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

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

galerkin s method for ordinary differential equations subject to generalized nonlinear boundary conditions where xk belongs to tc a finite dimensional subspace of cc l 11 r il ii and i qj is a projection mapping cc l 11 r i i x r onto a subspace of c 1 11 r 11 ii having the same dimension as rck there is a vast collection of literature concerning the application of galerkin s method to differential equations 1 3 12 16231 we make a special reference to the papers of cesari 4 5 and urabe 22 23 our results provide an extension and a unification of previous results of urabe that were conderned with the determination of periodic solutions to systems of ordinary differential equations 22 and with the solvability of 112 0022 0396192 3 00

projection methods for nonlinear boundary value problems where l d l c x y is a linear map n x y is nonlinear and x and y are banach spaces recently cesari and mckenna s proved that if the underlying spaces possess a schauder basis or more generally they have what the authors call property l it is theoretically possible to establish a finite dimensional alternative problem for 1 3 their paper unities previous results 12 131 that established conditions under which 1 3 could be reduced to finite 282 0022 0396 85 3 00

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

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

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

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

nonlinear discrete systems with global boundary conditions abstract this paper is devoted to the study of boundary value problems on infinite time intervals for nonlinear discrete time systems for problems of the form x k 1 f k x k h k k 0 1 2 subject to constraints or nonlocal boundary conditions of the form k 0 g k x k y we analyze how perturbations in h and y affect the existence of l solutions of this problem in this setting h is an element of l and y belongs to r p we also study the existence and behavior of bounded solutions to problems of the form x k 1 f k x k k 0 1 2 subject to k 0 g k x k 0 we place particular importance on the behavior of the solutions as a function of the parameter

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

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

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

local stabilization and controllability of a class of non triangular nonlinear systems this paper considers the problems of local asymptotic stabilization using continuous static state feedback lcfs and small time local controllability stlc of single input nonlinear systems a specific class of nontriangular systems called the essentially triangular form is introduced for this class of systems sufficient conditions for lcfs and necessary and sufficient conditions for stlc are obtained in particular it is shown that stlc implies lcfs a motivating physical example of the etf system is presented

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

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

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

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

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

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

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

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 alternative method for boundary value problems with large nonlinearities where g r r is continuously differentiable and b and d are nonsingular 12 x n matrices historically lyapunov schmidt and the alternative method are able to reduce the problem to a finite dimensional one provided the norm of the nonlinear term is sufficiently small in the region of interest that is the weakly nonlinear case recently the finite dimensional reduction for ordinary differential equations with periodic boundary conditions was accomplished 161 in this paper a constructive technique is developed that allows us to reduce 1 1 to a finite dimensional problem

on nonlinear discrete boundary value problems mo x 1 x n 0 1 4 where n is a fixed positive integer 8 represent n by n constant matrices a t is an n by n matrix for each te 0 l h t belongs to ir for each nonnegative integer t u is in r 1 is a real parameter f and g are continuously differentiable f r i ir and g r i r for systems 1 1 1 2 we prove that if the linear system x t l a l x t h t 1 5 subject to

nonsmooth stabilization of a class of nonlinear cascaded systems a global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization a stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique under suitable conditions and based on homogeneous properties it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system due to the versatility of the adding a power integrator technique and homogeneous properties the proposed controller not only can be used to stabilize the cascaded system asymptotically but also is able to lead to an interesting result of finite time stabilization under appropriate conditions