeed the inverse of the type ii wishart forms a conjugate family of priors for the covariance parameter of the graphical gaussian model and is strong directed hyper markov for every direction given to the graph by a perfect order of its cliques while the type i wishart is weak hyper markov moreover the inverse type ii wishart as a conjugate family presents the advantage of having a multidimensional shape parameter thus offering flexibility for the choice of a prior both type i and ii wishart distributions depend on multivariate shape parameters a shape parameter is acceptable if and only if it satisfies a certain eigenvalue property we show that the sets of acceptable shape parameters for a noncomplete g have dimension equal to at least one plus the number of cliques in g these families as conjugate families are richer than the traditional diaconis ylvisaker conjugate families which all have a shape parameter set of dimension one a decomposable graph which does not contain a three link chain as an induced subgraph is said to be homogeneous in this case our wisharts are particular cases of the wisharts on homogeneous cones as defined by andersson and wojnar j theoret probab 17 2004 781 818 and the dimension of the shape parameter set is even larger than in the nonhomogeneous case it is indeed equal to the number of cliques plus the number of distinct minimal separators using the model where g is a three link chain we show by computing a 7 tuple integral that in general we cannot expect the shape parameter sets to have dimension larger than the number of cliques plus one

improved fiber tractography with bayesian tensor regularization diffusion tensor tractography suffers from the effects of noise and partial volume averaging pva for reliable reconstruction of fiber pathways tracking algorithms that are robust to these artifacts are called for to meet this need the present study establishes a novel bayesian regularization framework for fiber tracking that takes into account the effects of noise and pva thereby improving tracking accuracy and precision with this framework the propagation of a fiber path follows an optimal vector determined by bayes decision rule the probability functions involved are modeled on the basis of multivariate normal distributions of diffusion tensor elements which allows the optimal solution with maximum a posteriori probability to be derived analytically parameters for the probability functions are estimated from the uncertainty of tensor elements and the variance among tensors within an oriented sampling volume weighted by fractional anisotropy experiments with monte carlo simulations synthetic and in vivo human diffusion tensor data demonstrate that this specialized scheme enhances the immunity of fiber tracking to noise and pva and hence enables fibers to be more faithfully reconstructed

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

distance estimation using wrapped phase measurements in noise measuring a distance using phase measurements is a common practice in many areas of engineering almost inevitably these measurements are accompanied by noise and are always subject to ambiguity resulting from the phase of modulo 2 pi in the presence of phase ambiguity where for instance the unknown distance is far longer than the wavelength of the signal carrying the phase measurement the distance cannot be uniquely determined one way to resolve this phase ambiguity is to measure the signal phase at multiple frequencies converting the phase ambiguity problem into one of solving a family of diophantine equations typically under some reasonable assumptions the diophantine problems can be solved using the chinese reminder theorem as documented in the literature however the existing algorithms can experience significant computational overhead for a given application because an exhaustive search is required in this paper a novel method addressing the phase ambiguity issue using lattice theoretic ideas is proposed and a closed form algorithm is presented for the estimation of the number of wavelengths in the unknown distance using the phase measurements taken at multiple wavelengths the algorithm is extremely efficient as the diophantine equations are solved without searching the unknown distance can then be estimated via a maximum likelihood method using the unwrapped phase measurement a statistical bound of the measurement noise which ensures that the number of whole wavelengths in the unknown distance can be found with a probability close to unity is derived the robustness efficiency and estimation accuracy of the proposed method are demonstrated by the simulated results presented

modified q functions and their use in detection analysis the marcum s q function is extended to complex arguments in particular a set of modified generalized q functions for imaginary values of one or both arguments are defined and their properties are investigated an extended probabilistic interpretation for the modified q functions is given appealing to a proposed generalization of the concept of random variable complex pseudo random variables pseudo events and pseudo probability measures are defined which formally obey the usual rules of composition of probability measures of independent events the modified q functions are then used to derive the rayleigh multivariate multidimensional distribution function and the error probability for partially coherent detection of equicorrelated signals

frequency estimation by phase unwrapping single frequency estimation is a long studied problem with application domains including radar sonar telecommunications astronomy and medicine one method of estimation called phase unwrapping attempts to estimate the frequency by performing linear regression on the phase of the received signal this procedure is complicated by the fact that the received phase is wrapped modulo and therefore must be unwrapped before the regression can be performed in this paper we propose an estimator that performs phase unwrapping in the least squares sense the estimator is shown to be strongly consistent and its asymptotic distribution is derived we then show that the problem of computing the least squares phase unwrapping is related to a problem in algorithmic number theory known as the nearest lattice point problem we derive a polynomial time algorithm that computes the least squares estimator the results of various simulations are described for different values of sample size and snr

nonparametric estimation of a probability density on a riemannian manifold using fourier expansions supposing a given collection y 1 cdots y n of i i d random points on a riemannian manifold we discuss how to estimate the underlying distribution from a differential geometric viewpoint the main hypothesis is that the manifold is closed and that the distribution is sufficiently smooth under such a hypothesis a convergence arbitrarily close to the n 1 2 rate is possible both in the l 2 and the l infty senses

on the optimal rates of convergence for nonparametric deconvolution problems deconvolution problems arise in a variety of situations in statistics an interesting problem is to estimate the density f of a random variable x based on n i i d observations from y x varepsilon where varepsilon is a measurement error with a known distribution in this paper the effect of errors in variables of nonparametric deconvolution is examined insights are gained by showing that the difficulty of deconvolution depends on the smoothness of error distributions the smoother the harder in fact there are two types of optimal rates of convergence according to whether the error distribution is ordinary smooth or supersmooth it is shown that optimal rates of convergence can be achieved by deconvolution kernel density estimators

chinese remaindering with errors the chinese remainder theorem states that a positive integer m is uniquely specified by its remainder module k relatively prime integers p sub 1 spl middot spl middot spl middot p sub k provided m spl pi sub i 1 sup k p sub i thus the residues of m module relatively prime integers p sub 1 p sub 2 spl middot spl middot spl middot p sub n form a redundant representation of m if m spl pi sub i 1 sup k p sub i and k n this gives a number theoretic construction of an error correcting code that has been considered often in the past in this code a message integer m spl pi sub i 1 sup k p sub i is encoded by the list of its residues module p sub 1 spl middot spl middot spl middot p sub n by the chinese remainder theorem if a codeword is corrupted in e n k 2 coordinates then there exists a unique integer m whose corresponding codesword differs from the corrupted word in at most e places furthermore mandelbaum 1976 1978 shows how m can be recovered efficiently given the corrupted word provided that the p sub i s are very close to one another to deal with arbitrary p sub i s we present a variant of his algorithm that runs in almost linear time and recovers from e log p sub 1 log p sub 1 log p sub n spl middot n k errors our main contribution is an efficient decoding algorithm for the case in which the error e may be larger than n k 2 specifically given n residues r sub 1 spl middot spl middot spl middot r sub n and an agreement parameter t we find a list of all integers m spl pi sub i 1 sup k p sub i such that m mod p sub i r sub i for at least t values of i spl isin 1 spl middot spl middot spl middot n provided t spl omega spl radic kn log p sub n log p sub 1 for n spl gt k and p sub n spl les p sub 1 sup o 1 the fraction of error corrected by the algorithm is almost twice that corrected by the previous work more significantly the algorithm recovers the message even when the amount of agreement between the received word and the codeword is much smaller than the number of errors

integrated wavelet processing and spatial statistical testing of fmri data we introduce an integrated framework for detecting brain activity from fmri data which is based on a spatial discrete wavelet transform unlike the standard wavelet based approach for fmri analysis we apply the suitable statistical test procedure in the spatial domain for a desired significance level this scheme has one remaining degree of freedom characterizing the wavelet processing which is optimized according to the principle of minimal approximation error this allows us to determine the threshold values in a way that does not depend on data while developing our framework we make only conservative assumptions consequently the detection of activation is based on strong evidence we have implemented this framework as a toolbox wspm for the spm2 software taking advantage of multiple options and functions of spm such as the setup of the linear model and the use of the hemodynamic response function we show by experimental results that our method is able to detect activation patterns the results are comparable to those obtained by spm even though statistical assumptions are more conservative

error detection and correction in communication channels using inverse gray rsns codes a novel number theoretic transform called inverse gray robust symmetrical number system igrsns is proposed for error control coding in this paper igrsns is obtained by modifying robust symmetrical number system rsns that was proposed earlier using inverse gray code property due to ambiguities present in each residue rsns has a short dynamic range dr compared to that in other number systems the short dr of rsns enables it to be effectively used for error detection without the addition of any redundant modulus as in redundant residue number system although rsns has a large redundant range its detection ability is not optimal due to the gray code property associated with it in an attempt to overcome this limitation we have proposed inverse gray coding to be combined with rsns in increasing its effectiveness in error detection the resulting igrsns thus inherits properties of both rsns and gray code analysis and simulations show that igrsns has a near optimal error detection ability the potential of igrsns for error correction is also investigated further a novel error correction algorithm using one redundant modulus is proposed simulations show that the proposed algorithm performs well under all cases of single bit errors

multiple error detection and correction based on redundant residue number systems this paper presents some results on multiple error detection and correction based on the redundant residue number system rrns rrns is often used in parallel processing environments because of its ability to increase the robustness of information passing between the processors the proposed multiple error correction scheme utilizes the chinese remainder theorem crt together with a novel algorithm that significantly simplifies the error correcting process for integers an extension of the scheme further reduces the computational complexity without compromising its error correcting capability proofs and examples are provided for the coding technique

rotation space random fields with an application to fmri data siegmund and worsley considered the problem of testing for a signal with unknown location and scale in a gaussian random field defined on r n the test statistic was the maximum of a gaussian random field in an n 1 dimensional scale space n dimensions for location and one dimension for the scale of a smoothing kernel siegmund and worsley used two methods one involving the expected euler characteristic of the excursion set and the other involving the volume of tubes to derive an approximate null distribution the purpose of this paper is to extend the scale space result to the rotation space random field when n 2 where the maximum is taken over all rotations of the filter as well as scales we apply this result to the problem of searching for activation in brain images obtained by functional magnetic resonance imaging fmri

a bayesian approach to tracking multiple targets using sensor arrays and particle filters we present a bayesian approach to tracking the direction of arrival doa of multiple moving targets using a passive sensor array the prior is a description of the dynamic behavior we expect for the targets which is modeled as constant velocity motion with a gaussian disturbance acting on the target s heading direction the likelihood function is arrived at by defining an uninformative prior for both the signals and noise variance and removing these parameters from the problem by marginalization advances in sequential monte carlo smc techniques specifically the particle filter algorithm allow us to model and track the posterior distribution defined by the bayesian model using a collection of target states that can be viewed as samples from the posterior of interest we describe two versions of this algorithm and finally present results obtained using synthetic data

maximum likelihood estimation based robust chinese remainder theorem for real numbers and its fast algorithm robust chinese remainder theorem crt has been recently investigated for both integers and real numbers where the folding integers are accurately recovered from erroneous remainders in this paper we consider the crt problem for real numbers with noisy remainders that follow wrapped gaussian distributions we propose the maximum likelihood estimation mle based crt when the remainder noises may not necessarily have the same variances furthermore we present a fast algorithm for the mle based crt algorithm that only needs to search for the solution among l elements where l is the number of remainders then a necessary and sufficient condition on the remainder errors for the mle crt to be robust is obtained which is weaker than the existing result finally we compare the performances of the newly proposed algorithm and the existing algorithm in terms of both theoretical analysis and numerical simulations the results demonstrate that the proposed algorithm not only has a better performance especially when the remainders have different error levels variances but also has a much lower computational complexity

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

modeling brain activation in fmri using group mrf noise confounds present serious complications to functional magnetic resonance imaging fmri analysis the amount of discernible signals within a single dataset of a subject is often inadequate to obtain satisfactory intra subject activation detection to remedy this limitation we propose a novel group markov random field gmrf that extends each subject s neighborhood system to other subjects to enable information coalescing a distinct advantage of gmrf over standard fmri group analysis is that no stringent one to one voxel correspondence is required instead intra and inter subject neighboring voxels are jointly regularized to encourage spatially proximal voxels to be assigned similar labels across subjects our proposed group extended graph structure thus provides an effective means for handling inter subject variability also adopting a group wise approach by integrating group information into intra subject activation as opposed to estimating a single average group map permits inter subject differences to be characterized and studied gmrf can be elegantly implemented as a single mrf thus enabling all subjects activation maps to be simultaneously and collaboratively segmented with global optimality guaranteed in the case of binary labeling we validate our technique on synthetic and real fmri data and demonstrate gmrf s superior performance over standard fmri analysis

on estimation of multiple frequencies in undersampled complex valued waveforms in this correspondence the determination of multiple frequencies in undersampled waveforms is studied using multiple smaller size discrete fourier transforms dft given the sizes of multiple dft a range for the detectable frequencies in undersampled waveforms is presented

towards robustness in residue number systems the problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli namely the robust remaindering problem may occur in many applications including phase unwrapping frequency detection from several undersampled waveforms wireless sensor networks etc assuming that the dynamic range of the large number is the maximal possible one i e the least common multiple lcm of all the moduli a method called robust chinese remainder theorem for solving the robust remaindering problem has been recently proposed in this paper by relaxing the assumption that the dynamic range is fixed to be the lcm of all the moduli a tradeoff between the dynamic range and the robustness bound for two modular systems is studied it basically says that a decrease in the dynamic range may lead to an increase of the robustness bound we first obtain a general condition on the remainder errors and derive the exact dynamic range with a closed form formula for the robustness to hold we then propose simple closed form reconstruction algorithms furthermore the newly obtained two modular results are applied to the robust reconstruction for multimodular systems and generalized to real numbers finally some simulations are carried out to verify our proposed theoretical results

tractography from hardi using an intrinsic unscented kalman filter a novel adaptation of the unscented kalman filter ukf was recently introduced in literature for simultaneous multitensor estimation and fiber tractography from diffusion mri this technique has the advantage over other tractography methods in terms of computational efficiency due to the fact that the ukf simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along this ukf and its variants reported later in literature however are not intrinsic to the space of diffusion tensors lack of this key property can possibly lead to inaccuracies in the multitensor estimation as well as in the tractography in this paper we propose a novel intrinsic unscented kalman filter iukf in the space of diffusion tensors which are symmetric positive definite matrices that can be used for simultaneous recursive estimation of multitensors and propagation of directional information for use in fiber tractography from diffusion weighted mr data in addition to being more accurate iukf retains all the advantages of ukf mentioned above we demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup challenge miccai 2009 and diffusion weighted mr scans acquired from human brains and rat spinal cords