multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

co registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization diffusion mri provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain echo planar imaging epi sequences which are frequently used for acquisition of diffusion images are sensitive to inhomogeneities in the primary magnetic b0 field that cause localized distortions in the reconstructed images we describe and evaluate a new method for correction of susceptibility induced distortion in diffusion images in the absence of an accurate b0 fieldmap in our method the distortion field is estimated using a constrained non rigid registration between an undistorted t1 weighted anatomical image and one of the distorted epi images from diffusion acquisition our registration framework is based on a new approach inversion inverse contrast normalization for very simple registration which exploits the inverted contrast relationship between t1 and t2 weighted brain images to define a simple and robust similarity measure we also describe how inversion can be used for rigid alignment of diffusion images and t1 weighted anatomical images our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters compared to other methods inversion shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non rigid distortion correction

on global implicit function theorem abstract we study some certain maximal implicit functions and we apply our results to prove the local and global existence and local unicity of the solutions of the corresponding differential equation

regularity of inverses of sobolev deformations with finite surface energy abstract let u be a sobolev w 1 p map from a bounded open set r n to r n we assume u to satisfy some invertibility properties that are natural in the context of nonlinear elasticity namely the topological condition inv and the orientation preserving constraint det d u 0 these deformations may present cavitation which is the phenomenon of void formation we also assume that the surface created by the cavitation process has finite area if p n 1 we show that a suitable defined inverse of u is a sobolev map a partial result is also given for the critical case p n 1 the proof relies on the techniques used in the study of cavitation

meaningful design and contrast estimability in fmri optimising the efficiency of an experimental design is known to be of great importance however existing methods for calculating design rank deficiency and contrast estimability an important aspect of experimental design relate to computational precision rather than image noise and are therefore not very meaningful for example a contrast between two experimental conditions may be mathematically estimable while requiring a huge differential bold response for statistical significance to be reached in this paper we formulate standard efficiency equations in terms of required bold effect and use this to generate measures of rank estimability which are meaningful this takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts we show how to re express several regressors and an associated contrast vector as a single equivalent regressor so that we can calculate the contrast s effective peak peak height unambiguously we also present some example results on typical designs and characterise noise results from a range of typical fmri acquisitions in order to allow experimenters to apply efficiency estimation in advance of acquiring data

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

a global implicit function theorem without initial point and its applications to control of non affine systems of high dimensions control system design for non affine systems is a difficult problem because of the lack of mathematical tools the key to the problem is solving for an implicit function but the known results for implicit functions are not applicable for higher dimensional systems except for single input and single output systems in this paper a new version of a global implicit function theorem in higher dimension is presented and proved this result can be applied to show the controllability of a class of non affine multi input and multi output mimo system so that approximation based control system design can be applied with ease

mr based attenuation correction for pet mri neurological studies with continuous valued attenuation coefficients for bone through a conversion from r2 to ct hounsfield units abstract aim mr based correction for photon attenuation in pet mri remains challenging particularly for neurological applications requiring quantitation of data existing methods are either not sufficiently accurate or are limited by the computation time required the goal of this study was to develop an mr based attenuation correction method that accurately separates bone tissue from air and provides continuous valued attenuation coefficients for bone materials and methods pet mri and ct datasets were obtained from 98 subjects mean age sd 66 yrs 9 8 57 females using an irb approved protocol and with informed consent subjects were injected with 352 29 mbq of 18 f florbetapir tracer and pet acquisitions were begun either immediately or 50 min after injection ct images of the head were acquired separately using a pet ct system dual echo ultrashort echo time ute images and two point dixon images were acquired regions of air were segmented via a threshold of the voxel wise multiplicative inverse of the ute echo 1 image regions of bone were segmented via a threshold of the r2 image computed from the ute echo 1 and ute echo 2 images regions of fat and soft tissue were segmented using fat and water images decomposed from the dixon images air fat and soft tissue were assigned linear attenuation coefficients lacs of 0 0 092 and 0 1 cm 1 respectively lacs for bone were derived from a regression analysis between corresponding r2 and ct values pet images were reconstructed using the gold standard ct method and the proposed car ridr method results the ridr segmentation method produces mean dice coefficient sd across subjects of 0 75 0 05 for bone and 0 60 0 08 for air the car model for bone lacs greatly improves accuracy in estimating ct values 28 2 3 0 mean error compared to the use of a constant ct value 46 9 5 8 p 6 finally the car ridr method provides a low whole brain mean absolute percent error mape sd in pet reconstructions across subjects of 2 55 0 86 regional pet errors were also low and ranged from 0 88 to 3 79 in 24 brain rois conclusion we propose an mr based attenuation correction method car ridr for quantitative pet neurological imaging the proposed method employs ute and dixon images and consists of two novel components 1 accurate segmentation of air and bone using the inverse of the ute1 image and the r2 image respectively and 2 estimation of continuous lac values for bone using a regression between r2 and ct hounsfield units from our analysis we conclude that the proposed method closely approaches

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

time domain study of arbitrary dipole in planar geometry with discontinuity in permittivity and permeability transient fields arising from a general impulsive dipole above ground characterized by permittivity and permeability are studied a detailed analysis for arbitrary electric dipole excitation is given and the fields arising from the analog magnetic sources can be obtained by applying the duality transform the mathematical description of this problem is done using the hertz vector whose solution in the time domain is derived in a novel way using the exact image theory from this solution which involves a definite integral the actual fields are obtained through simple differentiations the efficiency of the method is demonstrated by solving 14 previously unknown closed form results for various field components in certain specific cases seven of these are obtained for electric dipole excitation and listed whereas the corresponding results in the case of magnetic excitation can be easily written by applying the duality transform

low rank matrix factorization with adaptive graph regularizer in this paper we present a novel low rank matrix factorization algorithm with adaptive graph regularizer lmfagr we extend the recently proposed low rank matrix with manifold regularization mmf method with an adaptive regularizer different from mmf which constructs an affinity graph in advance lmfagr can simultaneously seek graph weight matrix and low dimensional representations of data that is graph construction and low rank matrix factorization are incorporated into a unified framework which results in an automatically updated graph rather than a predefined one the experimental results on some data sets demonstrate that the proposed algorithm outperforms the state of the art low rank matrix factorization methods

time domain analysis of the sommerfeld vmd problem based on the exact image theory a novel time domain solution of the sommerfeld half space problem is constructed through the exact image theory the radiation from a vertical magnetic dipole vmd above the planar interface of two lossless and dispersionless dielectric media is analyzed the reflection field is given as a laplace transform when the refraction index of the lower medium is greater the converse case of refraction indexes is also studied and the reflection field is written as originating from an image source located in homogeneous space the present theory is seen to lead to a numerically efficient result which is demonstrated with examples

fast nonnegative matrix factorization an active set like method and comparisons nonnegative matrix factorization nmf is a dimension reduction method that has been widely used for numerous applications including text mining computer vision pattern discovery and bioinformatics a mathematical formulation for nmf appears as a nonconvex optimization problem and various types of algorithms have been devised to solve the problem the alternating nonnegative least squares anls framework is a block coordinate descent approach for solving nmf which was recently shown to be theoretically sound and empirically efficient in this paper we present a novel algorithm for nmf based on the anls framework our new algorithm builds upon the block principal pivoting method for the nonnegativity constrained least squares problem that overcomes a limitation of the active set method we introduce ideas that efficiently extend the block principal pivoting method within the context of nmf computation our algorithm inherits the convergence property of the anls framework and can easily be extended to other constrained nmf formulations extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state of the art performance in terms of computational speed

on global implicit functions the prototype of this situation is furnished by the local implicit function theorem of the differential calculus in the banach spaces whenfis of class c1 and the partial differentialf x y is an isomorphism it is clearly interesting to have implicit functions that are not only defined on a small neighbourhood of a solution of e there exist conditions on a b and f that ensure the existence of implicit function defined all over a cf 20 pp 74 771 18 13 8 ch x section 2 paragraph 61 but intermediate situations can happen for which we have the local solvability without implicit functions defined all over a in the theory of ordinary differential equations for example

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

graph regularized restricted boltzmann machine the restricted boltzmann machine rbm has received an increasing amount of interest in recent years it determines good mapping weights that capture useful latent features in an unsupervised manner the rbm and its generalizations have been successfully applied to a variety of image classification and speech recognition tasks however most of the existing rbm based models disregard the preservation of the data manifold structure in many real applications the data generally reside on a low dimensional manifold embedded in high dimensional ambient space in this brief we propose a novel graph regularized rbm to capture features and learning representations explicitly considering the local manifold structure of the data by imposing manifold based locality that preserves constraints on the hidden layer of the rbm the model ultimately learns sparse and discriminative representations the representations can reflect data distributions while simultaneously preserving the local manifold structure of data we test our model using several benchmark image data sets for unsupervised clustering and supervised classification problem the results demonstrate that the performance of our method exceeds the state of the art alternatives

exact image theory for the sommerfeld half space problem part iii general formulation the general sommerfeld problem with both epsilon and mu discontinuous and a source consisting of arbitrarily oriented electric and or magnetic dipoles at the same location is considered in terms of image theory the problem is formulated with electric and magnetic fields instead of potential quantities resulting in a vector transmission line interpretation of the fourier transformed problem the image sources are seen to be located in complex space expressable in terms of a certain basic image current function which was encountered in part ii of this paper on the vertical electric dipole problem the horizontal electric magnetic dipole image is solved and found to consist of both vertical and horizontal current components the image concept is generalized to the most general three dimensional sources as a check the well known reflection coefficient method is obtained as the far field approximation of the present theory

spectral properties of the alignment matrices in manifold learning local methods for manifold learning generate a collection of local parameterizations which is then aligned to produce a global parameterization of the underlying manifold the alignment procedure is carried out through the computation of a partial eigendecomposition of a so called alignment matrix in this paper we present an analysis of the eigenstructure of the alignment matrix giving both necessary and sufficient conditions under which the null space of the alignment matrix recovers the global parameterization we show that the gap in the spectrum of the alignment matrix is proportional to the square of the size the precise definition of the size is given in section sec sp of the overlap of the local parameterizations thus deriving a quantitative measure of how stably the null space can be computed numerically we also give a perturbation analysis of the null space of the alignment matrix when the computation of the local parameterizations is subject to error our analysis provides insights into the behaviors and performance of local manifold learning algorithms

global homeomorphisms and covering projections on metric spaces for a large class of metric spaces with nice local structure which includes banach finsler manifolds and geodesic spaces of curvature bounded above we give sufficient conditions for a local homeomorphism to be a covering projection we first obtain a general condition in terms of a path continuation property as a consequence we deduce several conditions in terms of path liftings involving a generalized derivative and in particular we obtain an extension of hadamard global inversion theorem in this context next we prove that in the case of quasi isometric mappings some of these sufficient conditions are also necessary finally we give an application to the existence of global implicit functions

adaptive method for nonsmooth nonnegative matrix factorization nonnegative matrix factorization nmf is an emerging tool for meaningful low rank matrix representation in nmf explicit constraints are usually required such that nmf generates desired products or factorizations especially when the products have significant sparseness features it is known that the ability of nmf in learning sparse representation can be improved by embedding a smoothness factor between the products motivated by this result we propose an adaptive nonsmooth nmf ans nmf method in this paper in our method the embedded factor is obtained by using a data related approach so it matches well with the underlying products implying a superior faithfulness of the representations besides due to the usage of an adaptive selection scheme to this factor the sparseness of the products can be separately constrained leading to wider applicability and interpretability furthermore since the adaptive selection scheme is processed through solving a series of typical linear programming problems it can be easily implemented simulations using computer generated data and real world data show the advantages of the proposed ans nmf method over the state of the art methods

concept factorization with adaptive neighbors for document clustering in this paper a novel concept factorization cf method called cf with adaptive neighbors cfans is proposed the idea of cfan is to integrate an ans regularization constraint into the cf decomposition the goal of cfan is to extract the representation space that maintains geometrical neighborhood structure of the data similar to the existing graph regularized cf cfan builds a neighbor graph weights matrix the key difference is that the cfan performs dimensionality reduction and finds the neighbor graph weights matrix simultaneously an efficient algorithm is also derived to solve the proposed problem we apply the proposed method to the problem of document clustering on the 20 newsgroups reuters 21578 and tdt2 document data sets our experiments demonstrate the effectiveness of the method

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

a reproducing kernel hilbert space approach for q ball imaging diffusion magnetic resonance mr imaging has enabled us to reveal the white matter geometry in the living human brain the q ball technique is widely used nowadays to recover the orientational heterogeneity of the intra voxel fiber architecture this article proposes to employ the funk radon transform in a hilbert space with a reproducing kernel derived from the spherical laplace beltrami operator thus generalizing previous approaches that assume a bandlimited diffusion signal the function estimation problem is solved within a tikhonov regularization framework while a gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands shortcomings of q ball imaging are discussed

a multi centre evaluation of eleven clinically feasible brain pet mri attenuation correction techniques using a large cohort of patients abstract aim to accurately quantify the radioactivity concentration measured by pet emission data need to be corrected for photon attenuation however the mri signal cannot easily be converted into attenuation values making attenuation correction ac in pet mri challenging in order to further improve the current vendor implemented mr ac methods for absolute quantification a number of prototype methods have been proposed in the literature these can be categorized into three types template atlas based segmentation based and reconstruction based these proposed methods in general demonstrated improvements compared to vendor implemented ac and many studies report deviations in pet uptake after ac of only a few percent from a gold standard ct ac using a unified quantitative evaluation with identical metrics subject cohort and common ct based reference the aims of this study were to evaluate a selection of novel methods proposed in the literature and identify the ones suitable for clinical use methods in total 11 ac methods were evaluated two vendor implemented mr ac dixon and mr ac ute five based on template atlas information mr ac segbone koesters et al 2016 mr ac ontario anazodo et al 2014 mr ac boston izquierdo garcia et al 2014 mr ac ucl burgos et al 2014 and mr ac maxprob merida et al 2015 one based on simultaneous reconstruction of attenuation and emission mr ac mlaa benoit et al 2015 and three based on image segmentation mr ac munich cabello et al 2015 mr ac car ridr juttukonda et al 2015 and mr ac resolute ladefoged et al 2015 we selected 359 subjects who were scanned using one of the following radiotracers 18 f fdg 210 11 c pib 51 and 18 f florbetapir 98 the comparison to ac with a gold standard ct was performed both globally and regionally with a special focus on robustness and outlier analysis results the average performance in pet tracer uptake was within 5 of ct for all of the proposed methods with the average sd global percentage bias in pet fdg uptake for each method being mr ac dixon 11 3 3 5 mr ac ute 5 7 2 0 mr ac ontario 4 3 3 6 mr ac munich 3 7 2 1 mr ac mlaa 1 9 2 6 mr ac segbone 1 7 3 6 mr ac ucl 0 8 1 2 mr ac car ridr 0 4 1 9 mr ac maxprob 0 4 1 6 mr ac boston 0 3 1 8 and mr ac resolute 0 3 1 7 ordered by average bias the overall best performing methods mr ac boston mr ac maxprob mr ac resolute and mr ac ucl ordered alphabetically showed regional average errors within 3 of pet with ct ac in all regions of the brain with fdg and the same four methods as well as mr ac car ridr showed that for 95 of the patients 95 of brain voxels had an uptake that deviated by less than 15 from the reference comparable performance was obtained with pib and florbetapir conclusions all of the proposed novel methods have an average global performance within likely acceptable limits 5 of ct based reference and the main difference among the methods was found in the robustness outlier analysis and clinical feasibility overall the best performing methods were mr acboston mr acmaxprob mr acresolute and mr acucl ordered alphabetically these methods all minimized the number of outliers standard deviation and average global and local error the methods mr acmunich and mr accar ridr were both within acceptable quantitative limits so these methods should be considered if processing time is a factor the method mr acsegbone also demonstrates promising results and performs well within the likely acceptable quantitative limits for clinical routine scans where processing time can be a key factor this vendor provided solution currently outperforms most methods with the performance of the methods presented here it may be concluded that the challenge of improving the accuracy of mr ac in adult brains with normal anatomy has been solved to a quantitatively acceptable degree which is smaller than the quantification reproducibility in pet imaging

weak regularity of the inverse under minimal assumptions let omega subset mathbb r 3 be a domain and let f in bv text loc omega mathbb r 3 be a homeomorphism such that its distributional adjugate is a finite radon measure we show that its inverse has bounded variation f 1 in bv text loc the condition that the distributional adjugate is finite measure is not only sufficient but also necessary for the weak regularity of the inverse

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

nonlinear offset free model predictive control this paper addresses offset free reference tracking of asymptotically constant reference signals using model predictive control existing results for linear models are extended to general nonlinear models the core of the proposed method employs a disturbance model and an observer to estimate its state typical disturbance models are shown and the implications of using them are discussed conditions are given for which this setup eliminates the tracking error asymptotically basically we prove that error free output estimation and error free nominal tracking imply offset free model predictive control

the co area formula for sobolev mappings we extend federer s co area formula to mappings f belonging to the sobolev class w 1 p r n r m 1 m m and more generally to mappings with gradient in the lorentz space l m 1 r n this is accomplished by showing that the graph of f in r n m is a hausdorff n rectifiable set

local inversion theorems without assuming continuous differentiability in 6 it is proved that if d c r is open and f d r is frechet differentiable on d and f x e isom r r for every x e d then f is a local diffeomorphism on d we shall extend this theorem for infinite dimensional banach spaces e and mappings f d e d c e open f it where t d e is compact and i d e i x x for every x e d we shall also prove a generalization of the hadamard levi theorem for such mappings our methods are purely analytical since the single instrument we are using for establishing the results of the present paper is the topological degree theory our methods are different from 6 even in the finite dimensional case since we not use the results from s

efficient additive kernels via explicit feature maps large scale nonlinear support vector machines svms can be approximated by linear ones using a suitable feature map the linear svms are in general much faster to learn and evaluate test than the original nonlinear svms this work introduces explicit feature maps for the additive class of kernels such as the intersection hellinger s and 2 kernels commonly used in computer vision and enables their use in large scale problems in particular we 1 provide explicit feature maps for all additive homogeneous kernels along with closed form expression for all common kernels 2 derive corresponding approximate finite dimensional feature maps based on a spectral analysis and 3 quantify the error of the approximation showing that the error is independent of the data dimension and decays exponentially fast with the approximation order for selected kernels such as 2 we demonstrate that the approximations have indistinguishable performance from the full kernels yet greatly reduce the train test times of svms we also compare with two other approximation methods nystrom s approximation of perronnin et al 1 which is data dependent and the explicit map of maji and berg 2 for the intersection kernel which as in the case of our approximations is data independent the approximations are evaluated on a number of standard data sets including caltech 101 3 daimler chrysler pedestrians 4 and inria pedestrians 5

enhancing low rank subspace clustering by manifold regularization recently low rank representation lrr method has achieved great success in subspace clustering sc which aims to cluster the data points that lie in a union of low dimensional subspace given a set of data points lrr seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself however lrr only considers the global euclidean structure while the local manifold structure which is often important for many real applications is ignored in this paper to exploit the local manifold structure of the data a manifold regularization characterized by a laplacian graph has been incorporated into lrr leading to our proposed laplacian regularized lrr laplrr an efficient optimization procedure which is based on alternating direction method of multipliers admm is developed for laplrr experimental results on synthetic and real data sets are presented to demonstrate that the performance of lrr has been enhanced by using the manifold regularization

global univalence and global inversion theorems in banach spaces on etablit de nouveaux theoremes d inversion globaux on obtient des variantes globales du theoreme des fonctions implicite on demontre une generalisation du theoreme de hurwitz sur des suites de fonctions analytiques univalentes

homeomorphisms of bounded variation we show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation in higher dimensions we show that f 1 is of bounded variation provided that f w1 1 rn is a homeomorphism with df in the lorentz space ln 1 1

approximation of w1 p sobolev homeomorphism by diffeomorphisms and the signs of the jacobian abstract let r n n 4 be a domain and 1 p n 2 where a stands for the integer part of a we construct a homeomorphism f w 1 p 1 1 n r n such that j f det d f 0 on a set of positive measure and j f 0 on a set of positive measure it follows that there are no diffeomorphisms or piecewise affine homeomorphisms f k such that f k f in w 1 p

predicting ct image from mri data through feature matching with learned nonlinear local descriptors attenuation correction for positron emission tomography pet magnetic resonance mr hybrid imaging systems and dose planning for mr based radiation therapy remain challenging due to insufficient high energy photon attenuation information we present a novel approach that uses the learned nonlinear local descriptors and feature matching to predict pseudo computed tomography pct images from t1 weighted and t2 weighted magnetic resonance imaging mri data the nonlinear local descriptors are obtained by projecting the linear descriptors into the nonlinear high dimensional space using an explicit feature map and low rank approximation with supervised manifold regularization the nearest neighbors of each local descriptor in the input mr images are searched in a constrained spatial range of the mr images among the training dataset then the pct patches are estimated through k nearest neighbor regression the proposed method for pct prediction is quantitatively analyzed on a dataset consisting of paired brain mri and ct images from 13 subjects our method generates pct images with a mean absolute error mae of 75 25 18 05 hounsfield units a peak signal to noise ratio of 30 87 1 15 db a relative mae of 1 56 0 5 in pet attenuation correction and a dose relative structure volume difference of 0 055 0 107 in d 98 as compared with true ct the experimental results also show that our method outperforms four state of the art methods

on the bi sobolev planar homeomorphisms and their approximation abstract the first goal of this paper is to give a short description of the planar bi sobolev homeomorphisms providing simple and self contained proofs for some already known properties in particular for any such homeomorphism u one has d u x 0 for almost every point x for which j u x 0 as a consequence one can prove that 8 d u d u 1 notice that this estimate holds trivially if one is allowed to use the change of variables formula but this is not always the case for a bi sobolev homeomorphism as a corollary of our construction we will show that any w 1 1 homeomorphism u with w 1 1 inverse can be approximated with smooth diffeomorphisms or piecewise affine homeomorphisms u n in such a way that u n converges to u in w 1 1 and at the same time u n 1 converges to u 1 in w 1 1 this positively answers an open conjecture see for instance iwaniec et al 2011 question 4 for the case p 1

fracture surfaces and the regularity of inverses for bv deformations motivated by nonlinear elasticity theory we study deformations that are approximately differentiable orientation preserving and one to one almost everywhere and in addition have finite surface energy this surface energy mathcal e was used by the authors in a previous paper and has connections with the theory of currents in the present paper we prove that mathcal e measures exactly the area of the surface created by the deformation this is done through a proper definition of created surface which is related to the set of discontinuity points of the inverse of the deformation in doing so we also obtain an sbv regularity result for the inverse

second order necessary conditions for the infinite horizon variational problems we give new proofs of first order and second order necessary conditions for the infinite horizon variational problems in the framework of the continuous time we study the notion of conjugate points and we build new second order necessary conditions we also translate all of our results into the hamiltonian formalism moreover we apply these general results to the special lagrangians in the form e delta i lx dot x

ensemble manifold regularized sparse low rank approximation for multiview feature embedding in computer vision and pattern recognition researches the studied objects are often characterized by multiple feature representations with high dimensionality thus it is essential to encode that multiview feature into a unified and discriminative embedding that is optimal for a given task to address this challenge this paper proposes an ensemble manifold regularized sparse low rank approximation emr slra algorithm for multiview feature embedding the emr slra algorithm is based on the framework of least squares component analysis in particular the low dimensional feature representation and the projection matrix are obtained by the low rank approximation of the concatenated multiview feature matrix by considering the complementary property among multiple features emr slra simultaneously enforces the ensemble manifold regularization on the output feature embedding in order to further enhance its robustness against the noise the group sparsity is introduced into the objective formulation to impose direct noise reduction on the input multiview feature matrix since there is no closed form solution for emr slra this paper provides an efficient emr slra optimization procedure to obtain the output feature embedding experiments on the pattern recognition applications confirm the effectiveness of the emr slra algorithm compare with some other multiview feature dimensionality reduction approaches highlightsthis paper proposes a novel emr slra algorithm for multiview feature embedding the least squares component analysis is generalized to multiview version the ensemble manifold regularization is enforced to explore the complementarity the group sparsity is introduced to promote the robustness against the noise an efficient iterative procedure is developed to solve emr slra

descriptor learning via supervised manifold regularization for multioutput regression multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis however due to the huge image variability and ambiguity it is fundamentally challenging to handle the highly complex input target relationship of multioutput regression especially with indiscriminate high dimensional representations in this paper we propose a novel supervised descriptor learning sdl algorithm for multioutput regression which can establish discriminative and compact feature representations to improve the multivariate estimation performance the sdl is formulated as generalized low rank approximations of matrices with a supervised manifold regularization the sdl is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low dimensional space aligned to targets the achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression which enables more accurate and efficient multivariate estimation we conduct extensive evaluation of the proposed sdl on both synthetic data and real world multioutput regression tasks for both computer vision and medical image analysis experimental results have shown that the proposed sdl can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts our method establishes a novel sdl framework for multioutput regression which can be widely used to boost the performance in different applications

bi sobolev mappings with differential matrices in orlicz zygmund classes abstract bi sobolev mappings f r 2 onto r 2 have been defined as those homeomorphisms such that f and f 1 belong to w loc 1 1 we deduce regularity properties of the distortion of f from the regularity of the differential matrix d f 1 and conversely

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

nonnegative ranks decompositions and factorizations of nonnegative matrices the nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank one matrices into which the matrix can be decomposed additively such decompositions are useful in diverse scientific disciplines we obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm

laplacian regularized low rank representation and its applications low rank representation lrr has recently attracted a great deal of attention due to its pleasing efficacy in exploring low dimensional subspace structures embedded in data for a given set of observed data corrupted with sparse errors lrr aims at learning a lowest rank representation of all data jointly lrr has broad applications in pattern recognition computer vision and signal processing in the real world data often reside on low dimensional manifolds embedded in a high dimensional ambient space however the lrr method does not take into account the non linear geometric structures within data thus the locality and similarity information among data may be missing in the learning process to improve lrr in this regard we propose a general laplacian regularized low rank representation framework for data representation where a hypergraph laplacian regularizer can be readily introduced into i e a non negative sparse hyper laplacian regularized lrr model nshlrr by taking advantage of the graph regularizer our proposed method not only can represent the global low dimensional structures but also capture the intrinsic non linear geometric information in data the extensive experimental results on image clustering semi supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

variational bayes inference of spatial mixture models for segmentation mixture models are commonly used in the statistical segmentation of images for example they can be used for the segmentation of structural medical images into different matter types or of statistical parametric maps into activating and nonactivating brain regions in functional imaging spatial mixture models have been developed to augment histogram information with spatial regularization using markov random fields mrfs in previous work an approximate model was developed to allow adaptive determination of the parameter controlling the strength of spatial regularization inference was performed using markov chain monte carlo mcmc sampling however this approach is prohibitively slow for large datasets in this work a more efficient inference approach is presented this combines a variational bayes approximation with a second order taylor expansion of the components of the posterior distribution which would otherwise be intractable to variational bayes this provides inference on fully adaptive spatial mixture models an order of magnitude faster than mcmc we examine the behavior of this approach when applied to artificial data with different spatial characteristics and to functional magnetic resonance imaging statistical parametric maps

low rank matrix factorization with multiple hypergraph regularizer this paper presents a novel low rank matrix factorization method named multihmmf which incorporates multiple hypergraph manifold regularization to the low rank matrix factorization in order to effectively exploit high order information among the data samples the hypergraph is introduced to model the local structure of the intrinsic manifold specifically multiple hypergraph regularization terms are separately constructed to consider the local invariance the optimal intrinsic manifold is constructed by linearly combining multiple hypergraph manifolds then the regularization term is incorporated into a truncated singular value decomposition framework resulting in a unified objective function so that matrix factorization is changed into an optimization problem alternating optimization is used to solve the optimization problem with the result that the low dimensional representation of data space is obtained the experimental results of image clustering demonstrate that the proposed method outperforms state of the art data representation methods we propose a novel low rank matrix factorization method we incorporate multiple hypergraph manifold regularization to the matrix factorization we adopt alternating optimization to solve the optimization problem

rapid two step dipole inversion for susceptibility mapping with sparsity priors quantitative susceptibility mapping qsm is a post processing technique of gradient echo phase data that attempts to map the spatial distribution of local tissue magnetic susceptibilities to obtain these maps an ill posed field to source inverse problem must be solved to remove non local magnetic field perturbations current state of the art algorithms which aim to solve the dipole inversion problem are plagued by the trade off between reconstruction speed and accuracy a two step dipole inversion algorithm is proposed to bridge this gap our approach first addresses the well conditioned k space region which is reconstructed using a krylov subspace solver then the ill conditioned k space region is reconstructed by solving a constrained l1 minimization problem the proposed pipeline does not incorporate a priori information but utilizes sparsity constraints in the second step we compared our method to well established qsm algorithms with respect to cosmos in in vivo volunteer datasets compared to medi and heidi the proposed algorithm produces susceptibility maps with a lower root mean square error and a higher coefficient of determination with respect to cosmos while being 50 times faster our two step dipole inversion algorithm without a priori information yields improved qsm reconstruction quality at reduced computation times compared to current state of the art methods

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

feedback linearization using neural networks abstract for a class of single input single output continuous time nonlinear systems a multilayer neural network based controller that feedback linearizes the system is presented control action is used to achieve tracking performance for a state feedback linearizable but unknown nonlinear system the control structure consists of a feedback linearization portion provided by two neural networks plus a robustifying portion that keeps the control magniture bounded a stability proof is given in the sense of lyapunov it is shown that all the signals in the closed loop system are uniformly ultimately bounded no off line learning phase is needed initialization of the network weights is straightforward

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

injectivity and self contact in nonlinear elasticity let be a bounded open connected subset of 3 with a sufficiently smooth boundary the additional condition det dx vol is imposed on the admissible deformations of a hyperelastic body whose reference configuration is we show that the associated minimization problem provides a mathematical model for matter to come into frictionless contact with itself but not interpenetrate we also extend j ball s theorems on existence to this case by establishing the existence of a minimizer of the energy in the space w1 p 3 p 3 that is injective almost everywhere

a note on global inversion theorems and applications to differential equations analysing the proof of plastock s theorem given by m and s rbdulescu 4 we prove that for 1 o s cx we may obtain estimates of the balls on which diffeomorphisms take place secondly we shall use these results to find estimates for the existence interval of the solution of cauchy s problem for differential equation these results will generalize a theorem of m and s radulescu 3 throughout this paper e f g will denote banach spaces

background foreground modeling based on spatiotemporal sparse subspace clustering background estimation and foreground segmentation are important steps in many high level vision tasks many existing methods estimate background as a low rank component and foreground as a sparse matrix without incorporating the structural information therefore these algorithms exhibit degraded performance in the presence of dynamic backgrounds photometric variations jitter shadows and large occlusions we observe that these backgrounds often span multiple manifolds therefore constraints that ensure continuity on those manifolds will result in better background estimation hence we propose to incorporate the spatial and temporal sparse subspace clustering into the robust principal component analysis rpca framework to that end we compute a spatial and temporal graph for a given sequence using motion aware correlation coefficient the information captured by both graphs is utilized by estimating the proximity matrices using both the normalized euclidean and geodesic distances the low rank component must be able to efficiently partition the spatiotemporal graphs using these laplacian matrices embedded with the rpca objective function these laplacian matrices constrain the background model to be spatially and temporally consistent both on linear and nonlinear manifolds the solution of the proposed objective function is computed by using the linearized alternating direction method with adaptive penalty optimization scheme experiments are performed on challenging sequences from five publicly available datasets and are compared with the 23 existing state of the art methods the results demonstrate excellent performance of the proposed algorithm for both the background estimation and foreground segmentation

exploring the 3d geometry of the diffusion kurtosis tensor impact on the development of robust tractography procedures and novel biomarkers diffusion kurtosis imaging dki is a diffusion weighted technique which overcomes limitations of the commonly used diffusion tensor imaging approach this technique models non gaussian behaviour of water diffusion by the diffusion kurtosis tensor kt which can be used to provide indices of tissue heterogeneity and a better characterisation of the spatial architecture of tissue microstructure in this study the geometry of the kt is elucidated using synthetic data generated from multi compartmental models where diffusion heterogeneity between intra and extra cellular media is taken into account as well as the sensitivity of the results to each model parameter and to synthetic noise furthermore based on the assumption that the maxima of the kt are distributed perpendicularly to the direction of well aligned fibres a novel algorithm for estimating fibre direction directly from the kt is proposed and compared to the fibre directions extracted from dki based orientation distribution function odf estimates previously proposed in the literature synthetic data results showed that for fibres crossing at high intersection angles direction estimates extracted directly from the kt have smaller errors than the dki based odf estimation approaches dki odf nevertheless the proposed method showed smaller angular resolution and lower stability to changes of the simulation parameters on real data tractography performed on these kt fibre estimates suggests a higher sensitivity than the dki based odf in resolving lateral corpus callosum fibres reaching the pre central cortex when diffusion acquisition is performed with five b values using faster acquisition schemes kt based tractography did not show improved performance over the dki odf procedures nevertheless it is shown that direct kt fibre estimates are more adequate for computing a generalised version of radial kurtosis maps

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

exact image theory for the sommerfeld half space problem part ii vertical electrical dipole applying the laplace transform the exact distributed image current function is obtained for the classical sommerfeld half space problem with vertical magnetic current source the resulting field integral is well behaved when the image current is situated in complex space unlike previous approximate images the present theory is valid for any distance height of the source frequency and half space parameters it is demonstrated that the present image theory reduces to the well known dipole image at complex depth for large dielectric parameters of the half space also the reflection coefficient method is obtained as a farfield approximation calculation of fields through exact image integration is seen to be simple and accurate and require modest computer capacity and time in an appendix some properties of the multivalued green s function arising from a dipole source in complex space are also studied

dual graph regularized latent low rank representation for subspace clustering low rank representation lrr has received considerable attention in subspace segmentation due to its effectiveness in exploring low dimensional subspace structures embedded in data to preserve the intrinsic geometrical structure of data a graph regularizer has been introduced into lrr framework for learning the locality and similarity information within data however it is often the case that not only the high dimensional data reside on a non linear low dimensional manifold in the ambient space but also their features lie on a manifold in feature space in this paper we propose a dual graph regularized lrr model dglrr by enforcing preservation of geometric information in both the ambient space and the feature space the proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold furthermore we extend the dglrr model to include non negative constraint leading to a parts based representation of data experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state of the art approaches in image clustering

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

detecting network modules in fmri time series a weighted network analysis approach many network analyses of fmri data begin by defining a set of regions extracting the mean signal from each region and then analyzing the correlations between regions one essential question that has not been addressed in the literature is how to best define the network neighborhoods over which a signal is combined for network analyses here we present a novel unsupervised method for the identification of tightly interconnected voxels or modules from fmri data this approach weighted voxel coactivation network analysis wvcna is based on a method that was originally developed to find modules of genes in gene networks this approach differs from many of the standard network approaches in fmri in that connections between voxels are described by a continuous measure whereas typically voxels are considered to be either connected or not connected depending on whether the correlation between the two voxels survives a hard threshold value additionally instead of simply using pairwise correlations to describe the connection between two voxels wvcna relies on a measure of topological overlap which not only compares how correlated two voxels are but also the degree to which the pair of voxels is highly correlated with the same other voxels we demonstrate the use of wvcna to parcellate the brain into a set of modules that are reliably detected across data within the same subject and across subjects in addition we compare wvcna to ica and show that the wvcna modules have some of the same structure as the ica components but tend to be more spatially focused we also demonstrate the use of some of the wvcna network metrics for assessing a voxel s membership to a module and also how that voxel relates to other modules last we illustrate how wvcna modules can be used in a network analysis to find connections between regions of the brain and show that it produces reasonable results

regularity of the inverse of a planar sobolev homeomorphism let be a domain suppose that f w1 1loc r2 is a homeomorphism such that df x vanishes almost everywhere in the zero set of j f we show that f 1 w1 1loc f r2 and that df 1 y vanishes almost everywhere in the zero set of sharp conditions to quarantee that f 1 w1 q f r2 for some 1 q 2 are also given

existence of energy minimal diffeomorphisms between doubly connected domains the paper establishes the existence of homeomorphisms between two planar domains that minimize the dirichlet energy

mr ntd manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation with the advancement of data acquisition techniques tensor multidimensional data objects are increasingly accumulated and generated for example multichannel electroencephalographies multiview images and videos in these applications the tensor objects are usually nonnegative since the physical signals are recorded as the dimensionality of tensor objects is often very high a dimension reduction technique becomes an important research topic of tensor data from the perspective of geometry high dimensional objects often reside in a low dimensional submanifold of the ambient space in this paper we propose a new approach to perform the dimension reduction for nonnegative tensor objects our idea is to use nonnegative tucker decomposition ntd to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects to preserve geometric information in tensor data we employ a manifold regularization term for the core tensors constructed in the tucker decomposition an algorithm called manifold regularization ntd mr ntd is developed to solve the common projection matrices and core tensors in an alternating least squares manner the convergence of the proposed algorithm is shown and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects respectively these theoretical results show that the proposed algorithm can be efficient extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed mr ntd algorithm

a bayesian model of shape and appearance for subcortical brain segmentation automatic segmentation of subcortical structures in human brain mr images is an important but difficult task due to poor and variable intensity contrast clear well defined intensity features are absent in many places along typical structure boundaries and so extra information is required to achieve successful segmentation a method is proposed here that uses manually labelled image data to provide anatomical training information it utilises the principles of the active shape and appearance models but places them within a bayesian framework allowing probabilistic relationships between shape and intensity to be fully exploited the model is trained for 15 different subcortical structures using 336 manually labelled t1 weighted mr images using the bayesian approach conditional probabilities can be calculated easily and efficiently avoiding technical problems of ill conditioned covariance matrices even with weak priors and eliminating the need for fitting extra empirical scaling parameters as is required in standard active appearance models furthermore differences in boundary vertex locations provide a direct purely local measure of geometric change in structure between groups that unlike voxel based morphometry is not dependent on tissue classification methods or arbitrary smoothing in this paper the fully automated segmentation method is presented and assessed both quantitatively using leave one out testing on the 336 training images and qualitatively using an independent clinical dataset involving alzheimer s disease median dice overlaps between 0 7 and 0 9 are obtained with this method which is comparable or better than other automated methods an implementation of this method called first is currently distributed with the freely available fsl package

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

non parametric model selection for subject specific topological organization of resting state functional connectivity abstract in recent years graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain most of these networks have shown small world topological characteristics high efficiency in long distance communication between nodes combined with highly interconnected local clusters of nodes moreover functional studies performed at high resolutions have presented convincing evidence that resting state functional connectivity networks exhibits exponentially truncated scale free behavior such evidence however was mostly presented qualitatively in terms of linear regressions of the degree distributions on log log plots even when quantitative measures were given these were usually limited to the r 2 correlation coefficient however the r 2 statistic is not an optimal estimator of explained variance when dealing with truncated power law models recent developments in statistics have introduced new non parametric approaches based on the kolmogorov smirnov test for the problem of model selection in this work we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest the analysis performed at voxel level and in a subject specific fashion confirmed the superiority of a truncated power law model showing high consistency across subjects moreover the most highly connected voxels were found to be consistently part of the default mode network our results provide statistically sound support to the evidence previously presented in literature for a truncated power law model of resting state functional connectivity

an exploration of lp theory for forward backward stochastic differential equations with random coefficients on small durations abstract in the present paper under the lipschitz condition and a monotonicity assumption we obtain an l p result p 1 including the existence and uniqueness of the p th power integrable solutions and a pair of related p th power estimates for coupled forward backward stochastic differential equations with random coefficients on small durations a measurable global implicit function theorem has been established and plays a key role in our analysis it is the first measurable version of implicit function theorems to our best knowledge therefore the theorems themselves have been improved

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

local invertibility in sobolev spaces with applications to nematic elastomers and magnetoelasticity we define a class of deformations in w 1 p omega mathbb r n p n 1 with a positive jacobian that do not exhibit cavitation we characterize that class in terms of the non negativity of the topological degree and the equality det det that the distributional determinant coincides with the pointwise determinant of the gradient maps in this class are shown to satisfy a property of weak monotonicity and as a consequence they enjoy an extra degree of regularity we also prove that these deformations are locally invertible moreover the neighbourhood of invertibility is stable along a weak convergent sequence in w 1 p and the sequence of local inverses converges to the local inverse we use those features to show weak lower semicontinuity of functionals defined in the deformed configuration and functionals involving composition of maps we apply those results to prove the existence of minimizers in some models for nematic elastomers and magnetoelasticity

effects of diffusion weighting schemes on the reproducibility of dti derived fractional anisotropy mean diffusivity and principal eigenvector measurements at 1 5t diffusion tensor imaging dti is used to study tissue composition and architecture in vivo to increase the signal to noise ratio snr of dti contrasts studies typically use more than the minimum of 6 diffusion weighting dw directions or acquire repeated observations of the same set of dw directions simulation based studies have sought to optimize dti acquisitions and suggest that increasing the directional resolution of a dti dataset i e the number of distinct directions is preferable to repeating observations in an equal scan time comparison however it is not always clear how to translate these recommendations into practice when considering physiological noise and scanner stability furthermore the effect of different dw schemes on in vivo dti findings is not fully understood this study characterizes how the makeup of a dw scheme in terms of the number of directions impacts the precision and accuracy of in vivo fractional anisotropy fa mean diffusivity md and principal eigenvector pev findings orientation dependence of dti reliability is demonstrated in vivo and a principled theoretical framework is provided to support and interpret findings with simulation results as long as sampling orientations are well balanced differences in dti contrasts due to different dw schemes are shown to be small relative to intra session variability these differences are accentuated at low snr while minimized at high snr this result suggests that typical clinical studies which use similar protocols but different well balanced dw schemes are readily comparable within the experimental precision

quantitative susceptibility mapping using structural feature based collaborative reconstruction sfcr in the human brain the reconstruction of mr quantitative susceptibility mapping qsm from local phase measurements is an ill posed inverse problem and different regularization strategies incorporating a priori information extracted from magnitude and phase images have been proposed however the anatomy observed in magnitude and phase images does not always coincide spatially with that in susceptibility maps which could give erroneous estimation in the reconstructed susceptibility map in this paper we develop a structural feature based collaborative reconstruction sfcr method for qsm including both magnitude and susceptibility based information the sfcr algorithm is composed of two consecutive steps corresponding to complementary reconstruction models each with a structural feature based l 1 norm constraint and a voxel fidelity based l 2 norm constraint which allows both the structure edges and tiny features to be recovered whereas the noise and artifacts could be reduced in the m step the initial susceptibility map is reconstructed by employing a rm k space based compressed sensing model incorporating magnitude prior in the s step the susceptibility map is fitted in spatial domain using weighted constraints derived from the initial susceptibility map from the m step simulations and in vivo human experiments at 7t mri show that the sfcr method provides high quality susceptibility maps with improved rmse and mssim finally the susceptibility values of deep gray matter are analyzed in multiple head positions with the supine position most approximate to the gold standard cosmos result