extended convergence regions for the aor method abstract in this paper we give sufficient conditions for the convergence of the aor method when the matrix a for ax b is a strictly diagonally dominant matrix these results improve the conclusions obtained in the theorem 4 10 with the notion of generalized diagonal dominant matrix we enlarge the convergence regions given in theorem 9 10 when a is a nonsingular h matrix in the last section we generalize theorem 6 of robert 11 and we present some results which extend the convergence regions for the aor method

optimum accelerated overrelaxation method in a special case absbact in this paper we give the optimum parameters for the accelerated overrelaxation aor method in the special case where the matrix coefficient of the linear system which is solved is consistently ordered with nonvanishing diagonal elements under certain assumptions concerning the eigenvalues of the corresponding jacobi matrix it is shown that the optimum aor method gives better convergence rates than the optimum sor does while in the remaining cases the optimum aor method coincides with the optimum sor one

a unified sparse recovery and inference framework for functional diffuse optical tomography using random effect model diffuse optical tomography dot is a non invasive imaging technique to reconstruct optical properties of biological tissues using near infrared light and it has been successfully used to measure functional brain activities via changes in cerebral blood volume and cerebral blood oxygenation however dot presents a severely ill posed inverse problem so various types of regularization should be incorporated to overcome low spatial resolution and lack of depth sensitivity another limitation of the conventional dot reconstruction methods is that an inference step is separately performed after the reconstruction so complicated interaction between reconstruction and regularization is difficult to analyze to overcome these technical difficulties we propose a unified sparse recovery framework using a random effect model whose termination criterion is determined by the statistical inference both numerical and experimental results confirm that the proposed method outperforms the conventional approaches

asymptotic global confidence regions for 3 d parametric shape estimation in inverse problems this paper derives fundamental performance bounds for statistical estimation of parametric surfaces embedded in ropf3 unlike conventional pixel based image reconstruction approaches our problem is reconstruction of the shape of binary or homogeneous objects the fundamental uncertainty of such estimation problems can be represented by global confidence regions which facilitate geometric inference and optimization of the imaging system compared to our previous work on global confidence region analysis for curves two dimensional 2 d shapes computation of the probability that the entire surface estimate lies within the confidence region is more challenging because a surface estimate is an inhomogeneous random field continuously indexed by a 2 d variable we derive an asymptotic lower bound to this probability by relating it to the exceedence probability of a higher dimensional gaussian random field which can in turn be evaluated using the tube formula due to sun simulation results demonstrate the tightness of the resulting bound and the usefulness of the three dimensional global confidence region approach

classical and bayesian inference in neuroimaging theory this paper reviews hierarchical observation models used in functional neuroimaging in a bayesian light it emphasizes the common ground shared by classical and bayesian methods to show that conventional analyses of neuroimaging data can be usefully extended within an empirical bayesian framework in particular we formulate the procedures used in conventional data analysis in terms of hierarchical linear models and establish a connection between classical inference and parametric empirical bayes peb through covariance component estimation this estimation is based on an expectation maximization or em algorithm the key point is that hierarchical models not only provide for appropriate inference at the highest level but that one can revisit lower levels suitably equipped to make bayesian inferences bayesian inferences eschew many of the difficulties encountered with classical inference and characterize brain responses in a way that is more directly predicated on what one is interested in the motivation for bayesian approaches is reviewed and the theoretical background is presented in a way that relates to conventional methods in particular restricted maximum likelihood reml this paper is a technical and theoretical prelude to subsequent papers that deal with applications of the theory to a range of important issues in neuroimaging these issues include i estimating nonsphericity or variance components in fmri time series that can arise from serial correlations within subject or are induced by multisubject i e hierarchical studies ii spatiotemporal bayesian models for imaging data in which voxels specific effects are constrained by responses in other voxels iii bayesian estimation of nonlinear models of hemodynamic responses and iv principled ways of mixing structural and functional priors in eeg source reconstruction although diverse all these estimation problems are accommodated by the peb framework described in this paper

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

a survey of the iterative methods for the solution of linear systems by extrapolation relaxation and other techniques abstract for the iterative solution of linear systems of algebraic equations ax b 1 with a c n n x b c n and det a 0 numerous methods exist although a classification of them seems not to be possible one may note that the first step for the construction of an iterative method usually begins with a splitting of a in 1 thus a is written as a m n where det m 0 and m is easily inverted so that 1 is equivalent to x tx c 2 t m 1n c m 1 the discussion will be restricted to the so called linear stationary iterative methods although some nonstationary ones will be mentioned and emphasis will be given to those which fall into the categories of extrapolation relaxation and similar ones for this it will be assumed that the spectrum t of t in 2 is contained in a well defined compact region r whose complement with respect to the complex plane is simply connected and 1 r under these assumptions and for each specific class of methods described each time an attempt will be made to present the optimum one the optimum is the one out of the class of methods for which the sequence of vectors yielded converges asymptotically to the unique solution of 1 as fast as possible

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

detecting sparse signals in random fields with an application to brain mapping brain mapping data have been modeled as gaussian random fields and local increases in mean are detected by local maxima of a random field of test statistics derived from these data accurate p values for local maxima are readily available for isotropic data based on the expected euler characteristic of the excursion set of the test statistic random field in this article we give a simple method for dealing with nonisotropic data our approach has connections to the model of sampson and guttorp for nonisotropy in which there exists an unknown mapping of the support of the data to a space in which the random fields are isotropic heuristic justification for our approach comes from the nash embedding theorem formally we show that our method gives consistent unbiased estimators for the true p values based on new results of taylor and adler for random fields on manifolds which replace the euclidean metric by the variogram the results are used to detect gender differences in the cortical thickness of the b

second order analysis of improper complex random vectors and processes we present a comprehensive treatment of the second order theory of complex random vectors and wide sense stationary wss signals the main focus is on the improper case in which the complementary covariance does not vanish accounting for the information present in the complementary covariance requires the use of widely linear transformations based on these we present the eigenanalysis of complex vectors and apply it to the problem of rank reduction through principal components we also investigate joint properties of two complex vectors by introducing canonical correlations which paves the way for a discussion of the wiener filter and its rank reduced version we link the concepts of propriety and joint propriety to eigenanalysis and canonical correlation analysis respectively our treatment is extended to wss signals in particular we give a result on the asymptotic distribution of eigenvalues and examine the connection between wss proper and analytic signals

optimal block iterative schemes for certain large sparse and nonsymmetric linear systems abstract the problem of determining fast iterative solutions of certain large sparse and nonsymmetric linear systems arising in applications is addressed here several iterative schemes from the accelerated overrelaxation family are considered different geometrical algorithms are used for the explicit determination of the optimal factors direct comparisons of the spectral radii of the resulting optimal schemes reveal that the optimal extrapolated accelerated gauss seidel eags is always asymptotically faster than the optimal successive overrelaxation while the optimal eags and extrapolated gauss seidel strongly compete application of the collocation method on simple boundary value problems is used to demonstrate our results numerically

general multilevel linear modeling for group analysis in fmri this article discusses general modeling of multisubject and or multisession fmri data in particular we show that a two level mixed effects model where parameters of interest at the group level are estimated from parameter and variance estimates from the single session level can be made equivalent to a single complete mixed effects model where parameters of interest at the group level are estimated directly from all of the original single sessions time series data if the co variance at the second level is set equal to the sum of the co variances in the single level form using the blue with known covariances this result has significant implications for group studies in fmri since it shows that the group analysis requires only values of the parameter estimates and their co variance from the first level generalizing the well established summary statistics approach in fmri the simple and generalized framework allows different prewhitening and different first level regressors to be used for each subject the framework incorporates multiple levels and cases such as repeated measures paired or unpaired t tests and f tests at the group level explicit examples of such models are given in the article using numerical simulations based on typical first level covariance structures from real fmri data we demonstrate that by taking into account lower level covariances and heterogeneity a substantial increase in higher level z score is possible

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

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

on the equivalence of extrapolation and richardson s iteration and its applications abstract sometime ago two articles g opfer g schober richardson s iteration for nonsymmetric matrices linear algebra appl 58 1984 343 361 a hadjidimos the optimal solution to the problem of complex extrapolation of a first order scheme linear algebra appl 62 1984 241 261 appeared the same year in this journal solving the problem of optimizing the convergence factor of the stationary richardson s iteration i e x m 1 x m a ax m b m 0 1 2 for the solution of the system ax b a c n n det a 0 b c n in opfer and schober g opfer g schober richardson s iteration for nonsymmetric matrices linear algebra appl 58 1984 343 361 when the spectrum of a was contained in a certain compact set s 1 not including the origin the optimal parameter a was determined in hadjidimos a hadjidimos the optimal solution to the problem of complex extrapolation of a first order scheme linear algebra all 62 1984 241 261 for the solution of ax b the consistent linear scheme x m 1 tx m c m 0 1 2 for which the spectrum of t was contained in a certain compact convex set s 2 not including the point 1 was considered and the optimal extrapolation parameter of its extrapolation scheme i e x m 1 1 i t x m c m 0 1 2 was determined because the approach in obtaining the optimal parameters in the two articles was quite different it seems it was difficult for any one to notice their equivalence and therefore to use them even in trivial cases in this article we show the equivalence of the optimal results in opfer and schober g opfer g schober richardson s iteration for nonsymmetric matrices linear algebra appl 58 1984 343 361 and hadjidimos a hadjidimos the optimal solution to the problem of complex extrapolation of a first order scheme linear algebra all 62 1984 241 261 explore them further obtain new results and give applications for cases which may occur in practice finally based on observations regarding the optimal two cyclic successive overrelaxation sor and accelerated overrelaxation aor methods in two real case problems we solve the problem of optimal two cyclic aor in the more general complex case

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

hotelling s theorem on the volume of tubes some illustrations in simultaneous inference and data analysis we illustrate with contemporary examples hotelling s geometric approach to simultaneous probability calculations hotelling reduces the evaluation of certain normal theory significance probabilities to finding the volume of a tube about a curve in a hypersphere and shows that this volume is often exactly given by length times cross sectional area we review hotelling s result together with some recent complements and then use the approach to set simultaneous prediction regions for some data from gait analysis to study andrews plots in multivariate data analysis and to construct significance tests for projection pursuit regression a by product is a numerical criterion for tube self overlap relevant for example to uniqueness of certain nonlinear least squares estimates

fast optical signal in visual cortex improving detection by general linear convolution model abstract in this study we applied the general linear convolution model to fast optical signals fos we modeled the impulse response function irf as a rectangular function lasting 30 ms with variable time delay with respect to the stimulus onset simulated data confirmed the feasibility of this approach and its capability of detecting simulated activations in case of very unfavorable signal to noise ratio snr providing better results than the grand average method the model was tested in a cohort of 10 healthy volunteers who underwent to hemi field visual stimulation experimental data quantified the irf time delay at 80 100 ms after the stimulus onset in agreement with classical visual evoked potential literature and previous optical imaging studies based on grand average approach and a larger number of trails fos confirmed the expected contralateral activation in the occipital region correlational analysis between hemodynamic intensity signal phase and intensity fos supports diffusive rather than optical absorption changes associated with neuronal activity in the activated cortical volume our study provides a feasible method for detecting fast cortical activations by means of fos

the detection of local shape changes via the geometry of hotelling s t 2 fields this paper is motivated by the problem of detecting local changes or differences in shape between two samples of objects via the nonlinear deformations required to map each object to an atlas standard local shape changes are then detected by high values of the random field of hotelling s t 2 statistics for detecting a change in mean of the vector deformations at each point in the object to control the null probability of detecting a local shape change we use the recent result of adler that the probability that a random field crosses a high threshold is very accurately approximated by the expected euler characteristic ec of the excursion set of the random field above the threshold we give an exact expression for the expected ec of a hotelling s t 2 field and we study the behavior of the field near local extrema this extends previous results for gaussian random fields by adler and x 2 t and f fields by worsley and cao for illustration these results are applied to the detection of differences in brain shape between a sample of 29 males and 23 females

a survey of aor and tor methods abstract this paper makes a survey on the aor and tor methods we present the recent results about convergence and determination of the optimum parameters mainly those obtained by chinese authors

an extension of the accelerated overrelaxation aor theory for linear systems with heritian matrix abstract in this paper the convergence theory of the accelerated overrelaxation aor method for the solution of the linear system ax b where a is hermitian ah a is studied under the general splitting a d e eh where d is hermitian and e 1 2 d a s with sh s the purpose of the paper is to cover the case where d is hermitian and negative definite the case where d is hermitian and positive definite was covered in 8

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

a non iterative technique for phase noise ici mitigation in packet based ofdm systems a practical approach for detecting packet based orthogonal frequency division multiplexing ofdm signals in the presence of phase noise is presented an ofdm packet consists of several ofdm symbols with full pilot symbols at the beginning followed by consecutive data symbols based on the full pilot ofdm symbol a frequency domain joint phase noise and channel vector estimator is first derived it is shown that the phase noise vector can be estimated by maximizing a constrained quadratic form without requiring knowledge of the channel vector this estimated phase noise vector is then used to compute the least squares channel estimator assuming that the channel is constant during each packet the estimated channel is used in subsequent data ofdm symbols for equalization and data detection since phase noise changes from one ofdm symbol to the next the scattered pilots in each data ofdm symbol are used to non iteratively estimate and mitigate the phase noise induced interference a significant improvement in the signal to interference plus noise ratio is achieved using the proposed algorithm

reduction of global interference of scalp hemodynamics in functional near infrared spectroscopy using short distance probes abstract functional near infrared spectroscopy fnirs is used to measure cerebral activity because it is simple and portable however scalp hemodynamics often contaminates fnirs signals leading to detection of cortical activity in regions that are actually inactive methods for removing these artifacts using standard source detector distance channels long channel tend to over estimate the artifacts while methods using additional short source detector distance channels short channel require numerous probes to cover broad cortical areas which leads to a high cost and prolonged experimental time here we propose a new method that effectively combines the existing techniques preserving the accuracy of estimating cerebral activity and avoiding the disadvantages inherent when applying the techniques individually our new method accomplishes this by estimating a global scalp hemodynamic component from a small number of short channels and removing its influence from the long channels using a general linear model glm to demonstrate the feasibility of this method we collected fnirs and functional magnetic resonance imaging fmri measurements during a motor task first we measured changes in oxygenated hemoglobin concentration oxy hb from 18 short channels placed over motor related areas and confirmed that the majority of scalp hemodynamics was globally consistent and could be estimated from as few as four short channels using principal component analysis we then measured oxy hb from 4 short and 43 long channels the glm identified cerebral activity comparable to that measured separately by fmri even when scalp hemodynamics exhibited substantial task related modulation these results suggest that combining measurements from four short channels with a glm provides robust estimation of cerebral activity at a low cost

fast optical signals in the sensorimotor cortex general linear convolution model applied to multiple source detector distance based data abstract in this study we applied the general linear convolution model to detect fast optical signals fos in the somatosensory cortex and to study their dependence on the source detector separation distance 2 0 to 3 5 cm and irradiated light wavelength 690 and 830 nm we modeled the impulse response function as a rectangular function that lasted 30 ms with variable time delay with respect to the stimulus onset the model was tested in a cohort of 20 healthy volunteers who underwent supra motor threshold electrical stimulation of the median nerve the impulse response function quantified the time delay for the maximal response at 70 ms to 110 ms after stimulus onset in agreement with classical somatosensory evoked potentials in the literature previous optical imaging studies based on a grand average approach and grand average based processing phase signals at longer wavelength were used to identify fos for all the source detector separation distances but the shortest one intensity signals only detected fos at the greatest distance i e for the largest channel depth there was no activation for the shorter wavelength light correlational analysis between the phase and intensity of fos further confirmed diffusive rather than optical absorption changes associated with neuronal activity in the activated cortical volume our study demonstrates the reliability of our method based on the general linear convolution model for the detection of fast cortical activation through fos

optimum accelerated overrelaxation aor method for systems with positive definite coefficient matrix given a linear system with a hermitian positive definite coefficient matrix a a splitting of it of varga s type 18 is considered and the corresponding generalized accelerated overrelaxation aor scheme is formed under certain assumptions concerning one of the components of a and the convergence domains of the two parameters of the aor method an analysis analogous to that by varga enables one to determine optimum values for the parameters involved as both theory and numerical examples show the optimum aor method obtained in this way is faster than the corresponding sor one

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

non adaptive and adaptive saor cg algorithms abstract the paper is concerned with an improvement over the symmetric accelerated overrelaxation saor method for an iterative solution of large linear systems at first the conjugate gradient cg acceleration procedure is introduced to the saor method and the non adaptive saor cg algorithm is developed next the adaptive procedure to determine automatically the cg parameters n n and the saor parameters is constructed based on the adaptive procedure the adaptive saor cg algorithm is proposed and its characteristics are shown with numerical experiments a comparison with the optimum sor algorithm and the adaptive ssor algorithm is also given it is finally proved that the proposed adaptive saor cg algorithm is feasible and very efficient for the iterative solution

the convergence of accelerated overrelaxation iterations etablissement des conditions de convergence du processus de surrelaxation acceleree applique a la solution d un systeme d equations lineaires reelles

a necessary condition for the convergence of the accelerated overrelaxation aor method abstract the purpose of this note is to give a general necessary condition for the convergence of the aor method correcting and completing at the same time previous results of this type

on the convergence of the saor method and the error bounds for its acceleration given a linear system with hermitian positive definite coefficient matrix a a splitting of varga s type 1 is considered and the corresponding generalised saor scheme is presented we obtain the convergence theorem for the saor method and give the error bound for the a norm of the error vector for the saor semi iterative method hence extending the saor theory

extrapolated iterative methods for linear systems approximation in this note we present results on extrapolated iterative methods especially the extrapolated successive overrelaxation esor we show that they converge even if the original iteration diverges which increases considerably the scope of application of iterative schemes the esor method is discussed under this aspect for consistently ordered systems and complex eigenvalues of the jacobi iteration matrix comparison theorems are given to show that the esor is particularly useful if the sor diverges or its optimum parameter omega b cannot be determined but even if omega b is known the esor may be faster than the sor method further insight into the structure of the method is obtained by relating it to euler s integration method