document ink bleed through removal with two hidden markov random fields and a single observation field we present a new method for blind document bleed through removal based on separate markov random field mrf regularization for the recto and for the verso side where separate priors are derived from the full graph the segmentation algorithm is based on bayesian maximum a posteriori map estimation the advantages of this separate approach are the adaptation of the prior to the contents creation process e g superimposing two handwritten pages and the improvement of the estimation of the recto pixels through an estimation of the verso pixels covered by recto pixels moreover the formulation as a binary labeling problem with two hidden labels per pixels naturally leads to an efficient optimization method based on the minimum cut maximum flow in a graph the proposed method is evaluated on scanned document images from the 18th century showing an improvement of character recognition results compared to other restoration methods

blind bleed through removal for scanned historical document image with conditional random fields scanned images of historical documents often suffer from bleed through which refers to the ink on one side seeping through the paper and appearing on the other side in this paper a new conditional random field crf based method is proposed to remove the bleed through from the scanned images of historical images the proposed method only requires the scanned image of one side referred as a blind method in general the scanned historical document image is composed of three components foreground bleed through and background by assuming gaussian distributions of the three components the proposed method establishes conditional probability distribution cpd models of the three components first the parameters of the component cpd models are estimated based on an initial segmentation of the input image then crfs are used to capture the relations between observed pixels in the scanned image and the corresponding labels as well as the spatial relation between the adjacent labels the belief propagation algorithm is used to calculate the probabilities of different labels for each pixel once the labeling is completed by choosing the most possible label for each pixel the bleed through component is removed from the input historical image by a random filling inpainting algorithm experimental results on the real data set show that the proposed method preserves the foreground component very well and removes the bleed through effectively

the mean field theory in em procedures for markov random fields in many signal processing and pattern recognition applications the hidden data are modeled as markov processes and the main difficulty of using the maximisation em algorithm for these applications is the calculation of the conditional expectations of the hidden markov processes it is shown how the mean field theory from statistical mechanics can be used to calculate the conditional expectations for these problems efficiently the efficacy of the mean field theory approach is demonstrated on parameter estimation for one dimensional mixture data and two dimensional unsupervised stochastic model based image segmentation experimental results indicate that in the 1 d case the mean field theory approach provides results comparable to those obtained by baum s 1987 algorithm which is known to be optimal in the 2 d case where baum s algorithm can no longer be used the mean field theory provides good parameter estimates and image segmentation for both synthetic and real world images

a family of c 0 finite elements for kirchhoff plates i error analysis a new finite element formulation for the kirchhoff plate model is presented the method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the reissner mindlin model r stenberg in asymptotic methods for elastic structures p ciarlet l trabucho and j m viano eds de gruyter berlin 1995 and a method to treat a free boundary p destuynder and t nevers rairo model math anal numer 22 1988 pp 217 242 optimal a priori and a posteriori error estimates are derived

error estimators for nonconforming finite element approximations of the stokes problem in this paper we define and analyze a posteriori error estimators for nonconforming approximations of the stokes equations we prove that these estimators are equivalent to an appropriate norm of the error for the case of piecewise linear elements we define two estimators both of them are easy to compute but the second is simpler because it can be computed using only the right hand side and the approximate velocity we show how the first estimator can be generalized to higher order elements finally we present several numerical examples in which one of our estimators is used for adaptive refinement

some new residual based a posteriori error estimators for the mortar finite element methods in this paper we propose some new residual based a posteriori error estimators for the mortar finite element discretization of the second order elliptic equations with discontinuous coefficients reliability and efficiency of the estimators are given our analysis does not require any saturation assumptions and the mesh restrictions on the interface which are often needed in the literature numerical experiments are presented to confirm our theoretical analysis

quasi optimal convergence rate for an adaptive hybridizable c 0 discontinuous galerkin method for kirchhoff plates in this paper we present an adaptive hybridizable c 0 discontinuous galerkin hcdg method for kirchhoff plates a reliable and efficient a posteriori error estimator is produced for this hcdg method quasi orthogonality and discrete reliability are established with the help of a postprocessed bending moment and the discrete helmholtz decomposition based on these the contraction property between two consecutive loops and complexity of the adaptive hcdg method are studied thoroughly the key points in our analysis are a postprocessed normal normal continuous bending moment from the hcdg method solution and a lifting of jump residuals from inter element boundaries to element interiors

on reflecting diffusion processes and skorokhod decompositions letg be ad dimensional bounded euclidean domain h1 g the set off in l2 g such that f defined in the distribution sense is in l2 g reflecting diffusion processes associated with the dirichlet spaces h1 g on l2 g dx are considered in this paper where a aij is a symmetric bounded uniformly ellipticd d matrix valued function such thata ij h1 g for eachi j and h1 g is a positive bounded function ong which is bounded away from zero a skorokhod decomposition is derived for the continuous reflecting markov processes associated with h1 g having starting points ing under a mild condition which is satisfied when g has finite d 1 dimensional lower minkowski content

maximum likelihood blind image separation using nonsymmetrical half plane markov random fields this paper presents a maximum likelihood approach for blindly separating linear instantaneous mixtures of images the spatial autocorrelation within each image is described using nonsymmetrical half plane nshp markov random fields in order to simplify the joint probability density functions of the source images a first implementation assuming stationary sources is presented it is then extended to a more realistic nonstationary image model two approaches respectively based on blocking and kernel smoothing are proposed to cope with the nonstationarity of the images the estimation of the mixing matrix is performed using an iterative equivariant version of the newton raphson algorithm moreover score functions required for the computation of the updating rule are approximated at each iteration by parametric polynomial estimators results achieved with artificial mixtures of both artificial and real world images including an astrophysical application clearly prove the high performance of our methods as compared to classical algorithms

a posteriori error analysis for the morley plate element with general boundary conditions this paper introduces and analyses a local residual based a posteriori error indicator for the morley finite element method of the biharmonic kirchhoff plate bending problem in the theoretical part of the paper a recent approach presented by the authors for clamped boundaries is extended to general boundary conditions the error indicator is proven to be both reliable and efficient the numerical part of the paper presents a set of results on various benchmark computations with different kinds of domains and boundary conditions these tests verify the reliability and efficiency of the error estimator and illustrate the robustness of the method for adaptive mesh refinements copyright 2009 john wiley sons ltd

residual type a posteriori error estimates for elliptic obstacle problems a posteriori error estimators of residual type are derived for piecewise linear finite element approximations to elliptic obstacle problems an instrumental ingredient is a new interpolation operator which requires minimal regularity exhibits optimal approximation properties and preserves positivity both upper and lower bounds are proved and their optimality is explored with several examples sharp a priori bounds for the a posteriori estimators are given and extensions of the results to double obstacle problems are briefly discussed

adaptive langevin sampler for separation of t distribution modelled astrophysical maps we propose to model the image differentials of astrophysical source maps by student s t distribution and to use them in the bayesian source separation method as priors we introduce an efficient markov chain monte carlo mcmc sampling scheme to unmix the astrophysical sources and describe the derivation details in this scheme we use the langevin stochastic equation for transitions which enables parallel drawing of random samples from the posterior and reduces the computation time significantly by two orders of magnitude in addition student s t distribution parameters are updated throughout the iterations the results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains

convergence and optimality of the adaptive morley element method this paper is devoted to the convergence and optimality analysis of the adaptive morley element method for the fourth order elliptic problem a new technique is developed to establish a quasi orthogonality which is crucial for the convergence analysis of the adaptive nonconforming method by introducing a new parameter dependent error estimator and further establishing a discrete reliability property sharp convergence and optimality estimates are then fully proved for the fourth order elliptic problem

framework for the a posteriori error analysis of nonconforming finite elements this paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods the theory assures reliability and efficiency of explicit residual error estimates up to data oscillations under the conditions h1 h2 and applies to several nonconforming finite elements the crouzeix raviart triangle element the han parallelogram element the nonconforming rotated nr parallelogram element of rannacher and turek the constrained nr parallelogram element of hu and shi the p 1 element on parallelograms due to park and sheen and the dssy parallelogram element the theory is extended to include 1 irregular meshes with at most one hanging node per edge

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data

parallel and deterministic algorithms from mrfs surface reconstruction deterministic approximations to markov random field mrf models are derived one of the models is shown to give in a natural way the graduated nonconvexity gnc algorithm proposed by a blake and a zisserman 1987 this model can be applied to smooth a field preserving its discontinuities a class of more complex models is then proposed in order to deal with a variety of vision problems all the theoretical results are obtained in the framework of statistical mechanics and mean field techniques a parallel iterative algorithm to solve the deterministic equations of the two models is presented together with some experiments on synthetic and real images

convergence of an adaptive mixed finite element method for kirchhoff plate bending problems some reliable and efficient a posteriori error estimators are produced for a mixed finite element method the hellan herrmann johnson h h j method for kirchhoff plate bending problems cf k hellan acta polytech scand civil engrg ser 46 1967 pp 1 28 l herrmann j eng mech div asce 93 1967 pp 13 26 c johnson numer math 21 1973 pp 43 62 based on these results with k 0 1 where k denotes the polynomial order of the discrete moment field space an adaptive mixed finite element method amfem is set up and its convergence and complexity are studied thoroughly the key points of the theoretical analysis include achieving a discrete helmholtz decomposition and a discrete inf sup condition which serve as the main tools in deducing the quasi orthogonality of the moment field and the discrete reliability of the estimator it is shown that the amfem is a contraction for the sum of the moment field error in an energy norm and the scaled error estimator between two consecutive adaptive loops moreover an estimate for the amfem s complexity via the number of elements is developed

time delayed finite difference reaction diffusion systems with nonquasimonotone functions this paper is concerned with finite difference solutions of a system of reaction diffusion equations with coupled nonlinear boundary conditions and time delays the reaction functions and the boundary functions are not necessarily quasimonotone and the time delays may appear in the reaction functions as well as in the boundary functions the investigation is devoted to the finite difference system for both the time dependent problem and its corresponding steady state problem some monotone iteration processes for the finite difference systems are given and the asymptotic behavior of the time dependent solution in relation to the steady state solution is discussed the asymptotic behavior result leads to some local and global attractors of the time dependent problem including the convergence of the time dependent solution to a unique steady state solution an application and some numerical results to an enzyme substrate reaction diffusion problem are given all the results are directly applicable to parabolic ordinary systems and to reaction diffusion systems without time delays

independent factor analysis we introduce the independent factor analysis ifa method for recovering independent hidden sources from their observed mixtures ifa generalizes and unifies ordinary factor analysis fa principal component analysis pca and independent component analysis ica and can handle not only square noiseless mixing but also the general case where the number of mixtures differs from the number of sources and the data are noisy ifa is a two step procedure in the first step the source densities mixing matrix and noise covariance are estimated from the observed data by maximum likelihood for this purpose we present an expectation maximization em algorithm which performs unsupervised learning of an associated probabilistic model of the mixing situation each source in our model is described by a mixture of gaussians thus all the probabilistic calculations can be performed analytically in the second step the sources are reconstructed from the observed data by an optimal nonlinear estimator a variational approximation of this algorithm is derived for cases with a large number of sources where the exact algorithm becomes intractable our ifa algorithm reduces to the one for ordinary fa when the sources become gaussian and to an em algorithm for pca in the zero noise limit we derive an additional em algorithm specifically for noiseless ifa this algorithm is shown to be superior to ica since it can learn arbitrary source densities from the data beyond blind separation ifa can be used for modeling multidimensional data by a highly constrained mixture of gaussians and as a tool for nonlinear signal encoding

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

each averaging technique yields reliable a posteriori error control in fem on unstructured grids part i low order conforming nonconforming and mixed fem averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second order partial differential equations since they provide efficient a posteriori error estimates by a simple postprocessing in this paper their reliablility is shown for conforming nonconforming and mixed low order finite element methods in a model situation the laplace equation with mixed boundary conditions emphasis is on possibly unstructured grids nonsmoothness of exact solutions and a wide class of averaging techniques theoretical and numerical evidence supports that the reliability is up to the smoothness of given right hand sides

reflected brownian motion in a wedge semimartingale property in this paper the object of study is reflected brownian motion in a two dimensional wedge with constant direction of reflection on each side of the wedge the basic question considered here is when is this process a semimartingale it is first shown that a related process defined by specifying the corner of the wedge to be an absorbing state rather than an instantaneous one is a semimartingale conditions for the existence and uniqueness of the process for which the corner is an instantaneous state were given by vardhan and williams brownian motion in a wedge with oblique reflection comm pure appl math to appear under these conditions it is shown that starting away from the corner the process is a semimartingale if and only if there is a convex combination of the directions of reflection that points into the wedge this equivalence is also shown to hold starting from the corner except in one unresolved case for which the wedge angle exceeds and the directions of reflection are exactly opposed

a two grid discretization scheme of non conforming finite elements for transmission eigenvalues abstract in this paper for the helmholtz transmission eigenvalue problem we propose a two grid discretization scheme of non conforming finite elements with this scheme the solution of the transmission eigenvalue problem on a fine grid h is reduced to the solution of the primal and dual eigenvalue problem on a much coarser grid h and the solutions of two linear algebraic systems with the same positive definite hermitian and block diagonal coefficient matrix on the fine grid h we prove the resulting solution still maintains an asymptotically optimal accuracy and we report some numerical examples in two dimension and three dimension on the modified zienkiewicz element to validate the efficiency of our approach for solving transmission eigenvalues

a new class of zienkiewicz type non conforming element in any dimensions in this paper a new class of zienkiewicz type non conforming finite element in n spatial dimensions with n 2 is proposed the new finite element is proved to be convergent for the biharmonic equation

a skorohod type lemma and a decomposition of reflected brownian motion we consider two dimensional reflected brownian motions in sharp thorns pointed downward with horizontal vectors of reflection we present a decomposition of the process into a brownian motion and a process which has bounded variation away from the tip of the thorn the construction is based on a new skorohod type lemma

directional derivatives of oblique reflection maps given an oblique reflection map and functions documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document psi chi in mathcal d lim end document the space of k valued functions that have finite left and right limits at every point the directional derivative documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document nabla chi gamma psi end document of along evaluated at is defined to be the pointwise limit as documentclass aastex usepackage amsbsy usepackage amsfonts u

a posteriori error estimates for nonconforming finite element methods computable a posteriori error bounds for a large class of nonconforming finite element methods are provided for a model poisson problem in two and three space dimensions besides a refined residual based a posteriori error estimate an averaging estimator is established and an l 2 estimate is included the a posteriori error estimates are reliable and efficient the proof of reliability relies on a helmholtz decomposition

a dirichlet process characterization of a class of reflected diffusions for a class of stochastic differential equations with reflection for which a certain l p continuity condition holds with p 1 it is shown that any weak solution that is a strong markov process can be decomposed into the sum of a local martingale and a continuous adapted process of zero p variation when p 2 this implies that the reflected diffusion is a dirichlet process two examples are provided to motivate such a characterization the first example is a class of multidimensional reflected diffusions in polyhedral conical domains that arise as approximations of certain stochastic networks and the second example is a family of two dimensional reflected diffusions in curved domains in both cases the reflected diffusions are shown to be dirichlet processes but not semimartingales

finite element galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems abstract this paper establishes some refined estimates for the approximation of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems by finite element or more generally galerkin methods suppose lambda is an eigenvalue of multiplicity q of a selfajoint problem and let m lambda denote the space of eigenvectors corresponding to lambda keywords hilbert space

non conforming finite element methods for transmission eigenvalue problem abstract the transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory in this paper for the helmholtz transmission eigenvalue problem we give a weak formulation which is a nonselfadjoint linear eigenvalue problem based on the weak formulation we first discuss the non conforming finite element approximation and prove the error estimates of the discrete eigenvalues obtained by the adini element the morley zienkiewicz element the modified zienkiewicz element et al and we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem

a family of c0 finite elements for kirchhoff plates ii numerical results abstract a new family of c0 kirchhoff plate elements has been introduced by the authors in the theoretical counterpart of the present paper a family of c0 finite elements for kirchhoff plates i error analysis the method presented is a displacement formulation with the deflection and the rotation as unknowns in the theoretical part an a priori and an a posteriori error analysis has been accomplished for the family in the present contribution the authors first give a supplementary derivation of the method and recall the main theoretical results then focus on the computational aspects of the method and finally present a set of numerical results on various benchmark computations these tests verify the optimal convergence rate of the method and illustrate the robustness of the reliable and efficient residual based a posteriori error estimator for adaptive mesh refinements

mixed methods for the helmholtz transmission eigenvalues the ciarlet raviart mixed finite element method is popular for the biharmonic equations in this paper we apply this method to the helmholtz transmission eigenvalue problem which is quadratic and

nonconforming tetrahedral finite elements for fourth order elliptic equations this paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions the newly constructed elements include two nonconforming tetrahedral finite elements and one quasi conforming tetrahedral element these elements are proved to be convergent for a model bi harmonic equation in three dimensions in particular the quasi conforming tetrahedron element is a modified zienkiewicz element while the nonmodified zienkiewicz element a tetrahedral element of hermite type is proved to be divergent on a special grid

a unifying theory of a posteriori finite element error control residual based a posteriori error estimates are derived within a unified setting for lowest order conforming nonconforming and mixed finite element schemes the various residuals are identified for all techniques and problems as the operator norm l of a linear functional of the form in the variable of a sobolev space v the main assumption is that the first order finite element space is included in the kernel ker l of l as a consequence any residual estimator that is a computable bound of l can be used within the proposed frame without further analysis for nonconforming or mixed fe schemes applications are given for the laplace stokes and navier lame equations

an explicit formula for the skorokhod map on 0 a the skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions in this work an explicit formula for the skorokhod map 0 a on 0 a for any a 0 is derived specifically it is shown that on the space d 0 of right continuous functions with left limits taking values in r 0 a a o 0 where a d 0 d 0 is defined by a t t sups 0 t s a infu s t u and 0 d 0 d 0 is the skorokhod map on 0 which is given explicitly by 0 t t sup s 0 t s in addition properties of a are developed and comparison properties of 0 a are established

convergence and optimal complexity of adaptive finite element eigenvalue computations in this paper an adaptive finite element method for elliptic eigenvalue problems is studied both uniform convergence and optimal complexity of the adaptive finite element eigenvalue approximation are proved the analysis is based on a certain relationship between the finite element eigenvalue approximation and the associated finite element boundary value approximation which is also established in the paper

on discontinuity adaptive smoothness priors in computer vision a variety of analytic and probabilistic models in connection with markov random fields mrfs have been proposed in the last decade for solving low level vision problems involving discontinuities this paper presents a systematic study of these models and defines a general discontinuity adaptive da mrf model by analyzing the euler equation associated with the energy minimization it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points which is determined by the a priori smoothness constraint encoded into the energy function an important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing this forms the basis on which a class of adaptive interaction functions aifs is defined the da model is defined in terms of the euler equation constrained by this class of aifs its solution is c sup 1 continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities because of the continuous nature it is stable to changes in parameters and data a good property for regularizing ill posed problems experimental results are shown

on the necessity and sufficiency of the patch test for convergence of nonconforming finite elements this paper proposes a weak patch test that improves both the patch test and the generalized patch test under a weak superapproximation assumption which can be obtained from certain approximation and weak continuity property it is shown that the weak patch test is equivalent to the generalized patch test thus if a nonconforming finite element passes the patch test and satisfies some approximation and weak continuity property its convergence is then guaranteed furthermore the consistency term of such a nonconforming element can be proved to be of order o h it is shown that if a nonconforming element does not pass the patch test and a condition relative to subdividing a domain by the element is true then one can find a family of triangulations for which the element is divergent

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

the lower bound property of the morley element eigenvalues in this paper we prove that the morley element eigenvalues approximate the exact ones from below on regular meshes including adaptive local refined meshes for the fourth order elliptic eigenvalue problems with the clamped boundary condition in any dimension and we implement the adaptive computation with the morley element to obtain lower bounds of eigenvalues for the vibration problem of clamped plate under tension and a fourth order elliptic eigenvalue problem with variable coefficients

close form solution and parameter selection for convex minimization based edge preserving smoothing this work presents a new approach for the analysis of convex minimization based edge preserving image smoothing and the parameter selection therein the global solution that is the response of a convex smoothing model to the ideal step edge is derived in close form by analyzing the close form solution insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution based on this a scheme is proposed for selecting parameters to achieve desirable responses at edges the theoretic results are substantiated by experiments

the mean field theory in em procedures for blind markov random field image restoration a markov random field mrf model based em expectation maximization procedure for simultaneously estimating the degradation model and restoring the image is described the mrf is a coupled one which provides continuity inside regions of smooth gray tones and discontinuity at region boundaries constraints for the restoration problem which is in general ill posed the computational difficulty associated with the em procedure for mrfs is resolved by using the mean field theory from statistical mechanics an orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates experimental results on synthetic and real world images show that this approach provides good blur estimates and restored images the restored images are comparable to those obtained by a wiener filter in mean square error but are most visually pleasing

new error estimates of the morley element for the plate bending problems in this paper we derive some new error estimates of a nonconforming morley element for the plate bending problems our aim is fourfold first it shows that the consistency error of the morley element can be controlled by its corresponding approximation error up to an arbitrarily high order term especially which can be of arbitrary order provided that f on the right hand side is piecewise smooth enough thus the total energy norm is dominated alone by the approximation error second as a byproduct we derive the error estimate under the regularity assumption u h 2 s with s 0 1 which fills the gap in the a priori error estimate of the morley element with low regularity for s 0 1 2 third based on this new error bound a robust convergence is proved even if the solution is exactly in h 2 finally by a slight modification of the variational formulation a new error estimate is also derived for the case f h 1 the key role is played by some quasi interpolation operators and the weak continuous properties of morley finite element space the main ideas and results presented here are motivated by mao and shi 2010 and can be viewed as its extension to fourth order problems

data oscillation and convergence of adaptive fem data oscillation is intrinsic information missed by the averaging process associated with finite element methods fem regardless of quadrature ensuring a reduction rate of data oscillation together with an error reduction based on a posteriori error estimators we construct a simple and efficient adaptive fem for elliptic partial differential equations pdes with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance

a markov model for blind image separation by a mean field em algorithm this paper deals with blind separation of images from noisy linear mixtures with unknown coefficients formulated as a bayesian estimation problem this is a flexible framework where any kind of prior knowledge about the source images and the mixing matrix can be accounted for in particular we describe local correlation within the individual images through the use of markov random field mrf image models these are naturally suited to express the joint pdf of the sources in a factorized form so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained our model also includes edge variables to preserve intensity discontinuities mrf models have been proved to be very efficient in many visual reconstruction problems such as blind image restoration and allow separation and edge detection to be performed simultaneously we propose an expectation maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix the sources and their edge maps we tested this procedure on both synthetic and real images in the fully blind case i e no prior information on mixing is exploited and found that a source model accounting for local autocorrelation is able to increase robustness against noise even space variant furthermore when the model closely fits the source characteristics independence is no longer a strict requirement and cross correlated sources can be separated as well

a new a posteriori error estimate for the morley element in this paper we present a posteriori error analysis for the nonconforming morley element of the fourth order elliptic equation we propose a new residual based a posteriori error estimator and prove its reliability and efficiency these results refine those of beirao da veiga et al numer math 106 165 179 2007 by dropping two edge jump terms in both the energy norm of the error and the estimator and those of wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 by showing the efficiency in the sense of verfurth a review of a posteriori error estimation and adaptive mesh refinement techniques wiley teubner new york 1996 moreover the normal component in the estimators of beirao da veiga et al numer math 106 165 179 2007 and wang and zhang local a priori and a posteriori error estimates of finite elements for biharmonic equation research report 13 2006 is dropped and therefore only the tangential component of the stress on each edge comes into the estimator in addition we generalize these results to three dimensional case

a type of adaptive c0 non conforming finite element method for the helmholtz transmission eigenvalue problem abstract the transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering in this paper for the helmholtz transmission eigenvalue problem in r d d 2 3 we discuss the a posteriori error estimates and adaptive algorithm of a type of c 0 non conforming finite elements including the morley zienkiewicz element and the modified zienkiewicz element we give the a posteriori error estimators for approximate eigenpair and prove their reliability and efficiency for eigenfunctions we also analyze their reliability for eigenvalues numerical results not only in r 2 but also in r 3 indicate that the a posteriori error estimators are sharp and the adaptive algorithm is efficient for computing real and complex transmission eigenvalues as expected

the morley element for fourth order elliptic equations in any dimensions in this paper the well known nonconforming morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion the general n dimensional morley element consists of all quadratic polynomials defined on each n simplex with degrees of freedom given by the integral average of the normal derivative on each n 1 subsimplex and the integral average of the function value on each n 2 subsimplex explicit expressions of nodal basis functions are also obtained for this element on general n simplicial grids convergence analysis is given for this element when it is applied as a nonconforming finite element discretization for the biharmonic equation

a unifying theory of a posteriori error control for nonconforming finite element methods residual based a posteriori error estimates were derived within one unifying framework for lowest order conforming nonconforming and mixed finite element schemes in carstensen numer math 100 617 637 2005 therein the key assumption is that the conforming first order finite element space v h c annulates the linear and bounded residual l written v h c subseteq rm ker ell that excludes particular nonconforming finite element methods ncfems on parallelograms in that v h c not subset rm ker ell the present paper generalises the aforementioned theory to more general situations to deduce new a posteriori error estimates also for mortar and discontinuous galerkin methods the key assumption is the existence of some bounded linear operator pi v h c rightarrow v h nc with some elementary properties it is conjectured that the more general hypothesis h1 h3 can be established for all known ncfems applications on various nonstandard finite element schemes for the laplace stokes and navier lame equations illustrate the presented unifying theory of a posteriori error control for ncfem

convex duality and the skorokhod problem ii in this paper we consider skorokhod problems on polyhedral domains with a constant and possibly oblique constraint direction specified on each face of the domain and with a corresponding cone of constraint directions at the intersection of faces in part one of this paper we used convex duality to develop new methods for the construction of solutions to such skorokhod problems and for proving lipschitz continuity of the associated skorokhod maps the main alternative approach to skorokhod problems of this type is the reflection mapping technique introduced by harrison and reiman 8 in this part of the paper we apply the theory developed in part one to show that the reflection mapping technique of 8 is restricted to a slight generalization of the class of problems originally considered in 8 we further illustrate the power of the duality approach by applying it to two other classes of skorokhod problems those with normal directions of constraint and a new class that arises from a model of processor sharing in communication networks in particular we prove existence of solutions to and lipschitz continuity of the skorokhod maps associated with each of these skorokhod problems

sdes with oblique reflection on nonsmooth domains in this paper we consider stochastic differential equations with reflecting boundary conditions for domains that might have corners and for which the allowed directions of reflection at a point on the boundary of the domain are possibly oblique the main results are strong existence and uniqueness for solutions of such equations a key ingredient is a family of relatively regular functions appropriate to the given domain and directions of reflection two cases are treated in the paper in the first case the direction of reflection is single valued and varies smoothly and the main new feature is that the boundary of the domain may be nonsmooth in the second case the domain is taken to be the intersection of a finite number of domains with relatively smooth boundary and at the resulting corner points more than one oblique direction is allowed

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

convergence of adaptive finite element methods adaptive finite element methods fems have been widely used in applications for over 20 years now in practice they converge starting from coarse grids although no mathematical theory has been able to prove this assertion ensuring an error reduction rate based on a posteriori error estimators together with a reduction rate of data oscillation information missed by the underlying averaging process we construct a simple and efficient adaptive fem for elliptic partial differential equations we prove that this algorithm converges with linear rate without any preliminary mesh adaptation nor explicit knowledge of constants any prescribed error tolerance is thus achieved in a finite number of steps a number of numerical experiments in two and three dimensions yield quasi optimal meshes along with a competitive performance extensions to higher order elements and applications to saddle point problems are discussed as well

regularity results for elliptic equations in lipschitz domains abstract we develop a simple variational argument based on the usual nirenberg difference quotient technique to deal with the regularity of the solutions of dirichlet and neumann problems for some linear and quasilinear elliptic equation in lipschitz domains we obtain optimal regularity results in the natural family of sobolev spaces associated with the variational structure of the equations in the linear case we obtain in a completely different way some of the results of d jerison and c e kenig about the laplace equation

can we have superconvergent gradient recovery under adaptive meshes we study adaptive finite element methods for elliptic problems with domain corner singularities our model problem is the two dimensional poisson equation results of this paper are twofold first we prove that there exists an adaptive mesh gauged by a discrete mesh density function under which the recovered gradient by the polynomial preserving recovery ppr is superconvergent second we demonstrate by numerical examples that an adaptive procedure with an a posteriori error estimator based on ppr does produce adaptive meshes that asatisfy our mesh density assumption and the recovered gradient by ppr is indeed superconvergent in the adaptive process

a quadrilateral morley element for biharmonic equations in this paper we propose a morley type finite element for quadrilateral meshes to solve biharmonic problems for each quadrilateral q the finite element space is defined by the span of p 2 q plus two functions in p 3 q each of the cubic polynomials is the product of a pair of equations of opposite edges and the equation of the bimedian between them the degrees of freedom consist of the values at vertices and integrals of normal derivatives over edges optimal orders of convergence are proved both in discrete h 2 and h 1 seminorms several numerical tests confirm the convergence analysis

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

iterative methods for transmission eigenvalues transmission eigenvalues have important applications in inverse scattering theory they can be used to obtain useful information of the physical properties such as the index of refraction of the scattering target despite considerable effort devoted to the existence and estimation for the transmission eigenvalues the numerical treatment is limited since the problem is nonstandard classical finite element methods result in non hermitian matrix eigenvalue problems in this paper we focus on the computation of a few lowest transmission eigenvalues which are of practical importance instead of a non hermitian problem we work on a series of generalized hermitian problems we first use a fourth order reformulation of the transmission eigenproblem to construct functions involving an associated generalized eigenvalue problem the roots of these functions are the transmission eigenvalues then we apply iterative methods to compute the transmission eigenvalues we show the convergence of the numerical schemes the effectiveness of the methods is demonstrated using various numerical examples

the f e m test for convergence of nonconforming finite elements on etablit un nouveau critere de convergence pour les elements finis non conformes qui est facilement verifiable le long de chaque interface

a posteriori error analysis for conforming mitc elements for reissner mindlin plates this paper establishes a unified a posteriori error estimator for a large class of conforming finite element methods for the reissner mindlin plate problem the analysis is based on some assumption h on the consistency of the reduction integration to avoid shear locking the reliable and efficient a posteriori error estimator is robust in the sense that the reliability and efficiency constants are independent of the plate thickness t the presented analysis applies to all conforming mitc elements and all conforming finite element methods without reduced integration from the literature

convergence analysis of an adaptive nonconforming finite element method an adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement process and thus guarantees convergence of the nonconforming finite element approximations the analysis is carried out for the lowest order crouzeix raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite element algorithm with respect to the number of refinement levels important tools in the convergence proof are a discrete local efficiency and a quasi orthogonality property the proof does neither require regularity of the solution nor uses duality arguments as a consequence on the data control no particular mesh design has to be monitored

on the convergence properties of the quadrilateral elements of sander and beckers a class of nonconforming quadrilateral membrane elements introduced by sander and beckers is discussed in all details it is proved that two elements that do not pass the patch test may still yield convergence under a suitable condition on mesh subdivisions whereas one such element is found to be divergent for all mesh subdivisions all other finite elements in this class that pass the patch test are convergent the mathematical analysis provides a clear explanation of the convergence behavior appearing in the numerical examples of sander and beckers 1 introduction quadrilateral finite elements are attractive for discretizations of domains of arbitrary shapes but these approximations are hardly conforming therefore such elements have to be tested for convergence in connection with a variational interpretation of the patch test 2 sander and beckers 3 have recently introduced a class of nonconforming quadrilateral membrane elements having 8 to 16 degrees of freedom and have shown by numerical computations for a trapezoidal membrane problem that two elements that do not pass the patch test still exhibit convergence and yield good approximations whereas one such element diverges this result is of great interest and leads to the question whether the patch test is necessary for convergence of these nonconforming elements as stated in 3 additional investigations are certainly required to understand their behavior the present paper establishes a detailed mathematical analysis of these elements we formulate a condition on mesh subdivisions under which two elements that do not pass the patch test indeed yield convergence whereas another element is proved to be divergent whatever the mesh subdivision may be all other quadrilateral elements in this class that pass the patch test are convergent the theoretical analysis clearly explains the convergence behavior discussed in the numerical computations of sander and beckers in their examples a bisection scheme of mesh subdivisions is used for the discretization of the trapezoidal membrane in such cases the proposed condition on the mesh subdivisions is automatically fulfilled and thus convergence occurs for two elements it is seen therefore that the range of applicability of the patch test as a necessary condition for convergence is limited at this point it is worth noting that stummel 5 has presented basic examples which show that spaces of nonconforming trial functions

convergence properties of two nonconforming finite elements abstract two nonconforming triangular elements for second order problems are analyzed one element is found to be convergent the other does not yield approximate solutions converging to the solution of the given boundary value problem but to a wrong limit which is the solution of another variational equation this strange convergence behaviour may be typical for a wider class of nonconforming elements violating the basic precondition for convergence the problem of patch subdivisions is also considered

an explicit analysis of stummel s patch test examples a constructive approach for the treatment of stummel s examples to the patch test is presented together with generalizations of these examples the strange convergence phenomenon of nonconforming approximations is discussed in detail and a kind of modified variational equation for remedying these defects is introduced our variational equation uses a combination of hybrid and penalty methods that define a convergent procedure with optimal order of convergence to the exact solution with respect to a mesh dependent norm

convergence of adaptive finite element methods for general second order linear elliptic pdes we prove convergence of adaptive finite element methods afems for general nonsymmetric second order linear elliptic pdes thereby extending the result of morin nochetto and siebert it siam j numer anal 38 2000 pp 466 488 it siam rev 44 2002 pp 631 658 the proof relies on quasi orthogonality which accounts for the bilinear form not being a scalar product together with novel error and oscillation reduction estimates which now do not decouple we show that afems are a contraction for the sum of energy error plus oscillation numerical experiments including oscillatory coefficients and both coercive and noncoercive convection diffusion pde illustrate the theory and yield optimal meshes

discretization error for the discrete kirchhoff plate finite element approximation abstract we provide in this work the discretization error estimates that can guide an adaptive mesh refinement for the discrete kirchhoff plate finite elements the proposed developments are built upon the concept of error estimates for classical elasticity and adapted to suit the kirchhoff plate finite elements we give a detailed illustration of the proposed procedures for the discrete kirchhoff triangular plate element along with several different possibilities for constructing the enhancement of test space needed for error estimates the first novelty concerns the consistent displacement field in terms of the third order polynomial for the discrete kirchhoff triangle whereas the second novelty is the use of the argyris triangle with fifth order polynomials for constructing the enhanced test for error estimates we compare the latter against several alternatives that can be used for kirchhoff plates the results of numerical examples are given to illustrate the effectiveness of proposed discretization error estimates

each averaging technique yields reliable a posteriori error control in fem on unstructured grids part ii higher order fem averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing in the second paper of our analysis of their reliability we consider conforming h fem of higher i e not of lowest order in two or three space dimensions in this paper reliablility is shown for conforming higher order finite element methods in a model situation the laplace equation with mixed boundary conditions emphasis is on possibly unstructured grids nonsmoothness of exact solutions and a wide class of local averaging techniques theoretical and numerical evidence supports that the reliability is up to the smoothness of given right hand sides

the adaptive ciarlet raviart mixed method for biharmonic problems with simply supported boundary condition abstract in this paper we study the adaptive fashion of the ciarlet raviart mixed method for biharmonic equation eigenvalue problem with simply supported boundary condition in r d we propose an a posteriori error indicator of the ciarlet raviart approximate solution for the biharmonic equation and an a posteriori error indicator of the ciarlet raviart approximate eigenfuction and prove the reliability and efficiency of the indicators we also give an a posteriori error indicator for the approximate eigenvalue and prove its reliability we design an adaptive ciarlet raviart mixed method with piecewise polynomials of degree less than or equal to m and numerical experiments show that numerical eigenvalues obtained by the method can achieve the optimal convergence order o d o f 2 m d d 2 m 2 3 d 3 m 3

a convergence condition for the quadrilateral wilson element the paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test the convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation this result extends the range of applicability of wilson s element the necessity of the proposed condition is also discussed

a posteriori error estimates for nonconforming finite element methods for fourth order problems on rectangles the a posteriori error analysis of conforming finite element discretisations of the biharmonic problem for plates is well established but nonconforming discretisations are more easy to implement in practice the a posteriori error analysis for the morley plate element appears very particular because two edge contributions from an integration by parts vanish simultaneously this crucial property is lacking for popular rectangular nonconforming finite element schemes like the nonconforming rectangular morley finite element the incomplete biquadratic finite element and the adini finite element this paper introduces a novel methodology and utilises some conforming discrete space on macro elements to prove reliability and efficiency of an explicit residual based a posteriori error estimator an application to the morley triangular finite element shows the surprising result that all averaging techniques yield reliable error bounds numerical experiments confirm the reliability and efficiency for the established a posteriori error control on uniform and graded tensor product meshes

sur une integrale pour les processus a alpha variation bornee dans cet article l auteur obtient une formule d ito et l existence de temps locaux pour certains processus de dirichlet a partir des proprietes d une integrale faisant intervenir un processus a variation bornee et un autre a variation bornee cette integrale est definie comme limite de sommes de riemann

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

a local regularization operator for triangular and quadrilateral finite elements this paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes this operator is a variant of the regularization operator of clement however ours is constructed via a local projection in a reference domain we prove in this paper that it has the same optimal approximation properties as the standard interpolation operator and we present some applications

a discrete helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes the discrete reliability of a finite element method is a key ingredient to prove optimal convergence of an adaptive mesh refinement strategy and requires the interchange of a coarse triangulation and some arbitrary refinement of it one approach for this is the careful design of an intermediate triangulation with one level refinements and with the remaining difficulty to design some interpolation operator which maps a possibly nonconforming approximation into the finite element space based on the finer triangulation this paper enfolds the second possibility of some novel discrete helmholtz decomposition for the nonconforming morley finite element method this guarantees the optimality of a standard adaptive mesh refining algorithm for the biharmonic equation numerical examples illustrate the crucial dependence of the bulk parameter and the surprisingly short pre asymptotic range of the adaptive morley finite element method

p1 nonconforming quadrilateral finite element methods for second order elliptic problems a p1 nonconforming quadrilateral finite element is introduced for second order elliptic problems in two dimensions unlike the usual quadrilateral nonconforming finite elements which contain quadratic polynomials or polynomials of degree greater than 2 our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges one of the benefits of using our element is convenience in using rectangular or quadrilateral meshes with the least degrees of freedom among the nonconforming quadrilateral elements an optimal rate of convergence is obtained also a nonparametric reference scheme is introduced in order to systematically compute stiffness and mass matrices on each quadrilateral an extension of the p1 nonconforming element to three dimensions is also given finally several numerical results are reported to confirm the effective nature of the proposed new element

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

a posteriori error estimates for the morley plate bending element a local a posteriori error indicator for the well known morley element for the kirchhoff plate bending problem is presented the error indicator is proven to be both reliable and efficient the technique applied is general and it is shown to have also other applications

multichannel blind separation and deconvolution of images for document analysis in this paper we apply bayesian blind source separation bss from noisy convolutive mixtures to jointly separate and restore source images degraded through unknown blur operators and then linearly mixed we found that this problem arises in several image processing applications among which there are some interesting instances of degraded document analysis in particular the convolutive mixture model is proposed for describing multiple views of documents affected by the overlapping of two or more text patterns we consider two different models the interchannel model where the data represent multispectral views of a single sided document and the intrachannel model where the data are given by two sets of multispectral views of the recto and verso side of a document page in both cases the aim of the analysis is to recover clean maps of the main foreground text but also the enhancement and extraction of other document features such as faint or masked patterns we adopt bayesian estimation for all the unknowns and describe the typical local correlation within the individual source images through the use of suitable gibbs priors accounting also for well behaved edges in the images this a priori information is particularly suitable for the kind of objects depicted in the images treated i e homogeneous texts in homogeneous background and as such is capable to stabilize the ill posed inverse problem considered the method is validated through numerical and real experiments that are representative of various real scenarios