removing the effects of task related motion using independent component analysis task related motion is a major source of noise in functional magnetic resonance imaging fmri time series the motion effect usually persists even after perfect spatial realignment is achieved here we propose a new method to remove a certain type of task related motion effect that persists after realignment the procedure consists of the following the decomposition of the realigned time series data into spatially independent components using independent component analysis ica the automatic classification and rejection of the ics of the task related residual motion effects and finally a reconstruction without them to classify the ics we utilized the associated task related changes in signal intensity and variance the effectiveness of the method was verified using an fmri experiment that explicitly included head motion as a main effect the results indicate that our ica based method removed the task related motion effects more effectively than the conventional voxel wise regression based method

the zig zag power series a two way version of the operator abstract this paper deals with the zig zag power series as introduced in 1 that is with a two way version of the star operator over formal languages and power series the main result is a double characterization of rationality of zig zag power series by a condition over the structure of the starting language and another over some associated two way automata for rational zig zag power series we present the construction of some one way automata recognizing them

an evaluation of thresholding techniques in fmri analysis abstract this paper reviews and compares individual voxel wise thresholding methods for identifying active voxels in single subject fmri datasets different error rates are described which may be used to calibrate activation thresholds we discuss methods which control each of the error rates at a prespecified level including simple procedures which ignore spatial correlation among the test statistics as well as more elaborate ones which incorporate this correlation information the operating characteristics of the methods are shown through a simulation study indicating that the error rate used has an important impact on the sensitivity of the thresholding method but that accounting for correlation has little impact therefore the simple procedures described work well for thresholding most single subject fmri experiments and are recommended the methods are illustrated with a real bilateral finger tapping experiment

space time separability in fmri asymptotic power analysis and cramer rao lower bounds the space time separability of covariance equivalently spectrum has been assumed and applied to most studies in functional magnetic resonance imaging fmri however until even very recently almost no scientific justifications for it has been shown and its empirical validity has not been tested yet in fmri in a recent work we developed a procedure for testing the space time separability in the framework of the parametric cepstrum in this correspondence we provide two new contributions to the fmri literature 1 a derivation of the theoretical asymptotic power of the proposed separability test as the numbers of voxels and time observations go to infinity and 2 the derivation of an asymptotic cramer rao lower bounds of signal and noise parameters this analysis allows us to assess the impact of space time non separability on its detection power and or the estimation accuracy of parametric cepstra uncovering various important statistical properties of the proposed space time separability test

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

maximum likelihood estimation of rician distribution parameters the problem of parameter estimation from rician distributed data e g magnitude magnetic resonance images is addressed the properties of conventional estimation methods are discussed and compared to maximum likelihood ml estimation which is known to yield optimal results asymptotically in contrast to previously proposed methods ml estimation is demonstrated to be unbiased for high signal to noise ratio snr and to yield physical relevant results for low snr

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

existence and uniqueness of periodic solution for a class of differential systems in this paper sufficient conditions are obtained for the existence of a unique periodic solution for a class of differential systems

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

rician distributed fmri asymptotic power analysis and cramer rao lower bounds traditional functional mri detection statistics for activation and hemodynamic response modeling assume gaussian data which is true only for high signal to noise ratio snr the correct distribution is rician in this correspondence we provide two new developments in the rician case first a derivation of the theoretical asymptotic power function as the number of samples goes to infinity second the derivation of a cramer rao lower bound this allows a correct assessment of the impact of various signal and noise levels on detection power for activation and or hemodynamic response parameter estimation accuracy based on our analysis we are able to extend existing definitions of snr by considering variation not only in baseline but also in drifts

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

an existence and uniqueness result for periodic solution of 2n order differential equations in this paper we are concerned with the existence and uniqueness of solution to the 2n order differential equation 1 n 1x 2 n f t x x x 2 n 1 0 with periodic boundary condition x i 0 x i 2 p i 0 1 2n 1 by using the initial value problem method we transform the periodic boundary value problem into a problem of finding fixed point of continuous mapping

unified framework for robust estimation of brain networks from fmri using temporal and spatial correlation analyses there is a rapidly growing interest in the neuroimaging field to use functional magnetic resonance imaging fmri to explore brain networks i e how regions of the brain communicate with one another this paper presents a general and novel statistical framework for robust and more complete estimation of brain functional connectivity from fmri based on correlation analyses and hypothesis testing in addition to the ability of examining the correlations with each individual seed as in the standard and existing methods the proposed framework can detect functional interactions by simultaneously examining multiseed correlations via multiple correlation coefficients spatially structured noise in fmri is also taken into account during the identification of functional interconnection networks through noncentral f hypothesis tests the associated issues for the multiple testing and the effective degrees of freedom are considered as well furthermore partial multiple correlations are introduced and formulated to measure any additional task induced but not stimulus locked relation over brain regions so that we can take the analysis of functional connectivity closer to the characterization of direct functional interactions of the brain evaluation for accuracy and advantages and comparisons of the new approaches in the presented general framework are performed using both realistic synthetic data and in vivo fmri data

wavelet based rician noise removal for magnetic resonance imaging it is well known that magnetic resonance magnitude image data obey a rician distribution unlike additive gaussian noise rician noise is signal dependent and separating signal from noise is a difficult task rician noise is especially problematic in low signal to noise ratio snr regimes where it not only causes random fluctuations but also introduces a signal dependent bias to the data that reduces image contrast this paper studies wavelet domain filtering methods for rician noise removal we present a novel wavelet domain filter that adapts to variations in both the signal and the noise

fast iterative image reconstruction for mri in the presence of field inhomogeneities in magnetic resonance imaging magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast fourier transform fft methods several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities but these methods assume that the field map that characterizes the off resonance frequencies is spatially smooth recently iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off resonance effects however straightforward implementations of such iterative methods suffer from inconveniently long computation times this paper describes a tool for accelerating iterative reconstruction of field corrected mr images a novel time segmented approximation to the mr signal equation we use a min max formulation to derive the temporal interpolator speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast fourier transform with normalized root mean squared approximation errors of 0 07 the proposed method provides fast accurate field corrected image reconstruction even when the field map is not smooth

a nonlocal maximum likelihood estimation method for rician noise reduction in mr images postacquisition denoising of magnetic resonance mr images is of importance for clinical diagnosis and computerized analysis such as tissue classification and segmentation it has been shown that the noise in mr magnitude images follows a rician distribution which is signal dependent when signal to noise ratio snr is low it is particularly difficult to remove the random fluctuations and bias introduced by rician noise the objective of this paper is to estimate the noise free signal from mr magnitude images we model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution we propose a nonlocal maximum likelihood nlml estimation method for rician noise reduction our method yields an optimal estimation result that is more accurate in recovering the true signal from rician noise than nl means algorithm in the sense of snr contrast and method error we demonstrate that nlml performs better than the conventional local maximum likelihood lml estimation method in preserving and defining sharp tissue boundaries in terms of a well defined sharpness metric while also having superior performance in method error

a majorize minimize framework for rician and non central chi mr images the statistics of many mr magnitude images are described by the non central chi ncc family of probability distributions which includes the rician distribution as a special case these distributions have complicated negative log likelihoods that are nontrivial to optimize this paper describes a novel majorize minimize framework for ncc data that allows penalized maximum likelihood estimates to be obtained by solving a series of much simpler regularized least squares surrogate problems the proposed framework is general and can be useful in a range of applications we illustrate the potential advantages of the framework with real and simulated data in two contexts 1 mr image denoising and 2 diffusion profile estimation in high angular resolution diffusion mri the proposed approach is shown to yield improved results compared to methods that model the noise statistics inaccurately and faster computation relative to commonly used nonlinear optimization techniques

a metric for arma processes autoregressive moving average arma models seek to express a system function of a discretely sampled process as a rational function in the z domain treating an arma model as a complex rational function we discuss a metric defined on the set of complex rational functions we give a natural measure of the distance between two arma processes the paper concentrates on the mathematics behind the problem and shows that the various algebraic structures endow the choice of metric with some interesting and remarkable properties which we discuss we suggest that the metric can be used in at least two circumstances i in which we have signals arising from various models that are unknown so we construct the distance matrix and perform cluster analysis and ii where there are several possible models m sub i all of which are known and we wish to find which of these is closest to an observed data sequence modeled as m

nonlocal regularization of inverse problems a unified variational framework we introduce a unifying energy minimization framework for nonlocal regularization of inverse problems in contrast to the weighted sum of square differences between image pixels used by current schemes the proposed functional is an unweighted sum of inter patch distances we use robust distance metrics that promote the averaging of similar patches while discouraging the averaging of dissimilar patches we show that the first iteration of a majorize minimize algorithm to minimize the proposed cost function is similar to current nonlocal methods the reformulation thus provides a theoretical justification for the heuristic approach of iterating nonlocal schemes which re estimate the weights from the current image estimate thanks to the reformulation we now understand that the widely reported alias amplification associated with iterative nonlocal methods are caused by the convergence to local minimum of the nonconvex penalty we introduce an efficient continuation strategy to overcome this problem the similarity of the proposed criterion to widely used nonquadratic penalties e g total variation and lp semi norms opens the door to the adaptation of fast algorithms developed in the context of compressive sensing we introduce several novel algorithms to solve the proposed nonlocal optimization problem thanks to the unifying framework these fast algorithms are readily applicable for a large class of distance metrics

a cure for noisy magnetic resonance images chi square unbiased risk estimation in this paper we derive an unbiased expression for the expected mean squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi square random variable we then consider the task of denoising squared magnitude magnetic resonance mr image data which are well modeled as independent noncentral chi square random variables on two degrees of freedom we consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate one in the general context of undecimated filterbank transforms and the other in the specific case of the unnormalized haar wavelet transform the resultant algorithms are computationally tractable and improve upon most state of the art methods for both simulated and actual mr image data

an expanded theoretical treatment of iteration dependent majorize minimize algorithms the majorize minimize mm optimization technique has received considerable attention in signal and image processing applications as well as in statistics literature at each iteration of an mm algorithm one constructs a tangent majorant function that majorizes the given cost function and is equal to it at the current iterate the next iterate is obtained by minimizing this tangent majorant function resulting in a sequence of iterates that reduces the cost function monotonically a well known special case of mm methods are expectation maximization algorithms in this paper we expand on previous analyses of mm due to fessler and hero that allowed the tangent majorants to be constructed in iteration dependent ways also this paper overcomes an error in one of those earlier analyses there are three main aspects in which our analysis builds upon previous work first our treatment relaxes many assumptions related to the structure of the cost function feasible set and tangent majorants for example the cost function can be nonconvex and the feasible set for the problem can be any convex set second we propose convergence conditions based on upper curvature bounds that can be easier to verify than more standard continuity conditions furthermore these conditions allow for considerable design freedom in the iteration dependent behavior of the algorithm finally we give an original characterization of the local region of convergence of mm algorithms based on connected e g convex tangent majorants for such algorithms cost function minimizers will locally attract the iterates over larger neighborhoods than typically is guaranteed with other methods this expanded treatment widens the scope of the mm algorithm designs that can be considered for signal and image processing applications allows us to verify the convergent behavior of previously published algorithms and gives a fuller understanding overall of how these algorithms behave

efficient spatio temporal gaussian regression via kalman filtering abstract we study the non parametric reconstruction of spatio temporal dynamical processes via gaussian processes gps regression from sparse and noisy data gps have been mainly applied to spatial regression where they represent one of the most powerful estimation approaches also thanks to their universal representing properties their extension to dynamical processes has been instead elusive so far since classical implementations lead to unscalable algorithms or require some sort of approximation we propose a novel procedure to address this problem by coupling gps regression and kalman filtering in particular assuming space time separability of the covariance kernel of the process and rational time spectrum we build a finite dimensional discrete time state space process representation amenable to kalman filtering with sampling over a finite set of fixed spatial locations our major finding is that the current kalman filter state represents a sufficient statistic to compute the minimum variance estimate of the process at any future time over the entire spatial domain in machine learning a representer theorem states that an important class of infinite dimensional variational problems admits a computable and finite dimensional exact solution in view of this our result can be interpreted as a novel dynamic representer theorem for gps we then extend the study to situations where the spatial input locations set varies over time the proposed algorithms are tested on both synthetic and real field data providing comparisons with standard gp and truncated gp regression techniques

a framework for callosal fiber distribution analysis this paper presents a framework for analyzing the spatial distribution of neural fibers in the brain with emphasis on interhemispheric fiber bundles crossing through the corpus callosum the proposed approach combines methodologies for fiber tracking and spatial normalization and is applied on diffusion tensor images and standard magnetic resonance images

the concave convex procedure the concave convex procedure cccp is a way to construct discrete time iterative dynamical systems that are guaranteed to decrease global optimization and energy functions monotonically this procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted in terms of it in particular we prove that all expectation maximization algorithms and classes of legendre minimization and variational bounding algorithms can be reexpressed in terms of cccp we show that many existing neural network and mean field theory algorithms are also examples of cccp the generalized iterative scaling algorithm and sinkhorn s algorithm can also be expressed as cccp by changing variables cccp can be used both as a new way to understand and prove the convergence of existing optimization algorithms and as a procedure for generating new algorithms

independent component analysis involving autocorrelated sources with an application to functional magnetic resonance imaging independent component analysis ica is an effective data driven method for blind source separation it has been successfully applied to separate source signals of interest from their mixtures most existing ica procedures are carried out by relying solely on the estimation of the marginal density functions either parametrically or nonparametrically in many applications correlation structures within each source also play an important role besides the marginal distributions one important example is functional magnetic resonance imaging fmri analysis where the brain function related signals are temporally correlated in this article we consider a novel approach to ica that fully exploits the correlation structures within the source signals specifically we propose to estimate the spectral density functions of the source signals instead of their marginal density functions this is made possible by virtue of the intrinsic relationship between the unobserved sources and the observed mixed signals

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

linear transforms for fourier data on the sphere application to high angular resolution diffusion mri of the brain this paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2 sphere in three dimensional fourier space this family of transforms generalizes the previously proposed funk radon transform frt which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data the new family of transforms is characterized theoretically and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics after these general discussions attention is focused on a particular new transform from this family that we name the funk radon and cosine transform fract based on theoretical arguments it is expected that fract based analysis should yield significantly better orientation information e g improved accuracy and higher angular resolution than frt based analysis while maintaining the strong characterizability and computational efficiency of the frt simulations are used to confirm these theoretical characteristics and the practical significance of the proposed approach is illustrated with real diffusion weighted mri brain data these experiments demonstrate that in addition to having strong theoretical characteristics the proposed approach can outperform existing state of the art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors

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

solving the periodic boundary value problem with the initial value problem method in this paper with the use of the initial value problem method the periodic boundary value problems of the systems of newton equations are investigated the existence and uniqueness of 2 periodic solutions of the systems are constructively established meanwhile this approach provides a global method for finding periodic solutions of the systems

decidability of zigzag codes french abstract this paper deals with zigzag factorizations and zigzag codes the language of zigzag over a regular language is represented by constructing a special family of two way automata decidability of zigzag codes previously shown for the finite languages is proved here for all regular languages by the analysis of the set of crossing sequences produced by a two way automation in the family we also obtain that it is decidable whether or not a two way automation of a certain type is non ambiguous

optimal imaging parameters for fiber orientation estimation in diffusion mri this study uses monte carlo simulations to investigate the optimal value of the diffusion weighting factor b for estimating white matter fiber orientations using diffusion mri with a standard spherical sampling scheme we devise an algorithm for determining the optimal echo time pulse width and pulse separation in the pulsed gradient spin echo sequence for a specific value of b the monte carlo simulations provide an estimate of the optimal value of b for recovering one and two fiber orientations we show that the optimum is largely independent of the noise level in the measurements and the number of gradient directions and that the optimum depends only weakly on the diffusion anisotropy the maximum gradient strength and the spin spin relaxation time the optimum depends strongly on the mean diffusivity in brain tissue the optima we estimate are in the ranges 0 7 1 0 x 10 9 s m 2 and 2 2 2 8 x 10 9 s m 2 for the one and two fiber cases respectively the best b for estimating the fractional anisotropy is slightly higher than for estimating fiber directions in the one fiber case and slightly lower in the two fiber case to estimate tr d in the one fiber case the optimal setting is higher still simulations suggest that a ratio of high to low b measurements of 5 to 1 is a good compromise for measuring fiber directions and size and shape indices

multi exponential transverse relaxation times estimation from magnetic resonance images under rician noise and spatial regularization relaxation signal inside each voxel of magnetic resonance images mri is commonly fitted by a multi exponential decay curve the estimation of a discrete multi component relaxation model parameters from magnitude mri data is a challenging nonlinear inverse problem since it should be conducted on the entire image voxels under non gaussian noise statistics this paper proposes an efficient algorithm allowing the joint estimation of relaxation time values and their amplitudes using different criteria taking into account a rician noise model combined with a spatial regularization accounting for low spatial variability of relaxation time constants and amplitudes between neighboring voxels the rician noise hypothesis is accounted for either by an adapted nonlinear least squares algorithm applied to a corrected least squares criterion or by a majorization minimization approach applied to the maximum likelihood criterion in order to solve the resulting large scale non negativity constrained optimization problem with a reduced numerical complexity and computing time an optimization algorithm based on a majorization approach ensuring separability of variables between voxels is proposed the minimization is carried out iteratively using an adapted levenberg marquardt algorithm that ensures convergence by imposing a sufficient decrease of the objective function and the non negativity of the parameters the importance of the regularization alongside the rician noise incorporation is shown both visually and numerically on a simulated phantom and on magnitude mri images acquired on fruit samples

on the periodic solution to the newtonian equation of motion on considere l equation du mouvement newtonienne d un systeme mecanique soumis a des forces internes conservatives et a des forces externes periodiques u t grad g u t p t ou p r r 11 est continue et de periode 2 et g a des derivees partielles d ordre 2 continues

existence and uniqueness results for periodic solution of nonlinear differential equations the existence and uniqueness of solutions for a class of 2nd order differential equations with periodic conditions are discussed

a theoretical signal processing framework for linear diffusion mri implications for parameter estimation and experiment design the data measured in diffusion mri can be modeled as the fourier transform of the ensemble average propagator eap a probability distribution that summarizes the molecular diffusion behavior of the spins within each voxel this fourier relationship is potentially advantageous because of the extensive theory that has been developed to characterize the sampling requirements accuracy and stability of linear fourier reconstruction methods however existing diffusion mri data sampling and signal estimation methods have largely been developed and tuned without the benefit of such theory instead relying on approximations intuition and extensive empirical evaluation this paper aims to address this discrepancy by introducing a novel theoretical signal processing framework for diffusion mri the new framework can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q space sampling and can be used to theoretically evaluate and compare the accuracy resolution and noise resilience of different data acquisition and parameter estimation techniques the framework is based on the eap and makes very limited modeling assumptions as a result the approach can even provide new insight into the behavior of model based linear diffusion estimation methods in contexts where the modeling assumptions are inaccurate the practical usefulness of the proposed framework is illustrated using both simulated and real diffusion mri data in applications such as choosing between different parameter estimation methods and choosing between different q space sampling schemes

low rank modeling of local k space neighborhoods loraks for constrained mri recent theoretical results on low rank matrix reconstruction have inspired significant interest in low rank modeling of mri images existing approaches have focused on higher dimensional scenarios with data available from multiple channels timepoints or image contrasts the present work demonstrates that single channel single contrast single timepoint k space data can also be mapped to low rank matrices when the image has limited spatial support or slowly varying phase based on this we develop a novel and flexible framework for constrained image reconstruction that uses low rank matrix modeling of local k space neighborhoods loraks a new regularization penalty and corresponding algorithm for promoting low rank are also introduced the potential of loraks is demonstrated with simulated and experimental data for a range of denoising and sparse sampling applications loraks is also compared against state of the art methods like homodyne reconstruction l1 norm minimization and total variation minimization and is demonstrated to have distinct features and advantages in addition while calibration based support and phase constraints are commonly used in existing methods the loraks framework enables calibrationless use of these constraints

concatention of inputs in a two way automation abstract to every input string of a two way automaton one associates a quadruple of partial functions or relations between the states this quadruple describes the behavior of the automaton on that input and can also be used to formulate acceptance or notions like the crossing sequence formulas are given that show how two such quadruples are combined multiplied as their corresponding input strings are concatenated

a diagnostic procedure based on local influence cook s 1986 normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models however there is no rigorous approach based on the normal curvature for addressing two fundamental issues to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated and to identify suspicious data points for which the discrepancy is most evident our purpose is to establish a theoretically sound procedure for resolving these issues for case weight perturbation under the framework of independent distributions we show that the local influence measure cook s distance and likelihood distance are asymptotically equivalent a diagnostic procedure based on local influence is proposed for evaluating model misspecification and for detecting influential points simultaneously we analyse two real datasets

on periodic solutions of nonlinear second order vector differential equations this paper considers existence of periodic solutions for vector lienard differential equations in our main result we write where q t x is a symmetric matrix and h t x is sublinear the key assumption relates the asymptotic behaviour as x of the eigenvalues of q t x to the spectrum of the linear operator d 2 dt 2 several choices for q t x are considered which lead to known theorems and extend others in the case of the duffing equation the assumptions are weakened our approach is based on leray schauder s degree theory and a priori estimates

periodic solutions for functional differential equations with infinite lead and delay abstract this paper discusses the existence of periodic solutions for functional differential equations with infinite lead and delay on the basis of fixed point theorems topological degree theories comparison principles and differential inequality methods some general results are proved

maximum a posteriori estimation of diffusion tensor parameters using a rician noise model why how and but the diffusion tensor is a commonly used model for diffusion weighted mr image data the parameters are typically estimated by ordinary or weighted least squares on log transformed data assuming normal or log normal distribution of measurement errors respectively this may not be adequate when using high b values and or performing high resolution scans resulting in poor snr in which case the difference between the assumed and the true rician noise model becomes important as a consequence the estimated diffusion parameters will be biased underestimating the true diffusion in this paper a computational framework is presented where parameters pertaining to a spectral decomposition of the diffusion tensor are estimated using a rician noise model the parameters are estimated using a fisher scoring scheme which gives robust and rapid convergence it is demonstrated how the fisher information matrix can be used as a generic tool for designing optimal experiments it is shown that the rician noise model leads to significantly less biased estimates for a large range of b values and snr but that the rician estimates have a poorer precision compared to the gaussian model for very low snr by pooling the rician estimates of uncertainty over neighbouring voxel estimates with higher precision but still not as high as with a gaussian model can be obtained we suggest the use of a rician estimator when it is important with truly quantitative values and when comparing different predictive models the higher precision of the gaussian estimates may be more important when the objective is to compare diffusion related parameters over time or across groups

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

modeling of two dimensional random fields by parametric cepstrum a method is presented for parametric modeling of stationary random fields the class of parametric models considered allows the most general elliptic field and by linear constraints can include such special cases as isotropic quarter plane and separable fields the technique based on the cepstrum has the great advantage of requiring only the use of fast fourier transforms in the fitting process thus unlike the fitting of two dimensional autoregressions no iteration is necessary other advantages are that any wiener filters constructed from the fitted spectrum are guaranteed to be stable and that the spectrum is guaranteed to be positive statistical tests for determining various special types of field from data are developed the choice of model order is discussed as well

a unified maximum likelihood framework for simultaneous motion and t_ 1 estimation in quantitative mr t_ 1 mapping in quantitative mr t1 mapping the spin lattice relaxation time t1 of tissues is estimated from a series of t1 weighted images as the t1 estimation is a voxel wise estimation procedure correct spatial alignment of the t1 weighted images is crucial conventionally the t1 weighted images are first registered based on a general purpose registration metric after which the t1 map is estimated however as demonstrated in this paper such a two step approach leads to a bias in the final t1 map in our work instead of considering motion correction as a preprocessing step we recover the motion free t1 map using a unified estimation approach in particular we propose a unified framework where the motion parameters and the t1 map are simultaneously estimated with a maximum likelihood ml estimator with our framework the relaxation model the motion model as well as the data statistics are jointly incorporated to provide substantially more accurate motion and t1 parameter estimates experiments with realistic monte carlo simulations show that the proposed unified ml framework outperforms the conventional two step approach as well as state of the art model based approaches in terms of both motion and t1 map accuracy and mean square error furthermore the proposed method was additionally validated in a controlled experiment with real t1 weighted data and with two in vivo human brain t1 weighted data sets showing its applicability in real life scenarios

a non variational version of a max min principle f u w 4 2 milwl12 1 then there exists a unique uo e h such that vf ug 0 furthermoref uo min f u in 1975 ueh lazer landesman meyer l l m 3 extended these results to the following situation let x and y be two closed subspaces of h such that h x y x is finite dimensional and x and y are not necessarily orthogonal let t vf then t h h and is a c mapping its frechet derivative at u e his given by t rc d f u let ml and ml be two positive constants such that vu e h vx e x and vy e y we have

parameter estimation in the magnitude only and complex valued fmri data models abstract in functional magnetic resonance imaging voxel time courses are complex valued data but are traditionally converted to real magnitude only data ones at a large signal to noise ratio snr the magnitude only data ricean distribution is approximated by a normal distribution that has been suggested as reasonable in magnitude only data magnetic resonance images for an snr of 5 and potentially as low as 3 a complex activation model has been recently introduced by rowe and logan rowe d b and logan b r 2004 a complex way to compute fmri activation neuroimage 23 3 1078 1092 that is valid for all snrs the properties of the parameter estimators and activation statistic for these two models and a more accurate ricean approximation based on a taylor series expansion are characterized in terms of bias variance and cramer rao lower bound it was found that the unbiased estimators in the complex model continued to be unbiased for lower snrs while those of the normal magnitude only data model became biased as the snr decreased and at differing levels for the regression coefficients the unbiased parameter estimators from the approximate magnitude only ricean taylor model were unbiased to lower snrs than the magnitude only normal ones further the variances of the parameter estimators achieved their minimum value in the complex data model regardless of snr while the magnitude only data normal model and ricean approximation using a taylor series did not as the snr decreased finally the mean activation statistic for the complex data model was higher and not snr dependent while it decreased with snr in the magnitude only data models but less so for the approximate ricean model these results indicate that using the complex data model and not approximations to the true magnitude only ricean data model is more appropriate at lower snrs therefore since the computational cost is relatively low for the complex data model and since the snr is not inherently known a priori for all voxels the complex data model is recommended at all snrs

an application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations abstract in this paper a class of systems of nonlinear differential equations at resonance is considered with the use of a global inversion theorem which is an extended form of a non variational version of a max min principle we prove that this class of equations possesses a unique 2 periodic solution under a rather weaker condition for existence and uniqueness than those given in papers j chen w li periodic solution for 2 k th boundary value problem with resonance j math anal appl 314 2006 661 671 f cong periodic solutions for 2 k th order ordinary differential equations with nonresonance nonlinear anal 32 1998 787 793 f cong periodic solutions for second order differential equations appl math lett 18 2005 957 961 w li periodic solutions for 2 k th order ordinary differential equations with resonance j math anal appl 259 2001 157 167 w li h li a min max theorem and its applications to nonconservative systems int j math math sci 17 2003 1101 1110 w li z shen a constructive proof of existence and uniqueness of 2 periodic solution to duffing equation nonlinear anal 42 2000 1209 1220 this result extends the results known so far

the operation on formal power series we introduce a new operation over formal power series which we denote by it is based on zigzag factorizations of a word i e factorizations obtained allowing some backward coming in concatenation this operation is not rational moreover the image of rational power series is not always algebraic we represent power series s by two way finite automata with multiplicity for ser rat a we doubly characterize the rationality of the image s and show its decidability

nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain we present an algorithm for blindly recovering constituent source spectra from magnetic resonance mr chemical shift imaging csi of the human brain the algorithm which we call constrained nonnegative matrix factorization cnmf does not enforce independence or sparsity instead only requiring the source and mixing matrices to be nonnegative it is based on the nonnegative matrix factorization nmf algorithm extending it to include a constraint on the positivity of the amplitudes of the recovered spectra this constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative we demonstrate and characterize the algorithm s performance using sup 31 p volumetric brain data comparing the results with two different blind source separation methods bayesian spectral decomposition bsd and nonnegative sparse coding nnsc we then incorporate the cnmf algorithm into a hierarchical decomposition framework showing that it can be used to recover tissue specific spectra given a processing hierarchy that proceeds coarse to fine we demonstrate the hierarchical procedure on sup 1 h brain data and conclude that the computational efficiency of the algorithm makes it well suited for use in diagnostic work up

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

two point boundary value problem of 2mth order differential equations an existence and uniqueness result for the boundary value problem x 2 m email protected k 1 ma kx 2 k 1 1 m 1f t x e t x j 0 x j p 0 j 0 1 m 1 is given