the smooth cohomology of n 2 supersymmetric landau ginzburg field theories we compute the smooth cohomology both unrestricted and compactly supported of the supercharge of an ultraviolet cutoffn 2 supersymmetric landau ginzburg field theory

gaps in the differential forms spectrum on cyclic coverings we are interested in the spectrum of the hodge de rham operator on a mathbb z covering x over a compact manifold m of dimension n 1 let be a hypersurface in m which does not disconnect m and such that m is a fundamental domain of the covering if the cohomology group hn 2 is trivial we can construct for each n in mathbb n a metric g gn on m such that the hodge de rham operator on the covering x g has at least n gaps in its essential spectrum if h n 2 sigma ne 0 the same statement holds true for the hodge de rham operators on p forms provided p notin n 2 n 2 1

supersymmetry and singular perturbations abstract first it is shown in an abstract framework that supersymmetric quantum theory may give rise to very singular perturbations which make perturbation theories invalid then the abstract results are applied to a model of 1 dimensional supersymmetric quantum mechanics witten s model to obtain some families of singular hamiltonians some concrete examples which reveal their singularness are discussed in detail

the index of the scattering operator on the positive spectral subspace we construct the scattering operator for a spinor field in a time dependent background by the dyson expansion then we show that the restriction of the scattering operator to the positive spectral subspace with respect to a reference hamiltonian is fredholm the computation of the index of this restriction is reduced to the index computation for an elliptic pseudodifferential operator of order zero we obtain the index in terms of a cohomological formula by means of the atiyah singer index theorem

an effective algorithm for the generation of patient specific purkinje networks in computational electrocardiology the purkinje network is responsible for the fast and coordinated distribution of the electrical impulse in the ventricle that triggers its contraction therefore it is necessary to model its presence to obtain an accurate patient specific model of the ventricular electrical activation in this paper we present an efficient algorithm for the generation of a patient specific purkinje network driven by measures of the electrical activation acquired on the endocardium the proposed method provides a correction of an initial network generated by means of a fractal law and it is based on the solution of eikonal problems both in the muscle and in the purkinje network we present several numerical results both in an ideal geometry with synthetic data and in a real geometry with patient specific clinical measures these results highlight an improvement of the accuracy provided by the patient specific purkinje network with respect to the initial one in particular a cross validation test shows an accuracy increase of 19 when only the 3 of the total points are used to generate the network whereas an increment of 44 is observed when a random noise equal to 20 of the maximum value of the clinical data is added to the measures

on a spectral flow formula for the homological index abstract consider a selfadjoint unbounded operator d on a hilbert space h and a one parameter norm continuous family of selfadjoint bounded operators a t t r that converges in norm to asymptotes a at then under certain conditions 22 that include the assumption that the operators d t d a t t r all have discrete spectrum the spectral flow along the path d t can be shown to be equal to the index of t d t when the latter is an unbounded fredholm operator on l 2 r h in 16 an investigation of the index spectral flow question when the operators in the path may have some essential spectrum was started but under restrictive assumptions that rule out differential operators in general in 11 the question of what happens when the fredholm condition is dropped altogether was investigated in these circumstances the fredholm index is replaced by the witten index in this paper we take the investigation begun in 11 much further we show how to generalize a formula known from the setting of the l 2 index theorem to the non fredholm setting restricting back to the case of selfadjoint fredholm operators our formula extends the result of 22 in the sense of relaxing the discrete spectrum condition it also generalizes some other fredholm operator results of 21 16 11 that permit essential spectrum for the operators in the path our result may also apply however when the operators d t have essential spectrum equal to the whole real line our main theorem gives a trace formula relating the homological index of 7 to an integral formula that is known for a path of selfadjoint fredholms with compact resolvent and with unitarily equivalent endpoints to compute spectral flow our formula however applies to paths of selfadjoint non fredholm operators we interpret this as indicating there is a generalization of spectral flow to the non fredholm setting

efficient algorithm for nonconvex minimization and its application to pm regularization in image processing nonconvex regularization has the ability to smooth homogeneous regions and sharpen edges but leads to challenging computation we propose some iterative schemes to minimize the energy function with nonconvex edge preserving potential the schemes are derived from the duality based algorithm proposed by bermudez and moreno and the fixed point iteration the convergence is proved for the convex energy function with nonconvex potential and the linear convergence rate is given applying the proposed schemes to perona and malik s nonconvex regularization we present some efficient algorithms based on our schemes and show the approximate convergence behavior for nonconvex energy function experimental results are presented which show the efficiency of our algorithms including better denoised performance of nonconvex regularization faster convergence speed higher calculation precision lower calculation cost under the same number of iterations and less implementation time under the same peak signal noise ratio level

relative index theorems and supersymmetric scattering theory we discuss supersymmetric scattering theory and employ krein s theory of spectral shift functions to investigate supersymmetric scattering systems this is the basis for the derivation of relative index theorems on some classes of open manifolds as an example we discuss the de rham complex for obstacles in n and asymptotically flat manifolds it is shown that the absolute or relative euler characteristic of an obstacle in n may be obtained from scattering data for the laplace operator on forms with absolute or relative boundary conditions respectively in the case of asymptotically flat manifolds we obtain the chern gauss bonnet theorem for thel2 euler characteristic

restoration of images based on subspace optimization accelerating augmented lagrangian approach we propose a new fast algorithm for solving a tv based image restoration problem our approach is based on merging subspace optimization methods into an augmented lagrangian method the proposed algorithm can be seen as a variant of the alm augmented lagrangian method and the convergence properties are analyzed from a drs douglas rachford splitting viewpoint experiments on a set of image restoration benchmark problems show that the proposed algorithm is a strong contender for the current state of the art methods

preconditioning for pde constrained optimization with total variation regularization abstract the efficient solution of pde constrained optimization problems is of great significance in many scientific and engineering applications the key point of achieving this goal is to solve the linear systems arising from such problems more efficiently by preconditioning in this paper we consider preconditioning the linear systems arising from pde constrained optimization problems with total variation tv regularization based on the block structure of the coefficient matrix or its row and column transformed forms we propose three kinds of new preconditioners by approximating the schur complements in different ways we analyze the eigenvalue properties of the preconditioned coefficient matrices and provide the eigenvalue bounds independent of mesh size we also show the relations of eigenvalue bounds corresponding to different preconditioners numerical results illustrate the efficiency of the proposed preconditioners by comparison with other existing methods

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

the estimation of eigenvalues of sum difference and tensor product of matrices over quaternion division algebra in this paper the estimation problems of eigenvalues of sum difference and tensor product of matrices over quaternion division algebra are studied a pair of inequalities about eigenvalues of self conjugate quaternion matrix is established the famous brauer theorem is generalized to quaternion division algebra and the form of cassini theorem over quaternion division algebra is also worked out successfully

index formulas for generalized wiener hopf operators and boson fermion correspondence in 2n dimensions the kernels of operators associated with special chiral gauge trans formations kinks in the 2 dimensional dirac theory are explicitly deter mined the result is used to obtain index formulas for fredholm operators corresponding to continuous chiral gauge transformations moreover the fock space quadratic forms corresponding to the kinks are proved to converge to the dirac field as the kink size goes to zero it is also shown that for n i 2 mod4 the majorana field can be reached in a similar fashion

statistical inverse problems discretization model reduction and inverse crimes the article discusses the discretization of linear inverse problems when an inverse problem is formulated in terms of infinite dimensional function spaces and then discretized for computational purposes a discretization error appears since inverse problems are typically ill posed neglecting this error may have serious consequences to the quality of the reconstruction the bayesian paradigm provides tools to estimate the statistics of the discretization error that is made part of the measurement and modelling errors of the estimation problem this approach also provides tools to reduce the dimensionality of inverse problems in a controlled manner the ideas are demonstrated with a computed example

a class of accelerated uzawa algorithms for saddle point problems in this paper we establish a class of accelerated uzawa au algorithms for solving the large sparse nonsingular saddle point problems by making use of the extrapolation technique this extrapolation technique is based on the eigenvalues of the iterative matrix these au algorithms involve two iteration parameters whose special choices can cover the known classical uzawa method as well as yield new ones firstly the accelerated model for the uzawa algorithm is established and the detail algorithm description of au method is presented then the convergence analyse of the au method is given moreover theoretical analyses show that the au algorithm converges faster than some uzawa type methods the uzawa method is also included in when the eigenvalues of the iterative matrix and the parameter satisfy some conditions numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the au method

an iterative shrinkage approach to total variation image restoration the problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications a particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill conditioned operator in such a situation the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties such a priori information commonly referred to as simply priors is essential for image restoration rendering it stable and robust to noise moreover using the priors makes the recovered images exhibit some plausible features of their original counterpart particularly if the original image is known to be a piecewise smooth function one of the standard priors used in this case is defined by the rudin osher fatemi model which results in total variation tv based image restoration the current arsenal of algorithms for tv based image restoration is vast in this present paper a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage aka iterated thresholding in the proposed method the tv based image restoration is performed through a recursive application of two simple procedures viz linear filtering and soft thresholding therefore the method can be identified as belonging to the group of first order algorithms which are efficient in dealing with images of relatively large sizes another valuable feature of the proposed method consists in its working directly with the tv functional rather then with its smoothed versions moreover the method provides a single solution for both isotropic and anisotropic definitions of the tv functional thereby establishing a useful connection between the two formulae finally a number of standard examples of image deblurring are demonstrated in which the proposed method can provide restoration results of superior quality as compared to the case of sparse wavelet deconvolution

on 3d numerical inverse problems for the bidomain model in electrocardiology in the inverse problem en electrocardiology the goal is to recover electrophysiological activity in the heart without measuring directly on its surface without using catheter interventions note that today the inverse computation is frequently used by solving the quasi static model this model doesnt take into account the heart dynamic in time and may result in considerable errors in the reconstruction of the solution on the heart in this paper a 3d numerical inverse problem constrained by the bidomain equations in electrocardiology is investigated the state equations consisting in a coupled reaction diffusion system modelling the propagation of the intracelullar and extracellular electrical potentials and ionic currents are extended to further consider the effect of an external bathing medium thus we demonstrate that the novel concept of applying electrophysiological data might be useful to improve noninvasive reconstruction of electrical heart activity finally we present numerical experiments representing the effect of the heart dynamic on the inverse solutions

commutation methods applied to the mkdv equation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided our theory is based on commutation methods i e n 1 supersymmetry underlying miura s transformation that links solutions of the two evolution equations

a multilevel algorithm for simultaneously denoising and deblurring images in this paper we develop a fast multilevel algorithm for simultaneously denoising and deblurring images under the total variation regularization although much effort has been devoted to developing fast algorithms for the numerical solution and the denoising problem was satisfactorily solved fast algorithms for the combined denoising and deblurring model remain to be a challenge recently several successful studies of approximating this model and subsequently finding fast algorithms were conducted which have partially solved this problem the aim of this paper is to generalize a fast multilevel denoising method to solving the minimization model for simultaneously denoising and deblurring our new idea is to overcome the complexity issue by a detailed study of the structured matrices that are associated with the blurring operator a fast algorithm can then be obtained for directly solving the variational model supporting numerical experiments on gray scale images are presented

total variation stokes strategy for sparse view x ray ct image reconstruction previous studies have shown that by minimizing the total variation tv of the to be estimated image with some data and or other constraints a piecewise smooth x ray computed tomography image can be reconstructed from sparse view projection data however due to the piecewise constant assumption for the tv model the reconstructed images are frequently reported to suffer from the blocky or patchy artifacts to eliminate this drawback we present a total variation stokes projection onto convex sets tvs pocs reconstruction method in this paper the tvs model is derived by introducing isophote directions for the purpose of recovering possible missing information in the sparse view data situation thus the desired consistencies along both the normal and the tangent directions are preserved in the resulting images compared to the previous tv based image reconstruction algorithms the preserved consistencies by the tvs pocs method are expected to generate noticeable gains in terms of eliminating the patchy artifacts and preserving subtle structures to evaluate the presented tvs pocs method both qualitative and quantitative studies were performed using digital phantom physical phantom and clinical data experiments the results reveal that the presented method can yield images with several noticeable gains measured by the universal quality index and the full width at half maximum merit as compared to its corresponding tv based algorithms in addition the results further indicate that the tvs pocs method approaches to the gold standard result of the filtered back projection reconstruction in the full view data case as theoretically expected while most previous iterative methods may fail in the full view case because of their artificial textures in the results

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

total variation projection with first order schemes this article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant the projection is computed through a dual formulation that is solved by first order non smooth optimization methods this yields an iterative algorithm that applies iterative soft thresholding to the dual vector field and for which we establish convergence rate on the primal iterates this projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint or for texture synthesis numerical results are reported to illustrate the usefulness and potential applicability of our tv projection algorithm on various examples including denoising texture synthesis inpainting deconvolution and tomography problems we also show that our projection algorithm competes favorably with state of the art tv projection methods in terms of convergence speed

consimilarity of quaternion matrices and complex matrices this paper discusses consimilarity of quaternion matrices obtains the jordan canonical form of a quaternion matrix under consimilarity and some necessary and sufficient conditions for consimilarity of quaternion matrices the consimilarity of quaternion matrices is a natural extension of the complex consimilarity of complex matrices has many good properties including some that are essentially different from those of complex consimilarity moreover using the consimilarity of quaternion matrices we obtain a new way to discuss complex consimilarity of complex matrices

parallel lagrange newton krylov schur methods for pde constrained optimization part i the krylov schur solver large scale optimization of systems governed by partial differential equations pdes is a frontier problem in scientific computation reduced quasi newton sequential quadratic programming sqp methods are state of the art approaches for such problems these methods take full advantage of existing pde solver technology and parallelize well however their algorithmic scalability is questionable for certain problem classes they can be very slow to converge in this two part article we propose a new method for steady state pde constrained optimization based on the idea of using a full space newton solver combined with an approximate reduced space quasi newton sqp preconditioner the basic components of the method are newton solution of the first order optimality conditions that characterize stationarity of the lagrangian function krylov solution of the karush kuhn tucker kkt linear systems arising at each newton iteration using a symmetric quasi minimum residual method preconditioning of the kkt system using an approximate state decision variable decomposition that replaces the forward pde jacobians by their own preconditioners and the decision space schur complement the reduced hessian by a bfgs approximation initialized by a two step stationary method accordingly we term the new method it lagrange newton krylov schur lnks it is fully parallelizable exploits the structure of available parallel algorithms for the pde forward problem and is locally quadratically convergent in part i of this two part article we investigate the effectiveness of the kkt linear system solver we test our method on two optimal control problems in which the state constraints are described by the steady state stokes equations the objective is to minimize dissipation or the deviation from a given velocity field the control variables are the boundary velocities numerical experiments on up to 256 cray t3e processors and on an sgi origin 2000 include scalability and performance assessment of the lnks algorithm and comparisons with reduced sqp for up to 1 000 000 state and 50 000 decision variables in part ii of the article we address globalization and inexactness issues and apply lnks to the optimal control of the steady incompressible navier stokes equations

parameter selection for total variation based image restoration using discrepancy principle there are two key issues in successfully solving the image restoration problem 1 estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2 development of efficient numerical techniques for computing the solution in this paper we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image the new approach is based on the total variation tv regularized strategy and morozov s discrepancy principle the tv norm is represented by the dual formulation that changes the minimization problem into a minimax problem a proximal point method is developed to compute the saddle point of the minimax problem by adjusting the regularization parameter adaptively in each iteration the solution is guaranteed to satisfy the discrepancy principle we will give the convergence proof of our algorithm and numerically show that it is better than some state of the art methods in terms of both speed and accuracy

multiplicative noise removal using variable splitting and constrained optimization multiplicative noise also known as speckle noise models are central to the study of coherent imaging systems such as synthetic aperture radar and sonar and ultrasound and laser imaging these models introduce two additional layers of difficulties with respect to the standard gaussian additive noise scenario 1 the noise is multiplied by rather than added to the original image 2 the noise is not gaussian with rayleigh and gamma being commonly used densities these two features of multiplicative noise models preclude the direct application of most state of the art algorithms which are designed for solving unconstrained optimization problems where the objective has two terms a quadratic data term log likelihood reflecting the additive and gaussian nature of the noise plus a convex possibly nonsmooth regularizer e g a total variation or wavelet based regularizer prior in this paper we address these difficulties by 1 converting the multiplicative model into an additive one by taking logarithms as proposed by some other authors 2 using variable splitting to obtain an equivalent constrained problem and 3 dealing with this optimization problem using the augmented lagrangian framework a set of experiments shows that the proposed method which we name midal multiplicative image denoising by augmented lagrangian yields state of the art results both in terms of speed and denoising performance

split bregman iteration algorithm for total bounded variation regularization based image deblurring many existing algorithms taking the seminorm in bv for regularization have achieved great success in image processing however this paper considers the total bounded variation regularization based approach to perform image deblurring based on this novel model we introduce an extended split bregman iteration to obtain the optimum solution quickly we also provide the rigorous convergence analysis of the iterative algorithm here compared with the results of the rof method numerical simulations illustrate the more excellent reconstruction performance of the proposed algorithm

computational acceleration for mr image reconstruction in partially parallel imaging in this paper we present a fast numerical algorithm for solving total variation and l1 tvl1 based image reconstruction with application in partially parallel magnetic resonance imaging our algorithm uses variable splitting method to reduce computational cost moreover the barzilai borwein step size selection method is adopted in our algorithm for much faster convergence experimental results on clinical partially parallel imaging data demonstrate that the proposed algorithm requires much fewer iterations and or less computational cost than recently developed operator splitting and bregman operator splitting methods which can deal with a general sensing matrix in reconstruction framework to get similar or even better quality of reconstructed images

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time we introduce a new method for image smoothing based on a fourth order pde model the method is tested on a broad range of real medical magnetic resonance images both in space and time as well as on nonmedical synthesized test images our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail even at poor signal to noise ratio we have also compared our method with related pde models

shearlet based total variation diffusion for denoising we propose a shearlet formulation of the total variation tv method for denoising images shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization common approaches in combining wavelet like representations such as curvelets with tv or diffusion methods aim at reducing gibbs type artifacts after obtaining a nearly optimal estimate we show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain we also analyze the performance of a shearlet based diffusion method numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform furthermore the shearlet tv scheme requires far fewer iterations than similar competitors

constructing solutions of the mkdv equation abstract using commutation methods i e n 1 supersymmetry underlying miura s transformation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided

convergence of a fixed point iteration method for the osv model in image processing image denoising and texture extraction are important problems in which many new methods recently have been developed one of the most important models is the osv model s osher a sole l vese image decomposition and restoration using total variation minimization and the h 1 norm multiscale model simul a siam interdisciplinary j 1 3 2003 349 370 which is constructed by the total variation and h 1 norm this paper proves the existence of the minimizer of the functional from the osv model and analyzes the convergence of an iterative method for solving the problems our iteration method is constructed by a fixed point iteration on the fourth order partial differential equation from the computation of the associated euler lagrange equation and the limit of our iterations satisfies the minimizer of the functional from the osv model in numerical experiments we compare the numerical results of our works with those of the rof model l i rudin s osher e fatemi nonlinear total variation based noise removal algorithms phys d 60 1992 259 268

meromorphic n 2 wess zumino supersymmetric quantum mechanics the ordinary holomorphic n 2 wess zumino model in supersymmetric quantum mechanics is extended to the case where the superpotential v z is a meromorphic function on c the extended model is analyzed in a mathematically rigorous way self adjoint extensions and the essential self adjointness of the supercharges are discussed the supersymmetric hamiltonian defined by one of the self adjoint extensions of the supercharges has no fermionic zero energy states vanishing theorem it is proven that if v z has only one pole at z 0 in c then the supercharges are essentially self adjoint on c 0 r2 0 c4 the special case where v z z p p n c 0 is analyzed in detail to prove the following facts i the number of the bosonic zero energy ground state s is equal to p 1 ii the supercharges are not fredholm

a 3d boundary optimal control for the bidomain bath system modeling the thoracic shock therapy for cardiac defibrillation this work is dedicated to study the cardiac defibrillation problem by using an optimal thoracic electroshock treatment the problem is formulated as an optimal control problem in a 3d domain surrounded by the bath and including the heart the control corresponds to the thoracic electroshock and the model describing the electrical activity in the heart is the bidomain model the bidomain model is coupled with the quasi static maxwell s equation to consider the effect of an external bathing medium the existence and uniqueness of a weak solution for the direct problem is assessed as well as the existence of a weak solution for the adjoint problem the numerical discretization is realized using a finite element method for the spatial discretization and linearly implicit runge kutta methods for the temporal discretization of the partial differential equations the numerical results are demonstrated for the termination of re entry waves

inverse electrocardiographic source localization of ischemia an optimization framework and finite element solution with the goal of non invasively localizing cardiac ischemic disease using body surface potential recordings we attempted to reconstruct the transmembrane potential tmp throughout the myocardium with the bidomain heart model the task is an inverse source problem governed by partial differential equations pde our main contribution is solving the inverse problem within a pde constrained optimization framework that enables various physically based constraints in both equality and inequality forms we formulated the optimality conditions rigorously in the continuum before deriving finite element discretization thereby making the optimization independent of discretization choice such a formulation was derived for the l 2 norm tikhonov regularization and the total variation minimization the subsequent numerical optimization was fulfilled by a primal dual interior point method tailored to our problem s specific structure our simulations used realistic fiber included heart models consisting of up to 18 000 nodes much finer than any inverse models previously reported with synthetic ischemia data we localized ischemic regions with roughly a 10 false negative rate or a 20 false positive rate under conditions up to 5 input noise with ischemia data measured from animal experiments we reconstructed tmps with roughly 0 9 correlation with the ground truth while precisely estimating the tmp in general cases remains an open problem our study shows the feasibility of reconstructing tmp during the st interval as a means of ischemia localization

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

a monolithic conservative level set method with built in redistancing abstract we introduce a new level set method for representing evolving interfaces in the case of divergence free velocity fields the new method satisfies a conservation principle conservation is important for many applications such as modeling two phase incompressible flow in the present implementation the conserved quantity is defined as the integral of a smoothed characteristic function the new approach embeds level sets into a volume of fluid formulation the evolution of an approximate signed distance function is governed by a conservation law for its smoothed sign the non linear level set transport equation is regularized by adding a flux correction term that assures a non singular jacobian and penalizes deviations from a distance function the result is a locally conservative level set method with built in elliptic redistancing the continuous model is monolithic in the sense that the level set transport model the volume of fluid law of mass conservation and the minimization problem that preserves the approximate distance function property are incorporated into a single equation there is no need for any extra stabilization artificial compression flux limiting redistancing mass correction and other numerical fixes which are commonly used in level set or volume of fluid methods in addition there is just one free parameter that controls the strength of regularization and penalization in the model the accuracy and conservation properties of the monolithic finite element level set method are illustrated by the results of numerical studies for passive advection of free interfaces

a lattice boltzmann method for image denoising in this paper we construct a lattice boltzmann scheme to simulate the well known total variation based restoration model that is rof model the advantages of the lattice boltzmann method include the fast computational speed and the easily implemented fully parallel algorithm a conservative property of the lb method is discussed the macroscopic pde associated with the lb algorithm is derived which is just the rof model moreover the linearized stability of the method is analyzed the numerical computations demonstrate that the lb algorithm is efficient and robust even though the quality of the restored images is slightly lower than those by using the rof model the restored images of the lb method are satisfactory furthermore computational speed of the lb method is much faster than rof model in general cpu time of the lb method for restored images is about one tenth of rof model

on two questions about quaternion matrices abstract this paper answers two questions proposed in fuzhen zhang linear algebra appl 251 1997 21 57 showing that there exists a 2 2 quaternion matrix with only two non similar left eigenvalues that is not diagonalizable and giving some necessary and sufficient conditions for a b b a 0

a class of triangular splitting methods for saddle point problems in this paper we study a class of efficient iterative algorithms for the large sparse nonsingular saddle point problems based on the upper and lower triangular ult splitting of the coefficient matrix we call these algorithms ult methods first the ult algorithm is established and the characteristic of eigenvalues of the iteration matrix of these new methods is analyzed then we give the sufficient and necessary conditions for the convergence of these ult methods moreover the optimal iteration parameters and the corresponding convergence factors for some special cases of the ult methods are presented numerical experiments on a few model problems are presented to support the theoretical results and examine the numerical effectiveness of these new methods

l2 index and the selberg trace formula abstract a method is developed for computing the l 2 index of a locally symmetric elliptic differential operator d acting on a locally symmetric manifold m g k with g semisimple of real rank one and of finite co volume based on applying the selberg trace formula to the difference of the two heat kernels associated to d the applications include an extension of the osborne warner multiplicity formula to certain non integrable discrete series derived from the l 2 spinor formula and showing the existence in some cases of non invariant l 2 cohomology classes in the middle dimension via the l 2 signature formula

an algorithm for image removals and decompositions without inverse matrices partial differential equation pde based methods in image processing have been actively studied in the past few years one of the effective methods is the method based on a total variation introduced by rudin oshera and fatemi rof l i rudin s osher e fatemi nonlinear total variation based noise removal algorithms physica d 60 1992 259 268 this method is a well known edge preserving model and an useful tool for image removals and decompositions unfortunately this method has a nonlinear term in the equation which may yield an inaccurate numerical solution to overcome the nonlinearity a fixed point iteration method has been widely used the nonlinear system based on the total variation is induced from the rof model and the fixed point iteration method to solve the rof model is introduced by dobson and vogel d c dobson c r vogel convergence of an iterative method for total variation denoising siam j numer anal 34 5 1997 1779 1791 however some methods had to compute inverse matrices which led to roundoff error to address this problem we developed an efficient method for solving the rof model we make a sequence like richardson s method by using a fixed point iteration to evade the nonlinear equation this approach does not require the computation of inverse matrices the main idea is to make a direction vector for reducing the error at each iteration step in other words we make the next iteration to reduce the error from the computed error and the direction vector we describe that our method works well in theory in numerical experiments we show the results of the proposed method and compare them with the results by d dobson and c vogel and then we confirm the superiority of our method

generalized supersymmetric quantum mechanics on riemann surfaces with meromorphic superpotentials the structure of generalized supersymmetry with mutually commuting involutions for the meromorphic supersymmetric quantum mechanics on the compact riemann surface is introduced for this purpose a riemann surface is considered as a self conjugate complex manifold on this basis the witten index for the new involution is calculated

salt and pepper noise removal by median type noise detectors and detail preserving regularization this paper proposes a two phase scheme for removing salt and pepper impulse noise in the first phase an adaptive median filter is used to identify pixels which are likely to be contaminated by noise noise candidates in the second phase the image is restored using a specialized regularization method that applies only to those selected noise candidates in terms of edge preservation and noise suppression our restored images show a significant improvement compared to those restored by using just nonlinear filters or regularization methods only our scheme can remove salt and pepper noise with a noise level as high as 90

a mixed formulation of the bingham fluid flow problem analysis and numerical solution in this paper we introduce a mixed formulation of the bingham fluid flow problem we consider both the original and a regularized version of the problem where a parameter e is introduced forcing the entire domain to be formally a fluid region in general common solvers for the regularized problem experience a performance degradation when the parameter e gets smaller the method studied here introduces an auxiliary tensor variable and shows enhanced numerical properties for small values of e a good performance is also observed for the non regularized case the well posedness for the regularized problem and the equivalence at the continuous level between the original primitive variables and the mixed formulation are demonstrated we analyze properties of linearized problems that are relevant for the convergence of numerical solvers a finite element method for the mixed formulation is discussed numerical results confirm the predicted better performances of the mixed formulation when compared to the primitive variables formulation a comparison to a non regularized solver based on the augmented duvaut lions glowinski formulation of the problem is carried out as well

on the local and semilocal convergence of a parameterized multi step newton method abstract this paper is devoted to a family of newton like methods with frozen derivatives used to approximate a locally unique solution of an equation we perform a convergence study and an analysis of the efficiency this analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation the method can be applied to many type of problems including the discretization of ordinary differential equations integral equations integro differential equations or partial differential equations moreover multi step iterative methods are computationally attractive

quaternionic eigenvalue problem we discuss the right eigenvalue equation for h c and r linear quaternionic operators the possibility to introduce an isomorphism between these operators and real complex matrices allows us to translate the quaternionic problem into an equivalent real or complex counterpart interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics

potential scattering in constant magnetic field spectral asymptotics and levinson formula the scattering problem related to the schrodinger operator with an external constant homogeneous magnetic field is considered the behaviour of the corresponding s matrix and resolvent operator near the landau thresholds is studied the large energy asymptotics of the resolvent operator are evaluated a levinson type formula is obtained it relates the number of bound states to the determinant of the scattering matrix in the scattering threshold

graph laplacian regularization for image denoising analysis in the continuous domain inverse imaging problems are inherently underdetermined and hence it is important to employ appropriate image priors for regularization one recent popular prior the graph laplacian regularizer assumes that the target pixel patch is smooth with respect to an appropriately chosen graph however the mechanisms and implications of imposing the graph laplacian regularizer on the original inverse problem are not well understood to address this problem in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of riemannian manifolds and perform analysis in the continuous domain providing insights into several fundamental aspects of graph laplacian regularization for image denoising specifically we first show the convergence of the graph laplacian regularizer to a continuous domain functional integrating a norm measured in a locally adaptive metric space focusing on image denoising we derive an optimal metric space assuming non local self similarity of pixel patches leading to an optimal graph laplacian regularizer for denoising in the discrete domain we then interpret graph laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations e g its tendency to promote piecewise smooth signals under certain settings to verify our analysis an iterative image denoising algorithm is developed experimental results show that our algorithm performs competitively with state of the art denoising methods such as bm3d for natural images and outperforms them significantly for piecewise smooth images

an iterative lagrange multiplier method for constrained total variation based image denoising various effective algorithms have been proposed in the past two decades for nonlinear pdes arising from the unconstrained total variation based image denoising problem regularizing the total variation constrained minimization model such algorithms can be used to obtain a satisfactory result as long as a suitable regularization parameter balancing the trade off between a good fit to the data and a regular solution is given however it is generally difficult to obtain a suitable regularization parameter without which restored images can be unsatisfactory if it is too large then the resulting solution is still contaminated by noise while if too small the solution is a poor approximation of the true noise free solution to provide an automatic method for the regularization parameter when the noise level is known a priori one way is to address the coupled karush kuhn tucker kkt systems from the constrained total variation optimization problem so far much less work has been done on this problem this

relative index theory abstract we develop the framework for the heat equation method in the relative index theory we study pairs of dirac operators on complete manifolds and give an analytic interpretation of the difference of the integrals over their local index densities this yields a generalization of the relative index theorem of gromov and lawson under some assumptions on the curvature we show that supersymmetric scattering theories of borisov muller and schrader arise naturally the scattering index is related to the relative topological index

quaternions and matrices of quaternions abstract we give a brief survey on quaternions and matrices of quaternions present new proofs for certain known results and discuss the quaternionic analogues of complex matrices the methods of converting a quaternion matrix to a pair of complex matrices and homotopy theory are emphasized

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

planar crack identification in 3d linear elasticity by the reciprocity gap method abstract we study the reciprocity gap method andrieux et al 1999 for the identification of planar cracks in the framework of three dimensional linear elasticity in order to achieve better accuracy on thick domains we propose to use polynomial test functions instead of fourier series we also propose to improve the solution by various regularization techniques that are tested and compared numerical assessments are provided in 2d and 3d

regularization operators for natural images based on nonlinear perception models image restoration requires some a priori knowledge of the solution some of the conventional regularization techniques are based on the estimation of the power spectrum density simple statistical models for spectral estimation just take into account second order relations between the pixels of the image however natural images exhibit additional features such as particular relationships between local fourier or wavelet transform coefficients biological visual systems have evolved to capture these relations we propose the use of this biological behavior to build regularization operators as an alternative to simple statistical models the results suggest that if the penalty operator takes these additional features in natural images into account it will be more robust and the choice of the regularization parameter is less critical

multimodal image registration using a variational approach this paper presents an approach to obtain a deformation which matches two images acquired from different medical imaging modalities this problem arises in the investigation of human brains two distance functionals for the images are proposed with different pros and cons these functionals are to be minimized we add a smoothing term to the minimization problem which retains certain desired elastic features in the solution at each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration furthermore we use a multiresolution minimization approach to obtain a suitable initial guess finally we present some experimental results for registration problems of synthetic images and for a real computer tomography ct magnetic resonance imaging mri registration

the index formula and the spectral shift function for relatively trace class perturbations we compute the fredholm index index da of the operator da d dt a on l2 r h associated with the operator path a t t where af t a t f t for a e t r and appropriate f l2 r h via the spectral shift function a a associated with the pair a a of asymptotic operators a a on the separable complex hilbert space h in the case when a t is generally an unbounded relatively trace class perturbation of the unbounded self adjoint operator a we derive a formula an extension of a formula due to pushnitski relating the spectral shift function a a for the pair a a and the corresponding spectral shift function h2 h1 for the pair of operators h2 h1 dada da da in this relative trace class context h2 h1 1 1 2 1 2 a a d 2 1 2for a e 0 this formula is then used to identify the fredholm index of da with 0 a a in addition we prove that index da coincides with the spectral flow spflow a t t of the family a t t r and also relate it to the fredholm perturbation determinant for the pair a a index da spflow a t t 0 a a 1lime 0im ln deth a iei a iei 1 0 h2 h1 with the choice of the branch of ln deth on c such that limim z ln deth a zi a zi 1 0 we also provide some applications in the context of supersymmetric quantum mechanics to zeta function and heat kernel regularized spectral asymmetries and the eta invariant

geometry of total variation regularized l p model in this paper the geometry and scale selection properties of the total variation tv regularized l p model are rigorously analyzed some intrinsic features different from the tv l 1 model are derived and demonstrated numerical algorithms based on recent developed augmented lagrangian methods are implemented and numerical results consistent with the theoretical results are provided

le saut en zero de la fonction de decalage spectral abstract we give a formula for the jump at zero of the spectral shift function associated with schrodinger operator on manifolds with conical ends we show that according to its decay a zero energy resonant state has a non integer contribution

n 2 supersymmetric quantum mechanics on riemann surfaces with meromorphic superpotentials we constructn 2 supersymmetric quantum hamiltonians with meromorphic superpotentials on compact riemann surfaces and investigate the topological properties of these hamiltonians l2 cohomology groups for supercharge a deformed bar partial operator are considered and the witten index for the supersymmetric hamiltonian with meromorphic superpotential is calculated in terms of euler characteristic of the riemann surface and the degree of a divisor of poles for the differential of the superpotential

an mathcal o 1 k convergence rate for the variable stepsize bregman operator splitting algorithm an earlier paper proved the convergence of a variable stepsize bregman operator splitting algorithm bosvs for minimizing phi bu h u where h and phi are convex functions and phi is possibly nonsmooth the algorithm was shown to be relatively efficient when applied to partially parallel magnetic resonance image reconstruction problems in this paper the convergence rate of bosvs is analyzed when h u au f 2 where a is a matrix it is shown that for an ergodic approximation bf u k obtained by averaging k bosvs iterates the error in the objective value phi b bf u k h bf u k is cal o 1 k when the optimization problem has a unique solution u we obtain the estimate bf u k u cal o 1 sqrt k the theoretical analysis is compared to observed convergence rates for partially parallel magnetic resonance image reconstruction problems where a is a large dense ill conditioned matrix

stability in yang mills theories at a solution of the yang mills equations ons4 or the yang mills higgs equation on 3 the hessian of the action functional defines a natural second order elliptic operator the number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge the proof of this assertion requires a relative index theorem for dirac type operators on n n 3

gersgorin type theorems for quaternionic matrices this paper aims to set an account of the left eigenvalue problems for real quaternionic finite matrices in particular we will present the gersgorin type theorems for the left and right eigenvalues of square quaternionic matrices we shall conclude the paper with examples showing and summarizing some differences between complex matrices and quaternionic matrices and right and left eigenvalues of quaternionic matrices

multichannel blind deconvolution of spatially misaligned images existing multichannel blind restoration techniques assume perfect spatial alignment of channels correct estimation of blur size and are prone to noise we developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral this stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise we observe that the exact knowledge of the blur size is not necessary and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process

an effective method for solving nonlinear equations and its application the linearized partial differential equation from the nonlinear partial differential equation which was proposed by rudin osher and fatemi l i rudin s osher and e fatemi nonlinear total variation based noise removal algorithms for solving image decomposition was introduced by chambolle a chambolle an algorithm for total variation minimization and applications and r acar and c r vogel r acar and c r vogel analysis of bounded variation penalty methods for ill posed problems in this paper we propose a method for solving the linearized partial differential equation and we show numerical results for denoising which demonstrate a significant improvement over other previous works

explicit ringing removal in image deblurring in this paper we present a simple yet effective image deblurring method to produce ringing free deblurred images our work is inspired by the observation that large scale deblurring ringing artifacts are measurable through a multi resolution pyramid of low pass filtering of the blurred deblurred image pair we propose to model such a quantification as a convex cost function and minimize it directly in the deblurring process in order to reduce ringing regardless of its cause an efficient primal dual algorithm is proposed as a solution to this optimization problem since the regularization is more biased toward ringing patterns the details of the reconstructed image are prevented from over smoothing an inevitable source of ringing is sensor saturation which can be detected costlessly contrary to most other sources of ringing however dealing with the saturation effect in deblurring introduces a non linear operator in optimization problem in this paper we also introduce a linear approximation as a solution to handling saturation in the proposed deblurring method as a result of these steps we significantly enhance the quality of the deblurred images experimental results and quantitative evaluations demonstrate that the proposed method performs favorably against state of the art image deblurring methods

on a class of ill posed minimization problems in image processing in this paper we show that minimization problems involving sublinear regularizing terms are ill posed in general although numerical experiments in image processing give very good results the energies studied here are inspired by image restoration and image decomposition rewriting the nonconvex sublinear regularizing terms as weighted total variations we give a new approach to perform minimization via the well known chambolle s algorithm the approach developed here provides an alternative to the well known half quadratic minimization one

image restoration based on the minimized surface regularization abstract we propose an image restoration model based on the minimized surface regularization the proposed model closely relates to the classical smoothing rof model rudin et al 1992 we deduce two different conjugation forms via coupling the gradient operator with the smoothing parameter or not and then provide the existence of the minimizer in the continuous setting in order to efficiently solving the proposed model we employ the primal dual method by reformulating the proposed model as a min max problem relying on the convex conjugation the convergence of the algorithm is provided as well numerical implementations mainly emphasize the effectiveness of the proposed method by comparing it to other two well known methods in terms of the cpu time and restoration quality

shapes from pixels continuous domain visual signals are usually captured as discrete digital images this operation is not invertible in general in the sense that the continuous domain signal cannot be exactly reconstructed based on the discrete image unless it satisfies certain constraints e g bandlimitedness in this paper we study the problem of recovering shape images with smooth boundaries from a set of samples thus the reconstructed image is constrained to regenerate the same samples consistency as well as forming a shape bilevel image we initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes next we relax the non convex shape constraint to transform the problem into minimizing the total variation over consistent non negative valued images we also introduce a requirement called reducibility that guarantees equivalence between the two problems we illustrate that the reducibility property effectively sets a requirement on the minimum sampling density we also evaluate the performance of the relaxed alternative in various numerical experiments

split bregman method for the modified lot model in image denoising in this paper a split bregman iteration is proposed for the modified lot model in image denoising we first use the split bregman method to solve the rof model which can be seen as an approximate form of the first step of the original lot model then we use a modified split bregman method to fit the second step of the lot model and give the convergence of the proposed split bregman method several numerical examples are arranged to show the effectiveness of the proposed method

wavelet frame based algorithm for 3d reconstruction in electron microscopy in electron microscopy three dimensional 3d reconstruction is one key component in many computerized techniques for solving 3d structures of large protein assemblies using electron microscopy images of particles main challenges in 3d reconstruction include very low signal to noise ratio and very large scale of data sets involved in the computation motivated by the recent advances of sparsity based regularization in the wavelet frame domain for solving various linear inverse problems in imaging science we proposed a wavelet tight frame based 3d reconstruction approach that exploits the sparsity of the 3d density map in a wavelet tight frame system the proposed approach not only runs efficiently in terms of cpu time but also requires a much lower memory footprint than existing framelet based regularization methods the convergence of the proposed iterative scheme and the functional it minimizes is also examined together with the connection to existing wavelet frame based regularizations the numeric

a multigrid method for a fourth order diffusion equation with application to image processing in this paper we are concerned with the efficient solution of the elliptic system alpha l nobreak i u nobreak f where l is the biharmonic operator supplemented by higher order boundary conditions this is a core task in image processing arising from the minimization of rotation invariant energy functionals for the purpose of numerical solution we approximate the partial differential equation by finite differences in order to obtain efficient and robust solution methods we discuss how the system can be treated efficiently by multigrid methods finally experimental results are reported that demonstrate the effectiveness of the multigrid approach

area and length preserving geometric invariant scale spaces in this paper area preserving multi scale representations of planar curves are described this allows smoothing without shrinkage at the same time preserving all the scale space properties the representations are obtained deforming the curve via geometric heat flows while simultaneously magnifying the plane by a homethety which keeps the enclosed area constant when the euclidean geometric heat flow is used the resulting representation is euclidean invariant and similarly it is affine invariant when the affine one is used the flows are geometrically intrinsic to the curve and exactly satisfy all the basic requirements of scale space representations in the case of the euclidean heat flow it is completely local as well the same approach is used to define length preserving geometric flows a similarity scale invariant geometric heat flow is studied as well in this work

remarks on the equivalence between the shape invariance condition and the factorisation condition it is shown that the shape invariance condition for supersymmetric potentials and the factorisation condition for sturm liouville eigenvalue problems are equivalent the roots of this self consistency condition in supersymmetric quantum mechanics and the factorisation method are found in the theory of riccati equations

a primal dual active set method for non negativity constrained total variation deblurring problems this paper studies image deblurring problems using a total variation based model with a non negativity constraint the addition of the non negativity constraint improves the quality of the solutions but makes the solution process a difficult one the contribution of our work is a fast and robust numerical algorithm to solve the non negatively constrained problem to overcome the nondifferentiability of the total variation norm we formulate the constrained deblurring problem as a primal dual program which is a variant of the formulation proposed by chan golub and mulet for unconstrained problems here dual refers to a combination of the lagrangian and fenchel duals to solve the constrained primal dual program we use a semi smooth newton s method we exploit the relationship between the semi smooth newton s method and the primal dual active set method to achieve considerable simplification of the computations the main advantages of our proposed scheme are no parameters need significant adjustment a standard inverse preconditioner works very well quadratic rate of local convergence theoretical and numerical numerical evidence of global convergence and high accuracy of solving the optimality system the scheme shows robustness of performance over a wide range of parameters a comprehensive set of numerical comparisons are provided against other methods to solve the same problem which show the speed and accuracy advantages of our scheme