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 existence and uniqueness of solution to wavelet collocation the study of the numerical solutions of pdes with wavelet collocation has yielded a number of substantial results however the existence and uniqueness of solution has not been discussed yet in this paper the existence and uniqueness of solution to wavelet collocation for elliptic equations is established and discussed moreover wavelet collocation is applied to numerical example to examine its appropriateness according to numerical example and analysis it is seen that the existence and uniqueness of solution of this paper is feasible and the new theory is meaningful for developing wavelet collocation

empirical analyses of bold fmri statistics ii spatially smoothed data collected under null hypothesis and experimental conditions in the companion to this paper e zarahn g k aguirre and m d esposito 1997 neuroimage 179 197 we describe an implementation of a general linear model for autocorrelated observations in which the voxel wise false positive rates in fmri noise datasets were stabilized and brought close to theoretical values here implementations of the model are tested for use with statistical parametric mapping analysis of spatially smoothed fmri data analyses using varying models of intrinsic temporal autocorrelation and either including or excluding a global signal covariate were conducted upon human subject data collected under null hypothesis as well as under experimental conditions we found that smoothing with an empirically derived impulse response function irf combined with a model of the intrinsic temporal autocorrelation in spatially smoothed fmri data resulted in a map wise false positive rate which did not exceed a 5 level when a nominal alpha 0 05 tabular threshold was applied use of other models of intrinsic temporal autocorrelation resulted in map wise false positive rates that significantly exceeded this level fmri data collected while subjects performed a behavioral task were used to examine a task dependent global signal changes and b the dependence of sensitivity on the temporal smoothing kernel and inclusion exclusion of a global signal covariate the global signal changes within an fmri dataset were shown to be influenced by the performance of a behavioral task however the inclusion of this measure as a covariate did not have an adverse affect upon our measure of sensitivity finally use of an empirically derived estimate of the irf of the system was shown to result in greater map wise sensitivity for signal changes than the use of a broader in time poisson parameter 8 s kernel

spatiotemporal analysis of event related fmri data using partial least squares partial least squares pls has proven to be a important multivariate analytic tool for positron emission tomographic and more recently event related potential erp data the application to erp incorporates the ability to analyze space and time together a feature that has obvious appeal for event related functional magnetic resonance imaging fmri data this paper presents the extension of spatiotemporal pls st pls to fmri explaining the theoretical foundation and application to an fmri study of auditory and visual perceptual memory analysis of activation effects with st pls was compared with conventional univariate random effects analysis showing general consensus for both methods but several unique observations by st pls including enhanced statistical power the application of st pls for assessment of task dependent brain behavior relationships is also presented singular features of st pls include 1 no assumptions about the shape of the hemodynamic response functions hrfs 2 robust statistical assessment at the image level through permutation tests 3 protection against outlier influences at the voxel level through bootstrap resampling 4 flexible analytic configurations that allow assessment of activation difference brain behavior relations and functional connectivity these features enable st pls to act as an important complement to other multivariate and univariate approaches used in neuroimaging research

estimation and classification of fmri hemodynamic response patterns in this paper we propose an approach to modeling functional magnetic resonance imaging fmri data that combines hierarchical polynomial models bayes estimation and clustering a cubic polynomial is used to fit the voxel time courses of event related design experiments the coefficients of the polynomials are estimated by bayes estimation in a two level hierarchical model which allows us to borrow strength from all voxels the voxel specific bayes polynomial coefficients are then transformed to the times and magnitudes of the minimum and maximum points on the hemodynamic response curve which are in turn used to classify the voxels as being activated or not the procedure is demonstrated on real data from an event related design experiment of visually guided saccades and shown to be an effective alternative to existing methods

properness and widely linear processing of quaternion random vectors in this paper the second order circularity of quaternion random vectors is analyzed unlike the case of complex vectors there exist three different kinds of quaternion properness which are based on the vanishing of three different complementary covariance matrices the different kinds of properness have direct implications on the cayley dickson representation of the quaternion vector and also on several well known multivariate statistical analysis methods in particular the quaternion extensions of the partial least squares pls multiple linear regression mlr and canonical correlation analysis cca techniques are analyzed showing that in general the optimal linear processing is full widely linear however in the case of jointly q proper or c proper vectors the optimal processing reduces respectively to the conventional or semi widely linear processing finally a measure for the degree of improperness of a quaternion random vector is proposed which is based on the kullback leibler divergence between two zero mean gaussian distributions one of them with the actual augmented covariance matrix and the other with its closest proper version this measure quantifies the entropy loss due to the improperness of the quaternion vector and it admits an intuitive geometrical interpretation based on kullback leibler projections onto sets of proper augmented covariance matrices

single shot compensation of image distortions and bold contrast optimization using multi echo epi for real time fmri abstract functional magnetic resonance imaging fmri is most commonly based on echo planar imaging epi with higher field strengths gradient performance and computational power real time fmri has become feasible that is brain activation can be monitored during the ongoing scan however epi suffers from geometric distortions due to inhomogeneities of the magnetic field especially close to air tissue interfaces thus functional activations might be mislocalized and assigned to the wrong anatomical structures several techniques have been reported which reduce geometric distortions for example mapping of the static magnetic field b0 or the point spread function for all voxels yet these techniques require additional reference scans and in some cases extensive computational time moreover only static field inhomogeneities can be corrected because the correction is based on a static reference scan we present an approach which allows for simultaneous acquisition and distortion correction of a functional image without a reference scan the technique is based on a modified multi echo epi data acquisition scheme using a phase encoding pe gradient with alternating polarity the images exhibit opposite distortions due to the inverted pe gradient after adjusting the contrast of the images acquired at different echo times this information is used for the distortion correction we present the theory implementation and applications of this single shot distortion correction significant reduction in geometric distortion is shown both for phantom images and human fmri data moreover sensitivity to the blood oxygen level dependent bold effect is increased by weighted summation of the undistorted images

searchlight based multi voxel pattern analysis of fmri by cross validated manova abstract multi voxel pattern analysis mvpa is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data we propose to replace the standard decoding approach to searchlight based mvpa measuring the performance of a classifier by its accuracy with a method based on the multivariate form of the general linear model following the well established methodology of multivariate analysis of variance manova we define a measure that directly characterizes the structure of multi voxel data the pattern distinctness d our measure is related to standard multivariate statistics but we apply cross validation to obtain an unbiased estimate of its population value independent of the amount of data or its partitioning into training and test sets the estimate d can therefore serve not only as a test statistic but also as an interpretable measure of multivariate effect size the pattern distinctness generalizes the mahalanobis distance to an arbitrary number of classes but also the case where there are no classes of trials because the design is described by parametric regressors it is defined for arbitrary estimable contrasts including main effects pattern differences and interactions pattern changes in this way our approach makes the full analytical power of complex factorial designs known from univariate fmri analyses available to mvpa studies moreover we show how the results of a factorial analysis can be used to obtain a measure of pattern stability the equivalent of cross decoding

sparse and kernel opls feature extraction based on eigenvalue problem solving orthonormalized partial least squares opls is a popular multivariate analysis method to perform supervised feature extraction usually in machine learning papers opls projections are obtained by solving a generalized eigenvalue problem however in statistical papers the method is typically formulated in terms of a reduced rank regression problem leading to a formulation based on a standard eigenvalue decomposition a first contribution of this paper is to derive explicit expressions for matching the opls solutions derived under both approaches and discuss that the standard eigenvalue formulation is also normally more convenient for feature extraction in machine learning more importantly since optimization with respect to the projection vectors is carried out without constraints via a minimization problem inclusion of penalty terms that favor sparsity is straightforward in the paper we exploit this fact to propose modified versions of opls in particular relying on the 1 norm we propose a sparse version of linear opls as well as a non linear kernel opls with pattern selection we also incorporate a group lasso penalty to derive an opls method with true feature selection the discriminative power of the proposed methods is analyzed on a benchmark of classification problems furthermore we compare the degree of sparsity achieved by our methods and compare them with other state of the art methods for sparse feature extraction highlightswe establish the connection between opls and reduced rank regression problem evd formulation a novel sparse opls is proposed which enhances the solution obtained following the procrustres approach we propose a novel sparse kernel opls feature extractor for improved performance interpretability and efficiency

bayesian second level analysis of functional magnetic resonance images we propose a new method for the second level analysis of functional mri data based on bayesian statistics our method does not require a computationally costly bayesian model on the first level of analysis rather modeling for single subjects is realized by means of the commonly applied general linear model on the basis of the resulting parameter estimates for single subjects we calculate posterior probability maps and maps of the effect size for effects of interest in groups of subjects a comparison of this method with the conventional analysis based on t statistics shows that the new approach is more robust against outliers moreover our method overcomes some of the severe problems of null hypothesis significance tests such as the need to correct for multiple comparisons and facilitates inferences which are hard to formulate in terms of classical inferences

nirs spm statistical parametric mapping for near infrared spectroscopy near infrared spectroscopy nirs is a non invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull as optically measured hemoglobin signals strongly correlate with bold signals simultaneous measurement using nirs and fmri promises a significant mutual enhancement of temporal and spatial resolutions although there exists a powerful statistical parametric mapping tool in fmri current public domain statistical tools for nirs have several limitations related to the quantitative analysis of simultaneous recording studies with fmri in this paper a new public domain statistical toolbox known as nirs spm is described it enables the quantitative analysis of nirs signal more specifically nirs data are statistically analyzed based on the general linear model glm and sun s tube formula the p values are calculated as the excursion probability of an inhomogeneous random field on a representation manifold that is dependent on the structure of the error covariance matrix and the interpolating kernels nirs spm not only enables the calculation of activation maps of oxy deoxy hemoglobin and total hemoglobin but also allows for the super resolution localization which is not possible using conventional analysis tools extensive experimental results using finger tapping and memory tasks confirm the viability of the proposed method

radiation conditions for a semi infinite elastic strip high frequency vibrations of a semi infinite elastic strip with traction free faces are considered the conditions on end data that are derived do not allow non radiating in sommerfeld s sense of polynomial modes at thickness resonance frequencies these represent a high frequency analogue of the well known decay conditions in statics that agree with the classical saint venant principle the proposed radiation conditions are applied to the construction of boundary conditions in the theories of high frequency long wave vibrations describing slow varying motions in the vicinity of thickness resonance frequencies the derivation is based on the laplace transform technique along with the asymptotic methodology that is typical for thin plates and shells

a new statistical approach to detecting significant activation in functional mri there are many ways to detect activation patterns in a time series of observations at a single voxel in a functional magnetic resonance imaging study the critical problem is to estimate the statistical significance which depends on the estimation of both the magnitude of the response to the stimulus and the serial dependence of the time series and especially on the assumptions made in that estimation we show that for experimental designs with periodic stimuli only a few aspects of the serial dependence are important and these can be estimated reliably via nonparametric estimation of the spectral density of the time series whereas existing techniques are biased by their assumptions the linear model with stationary serially dependent errors can be analyzed entirely in frequency domain and doing so provides many insights in particular we introduce a technique to detect periodic activations and show that it has a distribution theory that enables us to assign significance levels down to 1 in 100 000 levels which are needed when a whole brain image is under consideration nonparametric spectral density estimation is shown to be self calibrating and accurate when compared to several other time domain approaches the technique is especially resistant to high frequency artefacts that we have found in some datasets and we demonstrate that time domain approaches may be sufficiently susceptible to these effects to give misleading results the method is easily generalized to handle event related designs we found it necessary to consider the trends in the time series carefully and use nonlinear filters to remove the trends and robust techniques to remove spikes using this in connection with our techniques allows us to detect activations in clumps of a few even one voxel in periodic designs yet produce essentially no false positive detections at any voxels in null datasets

plurality and resemblance in fmri data analysis abstract we apply nine analytic methods employed currently in imaging neuroscience to simulated and actual bold fmri signals and compare their performances under each signal type starting with baseline time series generated by a resting subject during a null hypothesis study we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple convolved with spatially varying hemodynamic responses and highly spatially interactive we then apply these same nine methods to bold fmri time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study paired comparisons of results across methods include a voxel specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces receiver operating characteristic curves show considerable model differences in ranges less than 10 significance level false positives and greater than 80 power true positives concordance and resemblance measures reveal significant differences between activity surfaces in both data sets these measures can assist researchers by identifying groups of models producing similar and dissimilar results and thereby help to validate consolidate and simplify reports of statistical findings a pluralistic strategy for fmri data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain behavior relationships that may remain hidden if only a single method is employed

comparing methods of analyzing fmri statistical parametric maps approaches for the analysis of statistical parametric maps spms can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions these being type i error control thresholding false discovery rate fdr control thresholding and posterior probability thresholding to better understand the properties of these main approaches we carried out a simulation study to compare the approaches as they would be used on real data sets using default settings we find that posterior probability thresholding is the most powerful approach and type i error control thresholding provides the lowest levels of type i error false discovery rate control thresholding performs in between the other approaches for both these criteria although for some parameter settings this approach can approximate the performance of posterior probability thresholding based on these results we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach we conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods within this framework we highlight the role of the loss function which explicitly penalizes the types of errors that may occur in a given analysis

activation detection in fmri using a maximum energy ratio statistic obtained by adaptive spatial filtering an adaptive spatial filtering method is proposed that takes into account contextual information in fmri activation detection this filter replaces the time series of each voxel with a weighted average of time series of a small neighborhood around it the filter coefficients at each voxel are derived so as to maximize a test statistic designed to indicate the presence of activation this statistic is the ratio of the energy of the filtered time series in a signal subspace to the energy of the residuals it is shown that the filter coefficients and the maximum energy ratio can be found through a generalized eigenproblem this approach equates the filter coefficients to the elements of an eigenvector corresponding to the largest eigenvalue of a specific matrix while the largest eigenvalue itself becomes the maximum energy ratio that can be used as a statistic for detecting activation the distribution of this statistic under the null hypothesis is derived by a nonparametric permutation technique in the wavelet domain also in this paper we introduce a new set of basis vectors that define the signal subspace the space spanned by these basis vectors covers a wide range of possible hemodynamic response functions hrf and is applicable to both event related and block design fmri signal analysis this approach circumvents the need for a priori assumptions about the exact shape of the hrf resting state experimental fmri data were used to assess the specificity of the method showing that the actual false alarm rate of the proposed method is equal or less than its expected value analysis of simulated data and motor task fmri datasets from six volunteers using the method proposed here showed an improved sensitivity as compared to a conventional test with a similar statistic applied to spatially smoothed data

tests for distributed nonfocal brain activations abstract most approaches to detecting changes in functional brain images assume that activations are focal or very localized however the brain s response to cognitive of sensorimotor challenge may be spatially or anatomically distributed in this paper we consider the use fulness of a test based on the mean sum of squares of statistical parametric maps the performance of this test is evaluated using simulated and real data and is compared to the 2 test a test of the size of the activated region and a focal activation test based on the intensity of local maxima we demonstrate that the mean sum of squares test is more sensitive to nonfocal signals and propose that it could be used to complement approaches that are more sensitive to focal activations

wavelet optimized finite difference mesh for mhd flow in a circular duct abstract there is a large class of important problems in scientific and engineering applications where the solution shows very little variation in the core region but very rapid changes close to the boundary of the domain of interest magnetohydrodynamic flow problems belong to this category treatment of such problems numerically therefore requires a non uniform mesh which is very fine near the boundary the determination of the size of the grid in different parts of the domain is therefore a challenging problem some recent studies suggest that wavelet methods can be effectively applied to create an optimized mesh the method has mostly been used for one dimensional problems the present paper investigates the problem for fully developed mhd duct flow problems which are basically two dimensional the boundary layer character is more pronounced in one direction as compared to the other the governing equations comprise a coupled system of two partial differential equations with dirichlet boundary conditions wavelet based adaptive mesh is first created and then the system is discretized over this mesh computations have been carried out at different precision levels for various hartmann numbers for a pipe of circular section contours are also drawn to depict the core and the boundary layer region

linked independent component analysis for multimodal data fusion in recent years neuroimaging studies have increasingly been acquiring multiple modalities of data and searching for task or disease related changes in each modality separately a major challenge in analysis is to find systematic approaches for fusing these differing data types together to automatically find patterns of related changes across multiple modalities when they exist independent component analysis ica is a popular unsupervised learning method that can be used to find the modes of variation in neuroimaging data across a group of subjects when multimodal data is acquired for the subjects ica is typically performed separately on each modality leading to incompatible decompositions across modalities using a modular bayesian framework we develop a novel linked ica model for simultaneously modelling and discovering common features across multiple modalities which can potentially have completely different units signal and contrast to noise ratios voxel counts spatial smoothnesses and intensity distributions furthermore this general model can be configured to allow tensor ica or spatially concatenated ica decompositions or a combination of both at the same time linked ica automatically determines the optimal weighting of each modality and also can detect single modality structured components when present this is a fully probabilistic approach implemented using variational bayes we evaluate the method on simulated multimodal data sets as well as on a real data set of alzheimer s patients and age matched controls that combines two very different types of structural mri data morphological data grey matter density and diffusion data fractional anisotropy mean diffusivity and tensor mode

hybrid dirichlet mixture models for functional data summary in functional data analysis curves or surfaces are observed up to measurement error at a finite set of locations for say a sample of n individuals often the curves are homogeneous except perhaps for individual specific regions that provide heterogeneous behaviour e g damaged areas of irregular shape on an otherwise smooth surface motivated by applications with functional data of this nature we propose a bayesian mixture model with the aim of dimension reduction by representing the sample of n curves through a smaller set of canonical curves we propose a novel prior on the space of probability measures for a random curve which extends the popular dirichlet priors by allowing local clustering non homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations hybrids of a few canonical curves more precisely the prior proposed envisions a conceptual hidden factor with k levels that acts locally on each curve we discuss several models incorporating this prior and illustrate its performance with simulated and real data sets we examine theoretical properties of the proposed finite hybrid dirichlet mixtures specifically their behaviour as the number of the mixture components goes to 1 and their connection with dirichlet process mixtures

nonlinear regression in parametric activation studies parametric study designs can reveal information about the relationship between a study parameter e g word presentation rate and regional cerebral blood flow rcbf in functional imaging the brain s responses in relation to study parameters might be nonlinear therefore the linear correlation coefficient as often used in the analysis of parametric studies might not be a proper characterization we present a noninteractive method which fits nonlinear functions of stimulus or task parameters to rcbf responses using second order polynomial expansions this technique is implemented in the context of the general linear model and statistical parametric mapping we also consider the usefulness of statistical inferences based on f fields about similarities and differences of these nonlinear responses in different groups this approach is illustrated with a 12 run h 2 o pet activation study using an auditory paradigm of increasing word presentation rates a patient who had recovered from severe aphasia and a normal control were studied we demonstrate the ability of this new technique to identify brain regions where rcbf is closely related to increasing word presentation rate in both subjects without constraining the nature of this relationship and where these nonlinear responses differ r1996academic press inc

dynamic equivalence self equilibrated excitation and saint venant s principle for an elastic strip abstract the distinction between the near and far fields for a semi infinite elastic strip has been exploited to derive conditions under which different dynamic excitations can be considered as equivalent these different excitations are equivalent in the sense that they produce the same displacement field far from the excited end it is shown that dynamically equivalent excitations degenerate to statically equivalent loads in the limit of a vanishing frequency the no radiation condition is derived and its relation to self equilibrated dynamic and static loads is presented dynamically equivalent excitations are utilized to formulate a dynamic version of saint venant s principle for symmetric excitations with frequencies below the first cut off frequency of a strip it has been shown that the requirement of self equilibrium of a load for the decay of end effects for static fields can be deduced from the requirement of zero average power for the dynamic fields

linking functional and structural brain images with multivariate network analyses a novel application of the partial least square method abstract in this article we introduce a multimodal multivariate network analysis to characterize the linkage between the patterns of information from the same individual s complementary brain images and illustrate its potential by showing its ability to distinguish older from younger adults with greater power than several previously established methods our proposed method uses measurements from every brain voxel in each person s complementary co registered images and uses the partial least square pls algorithm to form a combined latent variable that maximizes the covariance among all of the combined variables it represents a new way to calculate the singular value decomposition from the high dimensional covariance matrix in a computationally feasible way analyzing fluorodeoxyglucose positron emission tomography pet and volumetric magnetic resonance imaging mri images this method distinguished 14 older adults from 15 younger adults p 4e 12 with no overlap between groups no need to correct for multiple comparisons and greater power than the univariate statistical parametric mapping spm multimodal spm or multivariate pls analysis of either imaging modality alone this technique has the potential to link patterns of information among any number of complementary images from an individual to use other kinds of complementary complex datasets besides brain images and to characterize individual state or trait dependent brain patterns in a more powerful way

application of principal component analysis to distinguish patients with schizophrenia from healthy controls based on fractional anisotropy measurements principal component analysis pca is often used to reduce the dimension of data before applying more sophisticated data analysis methods such as non linear classification algorithms or independent component analysis this practice is based on selecting components corresponding to the largest eigenvalues if the ultimate goal is separation of data in two groups then these set of components need not have the most discriminatory power we measured the distance between two such populations using mahalanobis distance and chose the eigenvectors to maximize it a modified pca method which we call the discriminant pca dpca dpca was applied to diffusion tensor based fractional anisotropy images to distinguish age matched schizophrenia subjects from healthy controls the performance of the proposed method was evaluated by the one leave out method we show that for this fractional anisotropy data set the classification error with 60 components was close to the minimum error and that the mahalanobis distance was twice as large with dpca than with pca finally by masking the discriminant function with the white matter tracts of the johns hopkins university atlas we identified left superior longitudinal fasciculus as the tract which gave the least classification error in addition with six optimally chosen tracts the classification error was zero

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

analysis of fmri data using improved self organizing mapping and spatio temporal metric hierarchical clustering the self organizing mapping som and hierarchical clustering hc methods are integrated to detect brain functional activation functional magnetic resonance imaging fmri data are first processed by som to obtain a primary merged neural nodes image and then by hc to obtain further brain activation patterns the conventional euclidean distance metric was replaced by the correlation distance metric in som to improve clustering and merging of neural nodes to improve the use of spatial and temporal information in fmri data a new spatial distance node coordinates in the 2 d lattice and temporal correlation correlation degree of each time course in the exemplar matrix are introduced in hc to merge the primary som results two simulation studies and two in vivo fmri data that both contained block design and event related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods our results demonstrate that the improved som and hc methods are clearly superior to the statistical parametric mapping spm independent component analysis ica and conventional som methods in the block design especially in the event related experiment as revealed by their performance measured by receiver operating characteristic roc analysis our results also suggest that the proposed new integrated approach could be useful in detecting block design and event related fmri data

characterizing the response of pet and fmri data using multivariate linear models this paper presents a new method for characterizing brain responses in both pet and fmri data the aim is to capture the correlations between the scans of an experiment and a set of external predictor variables that are thought to affect the scans such as type intensity or shape of stimulus response its main feature is a canonical variates analysis cva of the estimated effects of the predictors from a multivariate linear model mlm the advantage of this over current methods is that temporal correlations can be incorporated into the model making the mlm method suitable for fmri as well as pet data moreover tests for the presence of any correlation and inference about the number of canonical variates needed to capture that correlation can be based on standard multivariate statistics rather than simulations when applied to an fmri data set previously analyzed by another cva method the mlm method reveals a pattern of responses that is closer to that detected in an earlier non cva analysis

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

optimal spline smoothing of fmri time series by generalized cross validation linear parametric regression models of fmri time series have correlated residuals one approach to address this problem is to condition the autocorrelation structure by temporal smoothing smoothing splines with the degree of smoothing selected by generalized cross validation gcv spline provide a method to find an optimal smoother for an fmri time series the purpose of this study was to determine if gcv spline of fmri time series yields unbiased variance estimates of linear regression model parameters gcv spline was evaluated with a real fmri data set and bias of the variance estimator was computed for simulated time series with autocorrelation structures derived from fmri data this study only considered fmri experimental designs of boxcar type the results from the real data suggest that gcv spline determines appropriate amounts of smoothing the simulations show that the variance estimates are on average unbiased the unbiased variance estimates come at some cost to signal detection efficiency this study demonstrates that gcv spline is an appropriate method for smoothing fmri time series

semiparametric detection of significant activation for brain fmri functional magnetic resonance imaging fmri aims to locate activated regions in human brains when specific tasks are performed the conventional tool for analyzing fmri data applies some variant of the linear model which is restrictive in modeling assumptions to yield more accurate prediction of the time course behavior of neuronal responses the semiparametric inference for the underlying hemodynamic response function is developed to identify significantly activated voxels under mild regularity conditions we demonstrate that a class of the proposed semiparametric test statistics based on the local linear estimation technique follow x 2 distributions under null hypotheses for a number of useful hypotheses furthermore the asymptotic power functions of the constructed tests are derived under the fixed and contiguous alternatives simulation evaluations and real fmri data application suggest that the semiparametric inference procedure provides more efficient detection of activated brain areas than the popular imaging analysis tools afni and fsl

a cluster mass permutation test with contextual enhancement for fmri activation detection gaussian random field grf based methods are commonly used for statistical inference and to control the family wise error rate fwe in neuroimaging they require that the error fields are reasonable lattice approximations to an underlying continuous multivariate gaussian random field and have differentiable and invertible spatial autocorrelation function permutation test estimates the distribution of the test statistic from the data and adjusts automatically for the fwe here we present a new analysis procedure the cluster mass permutation test with contextual enhancement cmpce and compare it to grf in cmpce the data are first pre whitened to remove temporal autocorrelations the fwe rates the cluster detection probability and delineation accuracy of cmpce and grf were compared using measured null data and null data containing simulated activations we also applied both methods to an fmri experiment where tactile somatosensory stimulation into the right hand was used when analyzing the fwe using null data both cmpce and grf gave significantly higher fwes cmpce up to 0 12 grf up to 0 18 than the nominal significance level 0 05 indicating that the pre whitening motion correction or high pass filtering partially failed in the simulated activation data cmpce gave less falsely classified voxels for the same cluster detection probability level than grf the maximal cluster detection probability was on the other hand higher in the grf based method both methods gave qualitatively similar results in the tactile fmri data cmpce seems to be a promising fmri analysis method especially if high delineation accuracy is required

sparse canonical correlation analysis new formulation and algorithm in this paper we study canonical correlation analysis cca which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables the main contributions of the paper are 1 to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple cca problem 2 to obtain the explicit characterization for all solutions of the multiple cca problem even when the corresponding covariance matrices are singular 3 to develop a new sparse cca algorithm and 4 to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the cca problem we test several simulated and real world datasets in gene classification and cross language document retrieval to demonstrate the effectiveness of the proposed algorithm the performance of the proposed method is competitive with the state of the art sparse cca algorithms

multidimensional scaling of integrated neurocognitive function and schizophrenia as a disconnexion disorder multidimensional scaling mds is a multivariate statistical technique that can be used to define sub systems of functionally connected brain regions based on the analysis of functional magnetic resonance im aging fmri data here we introduce three way mul tidimensional scaling as a method for the analysis of a group of fmri data which yields both a generic inter regional configuration in low dimensional space and a measure of each individual s deviation from the ge neric configuration the distance between two generic interregional configurations obtained by mds of two groups of data can be minimized by generalized pro crustes analysis and the probability under the null hypothesis that the two groups are sampled from the same population of any residual group difference in interregional configurations can be assessed by a per mutation test these methods are developed and ap plied to activated fmri time series acquired from 19 patients with schizophrenia and 20 normal compari son subjects during the performance of a semantic categorization and subvocal rehearsal task the first three scaling dimensions are interpretable in terms of the major anatomical or functional subsystems of the activated system left right input processing other and subvocal output other we found no sig nificant global or local differences between groups in interregional configurations in this 3d space how ever there was significantly greater variability of interregional configurations within the group of patients with schizophrenia the implications for schizophrenia as a disconnexion disorder are

theoretical analysis of bayesian matrix factorization recently variational bayesian vb techniques have been applied to probabilistic matrix factorization and shown to perform very well in experiments in this paper we theoretically elucidate properties of the vb matrix factorization vbmf method through finite sample analysis of the vbmf estimator we show that two types of shrinkage factors exist in the vbmf estimator the positive part james stein pjs shrinkage and the trace norm shrinkage both acting on each singular component separately for producing low rank solutions the trace norm shrinkage is simply induced by non flat prior information similarly to the maximum a posteriori map approach thus no trace norm shrinkage remains when priors are non informative on the other hand we show a counter intuitive fact that the pjs shrinkage factor is kept activated even with flat priors this is shown to be induced by the non identifiability of the matrix factorization model that is the mapping between the target matrix and factorized matrices is not one to one we call this model induced regularization we further extend our analysis to empirical bayes scenarios where hyperparameters are also learned based on the vb free energy throughout the paper we assume no missing entry in the observed matrix and therefore collaborative filtering is out of scope

nonparametric inference of the hemodynamic response using multi subject fmri data estimation and inferences for the hemodynamic response functions hrf using multi subject fmri data are considered within the context of the general linear model two new nonparametric estimators for the hrf are proposed the first is a kernel smoothed estimator which is used to construct hypothesis tests on the entire hrf curve in contrast to only summaries of the curve as in most existing tests to cope with the inherent large data variance we introduce a second approach which imposes tikhonov regularization on the kernel smoothed estimator an additional bias correction step which uses multi subject averaged information is introduced to further improve efficiency and reduce the bias in estimation for individual hrfs by utilizing the common properties of brain activity shared across subjects this is the main improvement over the standard methods where each subject s data is usually analyzed independently a fast algorithm is also developed to select the optimal regularization and smoothing parameters the proposed methods are compared with several existing regularization methods through simulations the methods are illustrated by an application to the fmri data collected under a psychology design employing the monetary incentive delay mid task

a novel framework for parsimonious multivariate analysis abstract this paper proposes a framework in which a multivariate analysis method mva guides a selection of input variables that leads to a sparse feature extraction this framework called parsimonious mva is specially suited for high dimensional data such as gene arrays digital pictures etc the feature selection relies on the analysis of consistency in the behaviour of the input variables through the elements of an ensemble of mva projection matrices the ensemble is constructed following a bootstrap that builds on an efficient and generalized mva formulation that covers pca cca and opls moreover it allows the estimation of the relative relevance of each selected input variable experimental results point out that the features extracted by the parsimonious mva have excellent discrimination power comparing favorably with state of the art methods and are potentially useful to build interpretable features besides the parsimonious feature extractor is shown to be robust against to parameter selection as we all computationally efficient

statistical parametric mapping for event related potentials ii a hierarchical temporal model in this paper we describe a temporal model for event related potentials erp in the context of statistical parametric mapping spm in brief we project channel data onto a two dimensional scalp surface or into three dimensional brain space using some appropriate inverse solution we then treat the spatiotemporal data in a mass univariate fashion this implicitly factorises the model into spatial and temporal components the key contribution of this paper is the use of observation models that afford an explicit distinction between observation error and variation in the expression of erps this distinction is created by employing a two level hierarchical model in which the first level models the erp effects within subject and trial type while the second models differences in erp expression among trial types and subjects by bringing the analysis of erp data into a classical hierarchical i e mixed effects framework many apparently disparate approaches e g conventional p300 analyses and time frequency analyses of stimulus locked oscillations can be reconciled within the same estimation and inference procedure inference proceeds in the normal way using t or f statistics to test for effects that are localised in peristimulus time or in some time frequency window the use of f statistics is an important generalisation of classical approaches because it allows one to test for effects that lie in a multidimensional subspace i e of unknown but constrained form we describe the analysis procedures the underlying theory and compare its performance to established techniques

classification of fmri time series in a low dimensional subspace with a spatial prior we propose a new method for detecting activation in functional magnetic resonance imaging fmri data we project the fmri time series on a low dimensional subspace spanned by wavelet packets in order to create projections that are as non gaussian as possible our approach achieves two goals it reduces the dimensionality of the problem by explicitly constructing a sparse approximation to the dataset and it also creates meaningful clusters allowing the separation of the activated regions from the clutter formed by the background time series we use a mixture of gaussian densities to model the distribution of the wavelet packet coefficients we expect activated areas that are connected and impose a spatial prior in the form of a markov random field our approach was validated with in vivo data and realistic synthetic data where it outperformed a linear model equipped with the knowledge of the true hemodynamic response

removal of confounding effects of global signal in functional mri analyses local signals obtained from bold fmri are generally confounded by global effects in this paper we make an essential distinction between global effects and the global signal global effects have a similar influence on local signals from a large proportion of cerebral voxels they may reflect diffuse physiological processes or variations in scanner sensitivity and are difficult to measure directly global effects are often estimated from the global signal which is the spatial average of local signals from all cerebral voxels if the global signal is strongly correlated with experimental manipulations meaningfully different results may be obtained whether or not global effects are modeled g k aguirre et al 1998 neuroimage 8 302 306 in particular if local bold signals make a significant contribution to the global signal analyses using ancovaor proportional scaling models may yield artifactual deactivations in this paper we present a modification to the proportional scaling model that accounts for the contribution of local bold signals to the global signal an event related oddball stimulus paradigm and a block design working memory task were used to illustrate the efficacy of our model

wavelet moment method for solving fredholm integral equations of the first kind in this paper we suggest an efficient method for solving fredholm integral equations of the first kind using wavelets as basis functions in the moment method and reducing the order of the linear equation rather than making the matrix sparse in the end we give some numerical examples

estimating efficiency a priori a comparison of blocked and randomized designs this technical note deals with a priori estimation of efficiency of functional magnetic resonance imaging fmri designs the efficiency of an estimator is a measure of how reliable it is and depends on error variance the variance not modeled by explanatory variables in the design matrix and the design variance a function of the explanatory variables and the contrast tested changes in the experimental design can induce changes in the variance of estimated responses this translates into changes in the standard error of the response estimate or equivalently into changes in efficiency one consequence is that statistics testing for the same activation in different contexts i e experimental designs can change substantially even if the activation and error variance are exactly the same we demonstrate this effect using an event related fmri study of single word reading during blocked and randomized trial presentations furthermore we show that the error variance can change with the experimental design this highlights a problem with a priori comparison of efficiency for two or more experimental designs which usually assumes identical error variance

numerical solution of fredholm integral equations of the first kind by using linear legendre multi wavelets in this paper we suggest an efficient method for solving fredholm integral equations of the first kind the continuous legendre multi wavelets constructed on 0 1 are utilized as a basis in galerkin method to reduce the solution of linear integral equations to a system of algebraic equations illustrative examples are included to demonstrate the efficiency and the application of the technique

to smooth or not to smooth bias and efficiency in fmri time series analysis this paper concerns temporal filtering in fmri time series analysis whitening serially correlated data is the most efficient approach to parameter estimation however if there is a discrepancy between the assumed and the actual correlations whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates this bias although not expressed in terms of the estimated responses has profound effects on any statistic used for inference the special constraints of fmri analysis ensure that there will always be a misspecification of the assumed serial correlations one resolution of this problem is to filter the data to minimize bias while maintaining a reasonable degree of efficiency in this paper we present expressions for efficiency of parameter estimation and bias in estimating standard error in terms of assumed and actual correlation structures in the context of the general linear model we show that i whitening strategies can result in profound bias and are therefore probably precluded in parametric fmri data analyses ii band pass filtering and implicitly smoothing has an important role in protecting against inferential bias

effect of initial fmri data modeling on the connectivity reported between brain areas nearly all neuroimaging data analysis rests upon some form of variance partitioning conventional analyses with a general linear model glm partition the variance in the measured response variable into partitions described by a design matrix of explanatory variables this approach can also be adopted in the initial modeling of the data in studies using data led methods to summarize functional connectivity such as principle component analysis or studies of effective connectivity using for example structural equation modeling the point made in this technical note is that the partition of the original time series has to be precisely described to qualify the sources of variations that are taken into account for conventional analyses using the glm the partition investigated corresponds to the subspaces of the design matrix that are tested however in the analyses of functional and effective connectivity the particular subspaces considered are not always specified explicitly here we show that selecting different subspaces or variance partitions can have a profound effect both qualitatively and quantitatively on the sample covariances and the ensuing inferences about connectivity we will illustrate this using simulated data that include condition and block related effects and their interactions we will use these three subspaces to show how the correlation between two voxels depends on which sub partitions are examined we will also show how the partition of the design matrix influences the resulting correlation matrix observed when studying correlations between error terms we will finally demonstrate quantitatively the effect of the variance partitions considered on the correlations between two regions using a real fmri study of biological motion

how to estimate global activity independent of changes in local activity a method is suggested to ensure independence between the estimated global flow and changes in local flow in pet activation studies global flow is estimated as the average of all intracerebral voxels except those that exhibit a consistent change in flow as a consequence of the experimental design this is achieved by performing an initial analysis using all intracerebral voxels for estimation of global flow in which an f map depicting task related changes is produced a second analysis is performed now excluding all voxels with ap 0 05 in the f map when evaluating global flow thereby ensuring independence from areas changing in a task dependent manner the feasibility of the method is demonstrated on phantom data showing that the distribution is skewed in nonactivated areas when including the activated areas in the calculation of global flow by excluding these areas the distribution is translated toward zero and becomes consistent with the null hypothesis furthermore the usefulness of the suggested scheme is demonstrated on human data scans performed while subjects watched a movie featuring snakes were contrasted to scans performed while watching white noise producing highly significant activations of the visual system when using the traditional way of estimating global flow deactivations were observed in very large portions of the frontal parietal and temporal lobes when using the method suggested in the present paper these disappeared which would be more consistent with the expected effects of the stimulation the method was used in conjunction with both ratio and ancova adjustment with very similar results

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

elastodynamic completeness relations for scattered wavefields completeness relations that involve wavefields that have scattered from an inhomogeneity of compact spatial support are derived the scatterer itself can be fully anisotropic and is contained in an otherwise uniform three dimensional isotropic elastic medium of infinite extent roughly these relations are representations of the three dimensional spatial dirac delta function as a product of wavefields that are summed over all states as such the relations serve as the generators of transform pairs that use the wavefields as their underlying set of basis functions furthermore by exploiting the causal nature of the scattering system there are shown to be an infinite number of basis sets involving the wavefields corresponding to a given scatterer

robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model the assessment of significant activations in functional imaging using voxel based methods often relies on results derived from the theory of gaussian random fields these results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated end results i e p values associated with local maxima clusters or sets of clusters critically depend on this assessment which should be as exact and as reliable as possible in some earlier implementations of statistical parametric mapping spm spm94 spm95 the smoothness was assessed on gaussianized t fields gt f that are not generally free of physiological signal this technique has two limitations first the estimation is not stable the variance of the estimator being far from negligible and second physiological signal in the gt f will bias the estimation in this paper we describe an estimation method that overcomes these drawbacks the new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t field knowing the smoothness of these component fields is important because it allows one to compute corrected p values for statistical fields other than the t field or the gt f e g the f map and eschews bias due to deviation from the null hypothesis we validate the method on simulated data and demonstrate it using data from a functional mri study

dynamic version of saint venant s principle historical account and recent results abstract possible existence of a dynamic version of the quasi static saint venant s principle dsvp has been raised by boley five decades ago since then relatively few papers have been dedicated to the possible validity of a dsvp these papers are reviewed in the first part of a present communication an apparent observation is the absence of any consensus on whether there is a dynamic counterpart to the classical saint venant s principle svp with the same generality and validity on the other hand there is experimental support and numerical simulations regarded by several researchers as evidence for the existence and validity of a dsvp in conservative systems nevertheless no coherent versions of svp for dynamic problem in non dissipative systems have been proposed and those proposed are proved to be not valid the historical account emphasizes the apparent gap between the theoretical approach and the experimental insights in the second part of the present communication a new definition of a dynamic version of svp is suggested bridging over the apparent gap between the theoretical approach and experimental insights this is achieved by introducing the concept of dynamically equivalent system of loads analogous to the statically equipollent system of loads introduced by saint venant

a heuristic for the degrees of freedom of statistics based on multiple variance parameters in neuroimaging data are often modeled using general linear models here we focus on glms with error covariances which are modeled as a linear combination of multiple variance covariance components each of these components is weighted by one variance parameter in many analyses variance parameters are estimated using restricted maximum likelihood reml most classical approaches assume the error covariance matrix can be factorized into a single variance parameter and a nonspherical correlation matrix in this context the f test based on a single variance parameter with a suitable correction to the degrees of freedom is the standard inference tool this correction can also be adapted to models with multiple variance parameters however this extension overlooks the uncertainty about the variance parameter estimates and p values tend to be underestimated here we show how one can overcome this problem to render the f test more exact this issue is important because serial correlations in fmri time series are generally modeled using multiple variance parameters another application is to hierarchical linear models which are used for modeling multisubject data to illustrate our approach we apply it to some typical modeling scenarios in fmri data analysis

detection of consistently task related activations in fmri data with hybrid independent component analysis fmri data are commonly analyzed by testing the time course from each voxel against specific hypothesized waveforms despite the fact that many components of fmri signals are difficult to specify explicitly in contrast purely data driven techniques by focusing on the intrinsic structure of the data lack a direct means to test hypotheses of interest to the examiner between these two extremes there is a role for hybrid methods that use powerful data driven techniques to fully characterize the data but also use some a priori hypotheses to guide the analysis here we describe such a hybrid technique hybica which uses the initial characterization of the fmri data from independent component analysis and allows the experimenter to sequentially combine assumed task related components so that one can gracefully navigate from a fully data derived approach to a fully hypothesis driven approach we describe the results of testing the method with two artificial and two real data sets a metric based on the diagnostic predicted sum of squares statistic was used to select the best number of spatially independent components to combine and utilize in a standard regressional framework the proposed metric provided an objective method to determine whether a more data driven or a more hypothesis driven approach was appropriate depending on the degree of mismatch between the hypothesized reference function and the features in the data hybica provides a robust way to combine the data derived independent components into a data derived activation waveform and suitable confounds so that standard statistical analysis can be performed

penalized discriminant analysis of sup 15 o water pet brain images with prediction error selection of smoothness and regularization hyperparameters the authors propose a flexible comprehensive approach for analysis of sup 15 o water positron emission tomography pet brain images using a penalized version of linear discriminant analysis pda they applied it to scans from 20 subjects eight scans subject performing a finger movement task and analyzed 1 two classes to obtain a covariance normalized baseline activation image and 2 eight classes for the mean within subject temporal structure which contained baseline activation and time dependent changes in a two dimensional canonical subspace the authors imposed spatial smoothness on the resulting image s by expanding it in five tensor product b spline tps bases of varying smoothness and further regularized with a ridge type penalty on the noise covariance matrix the discrimination approach of pda provides a probabilistic framework within which prediction error pe estimates are derived the authors used these to optimize over tps bases and a ridge hyperparameter expressed as equivalent degrees of freedom edf they obtained unbiased low variance pe estimates using modern resampling tools 632 bootstrap and cross validation and compared pda of 1 tps projected mean normalized and unnormalized scans and 2 mean normalized scans with and without additional presmoothing by examining the tradeoffs between pe and edf as a function of basis selection and image smoothing the authors demonstrate the utility of pda the pe framework and the relationship between singular value decomposition and smooth tps bases in the analysis of functional neuroimages

multisubject fmri studies and conjunction analyses abstract in this paper we present an approach to making inferences about generic activations in groups of subjects using fmri in particular we suggest that activations common to all subjects reflect aspects of functional anatomy that may be typical of the population from which that group was sampled these commonalities can be identified by a conjunction analysis of the activation effects in which the contrasts testing for an activation are specified separately for each subject a conjunction is the joint refutation of multiple null hypotheses in this instance of no activation in any subject the motivation behind this use of conjunctions is that fixed effect analyses are generally more sensitive than equivalent random effect analyses this is because fixed effect analyses can harness the large degrees of freedom and small scan to scan variability relative to the variability in responses from subject to subject when assessing the significance of an estimated response the price one pays for the apparent sensitivity of fixed effect analyses is that the ensuing inferences pertain to and only to the subjects studied however a conjunction analysis using a fixed effect model allows one to infer i that every subject studied activated and ii that at least a certain proportion of the population would have shown this effect the second inference depends upon a meta analytic formulation in terms of a confidence region for this proportion this approach retains the sensitivity of fixed effect analyses when the inference that only a substantial proportion of the population activates is sufficient

numerical expansion methods for solving integral equations by interpolation and gauss quadrature rules in this paper we introduce a numerical method for solving linear integral equations the main idea based on interpolation for unknown function where is interpolated in the zeros of the chebyshev s polynomials next we use gauss quadrature rules as gauss chebyshev or clenshaw curtis the technique is very effective and simple specially for integral equations of first kind as fredholm s and volterra s types in the end for showing efficiency of this method we use numerical examples

increased sensitivity in neuroimaging analyses using robust regression robust regression techniques are a class of estimators that are relatively insensitive to the presence of one or more outliers in the data they are especially well suited to data that require large numbers of statistical tests and may contain outliers due to factors not of experimental interest both these issues apply particularly to neuroimaging data analysis we use simulations to compare several robust techniques against ordinary least squares ols regression and we apply robust regression to second level group brandom effectsq analyses in three fmri datasets our results show that robust iteratively reweighted least squares irls at the 2nd level is a computationally efficient technique that both increases statistical power and decreases false positive rates in the presence of outliers the benefits of irls are apparent with small samples n 10 and increase with larger sample sizes n 40 in the typical range of group neuroimaging experiments when no true effects are present irls controls false positive rates at an appropriate level we show that irls can have substantial benefits in analysis of group data and in estimating hemodynamic response shapes from time series data we provide software to implement irls in group neuroimaging analyses

wspm wavelet based statistical parametric mapping recently we have introduced an integrated framework that combines wavelet based processing with statistical testing in the spatial domain in this paper we propose two important enhancements of the framework first we revisit the underlying paradigm i e that the effect of the wavelet processing can be considered as an adaptive denoising step to improve the parameter map followed by a statistical detection procedure that takes into account the non linear processing of the data with an appropriate modification of the framework we show that it is possible to reduce the bias of the method with respect to the best linear estimate providing conservative results that are closer to the original data second we propose an extension of our earlier technique that compensates for the lack of shift invariance of the wavelet transform we demonstrate experimentally that both enhancements have a positive effect on performance in particular we present a reproducibility study for multi session data that compares wspm against spm with different amounts of smoothing the full approach is available as a toolbox named wspm for the spm2 software it takes advantage of multiple options and features of spm such as the general linear model

statistical tests for fmri based on experimental randomization statistical parametric mapping spm analysis of fmri data requires specifying correctly the temporal and spatial noise covariance structure this is a difficult if not impossible task when these assumptions are not satisfied statistical inference can be invalid or inefficient permutation tests are free of strong assumptions on the distribution of signal noise we propose permutation tests of fmri data based on experimental randomization of the stimulus sequences smooth hemodynamic response curves are estimated using quadratic b splines we study fmri data obtained from event related potential erp oddball paradigm tests of two tone and three tone stimulus sequences are conducted to illustrate the application of the proposed method comparisons of the spm and proposed method show that a permutation test is more specific and less susceptible to artifacts

group analysis in functional neuroimaging selecting subjects using similarity measures standard group analyses of fmri data rely on spatial and temporal averaging of individuals this averaging operation is only sensible when the mean is a good representation of the group this is not the case if subjects are not homogeneous and it is therefore a major concern in fmri studies to assess this group homogeneity we present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects the method allows a multivariate comparison between data sets of several subjects in the time or in the space domain these analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects at the population level we adapt the rv coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject s position with respect to other subjects in the group we also provide a measure for detecting subjects that may be outliers results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns and that despite the apparent loss of information restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fmri analyses

analysis of fmri time series revisited abstract this paper presents a general approach to the analysis of functional mri time series from one or more subjects the approach is predicated on an extension of the general linear model that allows for correlations between error terms due to physiological noise or correlations that ensue after temporal smoothing this extension uses the effective degrees of freedom associated with the error term the effective degrees of freedom are a simple function of the number of scans and the temporal autocorrelation function a specific form for the latter can be assumed if the data are smoothed in time to accentuate hemodynamic responses with a neural basis this assumption leads to an expedient implementation of a flexible statistical framework the importance of this small extension is that in contradistinction to our previous approach any parametric statistical analysis can be implemented we demonstrate this point using a multiple regression analysis that tests for effects of interest activations due to word generation while taking explicit account of some obvious confounds

probabilistic inference of regularisation in non rigid registration a long standing issue in non rigid image registration is the choice of the level of regularisation regularisation is necessary to preserve the smoothness of the registration and penalise against unnecessary complexity the vast majority of existing registration methods use a fixed level of regularisation which is typically hand tuned by a user to provide nice results however the optimal level of regularisation will depend on the data which is being processed lower signal to noise ratios require higher regularisation to avoid registering image noise as well as features and different pairs of images require registrations of varying complexity depending on their anatomical similarity in this paper we present a probabilistic registration framework that infers the level of regularisation from the data an additional benefit of this proposed probabilistic framework is that estimates of the registration uncertainty are obtained this framework has been implemented using a free form deformation transformation model although it would be generically applicable to a range of transformation models we demonstrate our registration framework on the application of inter subject brain registration of healthy control subjects from the nirep database in our results we show that our framework appropriately adapts the level of regularisation in the presence of noise and that inferring regularisation on an individual basis leads to a reduction in model over fitting as measured by image folding while providing a similar level of overlap

structure seeking multilinear methods for the analysis of fmri data in comprehensive fmri studies of brain function the data structures often contain higher order ways such as trial task condition subject and group in addition to the intrinsic dimensions of time and space while multivariate bilinear methods such as principal component analysis pca have been used successfully for extracting information about spatial and temporal features in data from a single fmri run the need to unfold higher order data sets into bilinear arrays has led to decompositions that are nonunique and to the loss of multiway linkages and interactions present in the data these additional dimensions or ways can be retained in multilinear models to produce structures that are unique and which admit interpretations that are neurophysiologically meaningful multiway analysis of fmri data from multiple runs of a bilateral finger tapping paradigm was performed using the parallel factor parafac model a trilinear model was fitted to a data cube of dimensions voxels by time by run similarly a quadrilinear model was fitted to a higher way structure of dimensions voxels by time by trial by run the spatial and temporal response components were extracted and validated by comparison to results from traditional svd pca analyses based on scenarios of unfolding into lower order bilinear structures

incorporating prior knowledge into image registration the first step in the spatial normalization of brain images is usually to determine the affine transformation that best maps the image to a template image in a standard space we have developed a rapid and automatic method for performing this registration which uses a bayesian scheme to incorporate prior knowledge of the variability in the shape and size of heads we compared affine registrations with and without incorporating the prior knowledge we found that the affine transformations derived using the bayesian scheme are much more robust and that the rate of convergence is greater

a novel temporal filtering strategy for functional mri using unfold a major challenge for fmri at high spatial resolution is the limited temporal resolution the unfold method increases image acquisition speed and potentially enables high acceleration factors in fmri spatial aliasing artifacts due to interleaved k space sampling are to be removed from the image time series by temporal filtering before statistical mapping in the time domain can be carried out so far low pass filtering and multi band filtering have been proposed particularly at high unfold factors both methods are non optimal low pass filtering severely degrades temporal resolution and multi band filtering leads to temporal autocorrelations affecting statistical modelling of activation in this work we present a novel temporal filtering strategy that significantly reduces temporal autocorrelations compared to multi band filtering two datasets finger tapping and resting state were post processed using the proposed and the multi band filter with varying set ups i e transition bands when the proposed filtering strategy was used a linear regression analysis revealed that the number of false positives was significantly decreased up to 34 whereas the number of activated voxels was not significantly affected for most filter parameters in total this led to an effective increase in the number of activated voxels per false positive for each filter set up at a significance level of 5 the number of activated voxels was increased up to 41 by using the proposed filtering strategy

global analytic solution of fully observed variational bayesian matrix factorization the variational bayesian vb approximation is known to be a promising approach to bayesian estimation when the rigorous calculation of the bayes posterior is intractable the vb approximation has been successfully applied to matrix factorization mf offering automatic dimensionality selection for principal component analysis generally finding the vb solution is a nonconvex problem and most methods rely on a local search algorithm derived through a standard procedure for the vb approximation in this paper we show that a better option is available for fully observed vbmf the global solution can be analytically computed more specifically the global solution is a reweighted svd of the observed matrix and each weight can be obtained by solving a quartic equation with its coefficients being functions of the observed singular value we further show that the global optimal solution of empirical vbmf where hyperparameters are also learned from data can also be analytically computed we illustrate the usefulness of our results through experiments in multi variate analysis

study of dynamic end effects in an elastic strip with sliding boundary conditions the dynamic response of an elastic semi infinite strip with sliding surfaces subjected to various forms of end excitations was solved analytically employing the property of bi orthogonality of wave modes an explicit relation between the amplitudes of evanescent waves and the form of the excitation was obtained quantitative measure for dynamic end effects was suggested termed saint venant ratio svr it was shown that two qualities of that ratio are useful for monitoring the health of structural joints shm being that ratio not affected by the intensity of the end excitation and its high sensitivity to small variations in the form of the excitation the axial behavior of the strip subjected to several forms of end excitations was further used to demonstrate the validity of a previously suggested dynamic version of saint venant s principle

set level threshold free tests on the intrinsic volumes of spms conventionally set level inference on statistical parametric maps spms is based on the topological features of an excursion set above some threshold for example the number of clusters or euler characteristic the expected euler characteristic under the null hypothesis can be predicted from an intrinsic measure or volume of the spm such as the resel counts or the lipschitz killing curvatures lkc we propose a new approach that performs a null hypothesis omnibus test on an spm by testing whether its intrinsic volume described by lkc coefficients is different from the volume of the underlying residual fields intuitively whether the number of peaks in the statistical field testing for signal and the residual fields noise are consistent or not crucially this new test requires no arbitrary feature defining threshold but is nevertheless sensitive to distributed or spatially extended patterns we show the similarities between our approach and conventional topological inference in terms of false positive rate control and sensitivity to treatment effects in two and three dimensional simulations the test consistently improves on classical approaches for moderate 20 degrees of freedom we also demonstrate the application to real data and illustrate the comparison of the expected and observed euler characteristics over the complete threshold range

a comparative evaluation of wavelet based methods for hypothesis testing of brain activation maps wavelet based methods for hypothesis testing are described and their potential for activation mapping of human functional magnetic resonance imaging fmri data is investigated in this approach we emphasise convergence between methods of wavelet thresholding or shrinkage and the problem of hypothesis testing in both classical and bayesian contexts specifically our interest will be focused on the trade off between type i probability error control and power dissipation estimated by the area under the roc curve we describe a technique for controlling the false discovery rate at an arbitrary level of error in testing multiple wavelet coefficients generated by a 2d discrete wavelet transform dwt of spatial maps of fmri time series statistics we also describe and apply change point detection with recursive hypothesis testing methods that can be used to define a threshold unique to each level and orientation of the 2d dwt and bayesian methods incorporating a formal model for the anticipated sparseness of wavelet coefficients representing the signal or true image the sensitivity and type i error control of these algorithms are comparatively evaluated by analysis of null images acquired with the subject at rest and an experimental data set acquired from five normal volunteers during an event related finger movement task we show that all three wavelet based algorithms have good type i error control the fdr method being most conservative and generate plausible brain activation maps the bayesian method being most powerful we also generalise the formal connection between wavelet based methods for simultaneous multiresolution denoising hypothesis testing and methods based on monoresolution gaussian smoothing followed by statistical testing of brain activation maps

nonadditive two way anova for event related fmri data analysis abstract asignificant recent development in functional magnetic resonance imaging fmri is the introduction of event related fmri also known as time resolved fmri because the exact shape of the mr response in an event related fmri experiment is often not known traditional methods developed for block design experiments such as t test and correlation analysis are not well suited for extracting activated pixels from the event related data in this work a statistical technique based on nonadditive two way analysis of variance is developed for use in event related studies theoretical and experimental work were carried out for establishing a statistical threshold to determine pixel activation experimental studies were performed to demonstrate the utility of this approach

enhanced signal detection in neuroimaging by means of regional control of the global false discovery rate in the context of neuroimaging experiments it is essential to account for the multiple comparisons problem when thresholding statistical mappings various methods are in use to deal with this issue but they differ in their signal detection power for small and large scale effects in this paper we comprehensively describe a new method that is based on control of the false discovery rate fdr our method increases sensitivity by exploiting the spatially clustered nature of neuroimaging effects this is achieved by using a sliding window technique in which fdr control is first applied at a regional level thus a new statistical map that is related to the regionally achieved fdr is derived from the available voxelwise p values on the basis of receiver operating characteristic roc curves thresholding based on this map is demonstrated to have better discriminatory power than conventional thresholding based on p values secondly it is shown that the resulting maps can be thresholded at a level that results in control of the global fdr by means of statistical arguments and numerical simulations under widely varying conditions our method is validated characterized and compared to some other common voxel based methods uncorrected thresholding bonferroni correction and conventional fdr control it is found that our method shows considerably higher sensitivity as compared to conventional fdr control while still controlling the achieved fdr at the same level or better finally our method is applied to two diverse neuroimaging experiments to assess its practical merits resulting in substantial improvements as compared to the other methods

generalizable patterns in neuroimaging how many principal components generalization can be defined quantitatively and can be used to assess the performance of principal component analysis pca the generalizability of pca depends on the number of principal components retained in the analysis we provide analytic and test set estimates of generalization we show how the generalization error can be used to select the number of principal components in two analyses of functional magnetic resonance imaging activation sets

canonical correlation analysis for multilabel classification a least squares formulation extensions and analysis canonical correlation analysis cca is a well known technique for finding the correlations between two sets of multidimensional variables it projects both sets of variables onto a lower dimensional space in which they are maximally correlated cca is commonly applied for supervised dimensionality reduction in which the two sets of variables are derived from the data and the class labels respectively it is well known that cca can be formulated as a least squares problem in the binary class case however the extension to the more general setting remains unclear in this paper we show that under a mild condition which tends to hold for high dimensional data cca in the multilabel case can be formulated as a least squares problem based on this equivalence relationship efficient algorithms for solving least squares problems can be applied to scale cca to very large data sets in addition we propose several cca extensions including the sparse cca formulation based on the 1 norm regularization we further extend the least squares formulation to partial least squares in addition we show that the cca projection for one set of variables is independent of the regularization on the other set of multidimensional variables providing new insights on the effect of regularization on cca we have conducted experiments using benchmark data sets experiments on multilabel data sets confirm the established equivalence relationships results also demonstrate the effectiveness and efficiency of the proposed cca extensions

empirical analyses of bold fmri statistics i spatially unsmoothed data collected under null hypothesis conditions temporal autocorrelation spatial coherency and their effects on voxel wise parametric statistics were examined in bold fmri null hypothesis or noise datasets seventeen normal young subjects were scanned using bold fmri while not performing any time locked experimental behavior temporal autocorrelation in these datasets was described well by a 1 frequency relationship voxel wise statistical analysis of these noise datasets which assumed independence i e ignored temporal autocorrelation rejected the null hypothesis at a higher rate than specified by the nominal alpha temporal smoothing in conjunction with the use of a modified general linear model worsley and friston 1995 neuroimage 2 173 182 brought the false positive rate closer to the nominal alpha it was also found that the noise fmri datasets contain spatially coherent time signals this observed spatial coherence could not be fully explained by a continuously differentiable spatial autocovariance function and was much greater for lower temporal frequencies its presence made voxel wise test statistics in a given noise dataset dependent and thus shifted their distributions to the right or left of 0 inclusion of a global signal covariate in the general linear model reduced this dependence and consequently stabilized i e reduced the variance of dataset false positive rates