2d finite rate of innovation reconstruction method for step edge and polygon signals in the presence of noise the finite rate of innovation fri principle is developed for sampling a class of non bandlimited signals that have a finite number of degrees of freedom per unit of time i e signals with fri this sampling scheme is later extended to three classes of sampling kernels with compact support and applied to the step edge reconstruction problem by treating the image row by row in this paper we regard step edges as 2d fri signals and reconstruct them block by block the step edge parameters are obtained from the 2d moments of a given image block experimentally our technique can reconstruct the edge more precisely and track the cramer rao bounds crbs closely with a signal to noise ratio snr larger than 4 db on synthetic step edge images experiments on real images show that our proposed method can reconstruct the step edges under practical conditions i e in the presence of various types of noise and using a real sampling kernel the results on locating the corners of data matrix barcodes using our method also outperform some state of the art barcode decoders

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

sampling moments and reconstructing signals of finite rate of innovation shannon meets strang fix consider the problem of sampling signals which are not bandlimited but still have a finite number of degrees of freedom per unit of time such as for example nonuniform splines or piecewise polynomials and call the number of degrees of freedom per unit of time the rate of innovation classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited recently it was shown that by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation it is possible to reconstruct such signals uniquely these sampling schemes however use kernels with infinite support and this leads to complex and potentially unstable reconstruction algorithms in this paper we show that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm the class of kernels that we can use is very rich and includes functions satisfying strang fix conditions exponential splines and functions with rational fourier transform this last class of kernels is quite general and includes for instance any linear electric circuit we thus show with an example how to estimate a signal of finite rate of innovation at the output of an rc circuit the case of noisy measurements is also analyzed and we present a novel algorithm that reduces the effect of noise by oversampling

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

wedgelets nearly minimax estimation of edges we study a simple horizon model for the problem of recovering an image from noisy data in this model the image has an edge with fi holder regularity adopting the viewpoint of computational harmonic analysis we develop an overcomplete collection of atoms called wedgelets dyadically organized indicator functions with a variety of locations scales and orientations the wedgelet representation provides nearly optimal representations of objects in the horizon model as measured by minimax description length we show how to rapidly compute a wedgelet approximation to noisy data by flnding a special edgelet decorated recursive partition which minimizes a complexity penalized sum of squares this estimate using su cient sub pixel resolution achieves nearly the minimax mean squared error in the horizon model in fact the method is adaptive in the sense that it achieves nearly the minimax risk for any value of the unknown degree of regularity of the horizon 1 fi 2 wedgelet analysis and de noising may be used successfully outside the horizon model we study images modelled as indicators of star shaped sets with smooth bound aries and show that complexity penalized wedgelet partitioning achieves nearly the minimax risk in that setting also

time discretized variational formulation of non smooth frictional contact the present work extends the non smooth contact class of algorithms introduced by kane et al to the case of friction the formulation specifically addresses contact geometries e g involving multiple collisions between tightly packed non smooth bodies for which neither normals nor gap functions can be properly defined a key aspect of the approach is that the incremental displacements follow from a minimum principle the objective function comprises terms which account for inertia strain energy contact friction and external forcing the euler lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact in addition to its value as a basis for formulating numerical algorithms the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non uniqueness we present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms as well as the ability of the approach to account for stick and slip conditions

biorthogonal bases with local support and approximation properties we construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree p in one dimension in contrast to earlier approaches these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree p 1 working with gaus lobatto nodes we find an interesting connection between biorthogonality and quadrature formulas one important application of these newly constructed biorthogonal basis functions are two dimensional mortar finite elements the weak continuity condition of the constrained mortar space is realized in terms of our new dual bases as a result local static condensation can be applied which is very attractive from the numerical point of view numerical results are presented for cubic mortar finite elements

a stable energy conserving approach for frictional contact problems based on quadrature formulas a common approach for the numerical simulation of non linear multi body contact problems is the use of lagrange multipliers to model the contact conditions the stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes by this the spurious algorithmic oscillations in the multiplier do not occur any more which facilitates the application of the primal dual active set strategy to dynamical contact problems the new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost in addition the conservation properties of the underlying algorithm are transferred to the modified mass version different numerical examples for frictional two body contact problems illustrate the improvement in the results for the contact stresses copyright 2007 john wiley sons ltd

automatic integration of euler lagrange equations with constraints abstract numerical difficulties in the integration of euler lagrange and similar equations are discussed a technique for reducing their index from three to two is introduced and it is shown that variable order variable step bdf methods converge for these index two problems the practical application of this reduction in a numerical setting is examined

hybrid mixed discretization of elasto dynamic contact problems using consistent singular mass matrices summary an alternative spatial semi discretization of dynamic contact based on a modified hamilton s principle is proposed the modified hamilton s principle uses displac ement velocity and momentum as variables which allows their independent spatial discretization al ong with a local static condensation for velocity and momentum it leads to an approach with a hybrid mixed consistent mass matrix hmcmm an attractive feature of such a formulation is the possibility to construc t hybrid singular mass matrices hsmm with zero components at those nodes where contact is collocated this improves numerical stability of the semidiscrete problem the differential index of the underlying differential algebraic system is reduced from 3 to 1 and spurious oscillations in the contact pressure whi ch are commonly reported for formulations with lagrange multipliers are significantly reduced resu lts of numerical experiments for truss and timoshenko beam elements are discussed in addition the properties of the novel discretization scheme for an unconstrained dynamic problem are assessed by a dispersion analysis copyright c 2010 john wiley sons ltd received

analytic gradient for the moment of fluid method in axisymmetric and on general polyhedrons in any dimension abstract the moment of fluid method mof is an interface reconstruction method similar to the volume of fluid method with piecewise linear interface reconstruction vof plic in the mof method the normal to the interface is found by minimizing the distance between the centroid of the polyhedron below the interface and a reference centroid under a volume constraint to solve this minimization problem the gradient of the objective function must be evaluated analytic formulas have been proposed by many authors to compute the gradient in 2d on general polygons with a polar parametrization and in 3d on convex polyhedrons with a spherical parametrization in this short note we propose a more general formula that covers non convex polyhedrons in any dimension and axisymmetric coordinates furthermore this formula does not depend on the parametrization of the normal to the interface we also provide some practical way to use the formula in a code

direct and sparse construction of consistent inverse mass matrices general variational formulation and application to selective mass scaling summary classical explicit finite element formulations rely on lumped mass matrices a diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector recently non diagonal mass matrices for explicit finite element analysis fea have received attention due to the selective mass scaling sms technique sms allows larger time step sizes without substantial loss of accuracy however an expensive solution for accelerations is required at each time step in the present study this problem is solved by directly constructing the inverse mass matrix first a consistent and sparse inverse mass matrix is built from the modified hamiltons principle with independent displacement and momentum variables usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix rmm secondly a variational mass scaling technique is applied to the rmm it is based on the penalized hamiltons principle with an additional velocity variable and a free parameter using element wise bases for velocity and a local elimination yields variationally scaled rmm thirdly examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed copyright 2014 john wiley sons ltd

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

sampling schemes for multidimensional signals with finite rate of innovation in this paper we consider the problem of sampling signals that are nonband limited but have finite number of degrees of freedom per unit of time and call this number the rate of innovation streams of diracs and piecewise polynomials are the examples of such signals and thus are known as signals with finite rate of innovation fri we know that the classical band limited sine sampling theory does not enable perfect reconstruction of such signals from their samples since they are not band limited however the recent results on fri sampling suggest that it is possible to sample and perfectly reconstruct such nonband limited signals using a rich class of kernels in this paper we extend those results in higher dimensions using compactly supported kernels that reproduce polynomials satisfy strang fix conditions in fact the polynomial reproduction property of the kernel makes it possible to obtain the continuous moments of the signal from its samples using these moments and the annihilating filter method prony s method the innovative part of the signal and therefore the signal itself is perfectly reconstructed in particular we present local directional derivatives based and global complex moments based radon transform based sampling schemes for classes of fri signals such as sets of diracs bilevel and planar polygons quadrature domains e g circles ellipses and cardioids 2d polynomials with polygonal boundaries and n dimensional diracs and convex polytopes this work has been explored in a promising way in super resolution algorithms and distributed compression and might find its applications in photogrammetry computer graphics and machine vision

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

a time discretization scheme based on rothe s method for dynamical contact problems with friction abstract we present a new dissipative and contact stabilized time discretization scheme for dynamic frictional contact problems which is based on rothe s method especially for the case of coulomb friction the stability of the contact stresses is of crucial importance as they directly influence the frictional behavior in our approach we obtain an accurate description of the frictional stresses by a time discretized friction law allowing for an implicit treatment of the contact forces in the framework of the newmark scheme moreover undesirable oscillations at the contact interface are removed by employing an additional l 2 projection within the predictor step since the implicit treatment of the material behavior and the frictional response requires a quasi variational inequality to be solved in each time step we derive a non smooth multiscale method which allows for the efficient and robust solution of these highly non linear problems the convergence of this multiscale method is proven for the case of tresca friction for the case of coulomb friction an inexact fixed point iteration in the normal stresses is used we furthermore consider the case of two body contact here the information transfer at the contact interface is realized by means of mortar methods which provide a stable discretization of the relative displacements and the stresses at the contact boundary numerical results for the resulting fully discrete scheme in 3d are presented showing the high accuracy of the proposed method

the singular dynamic method for constrained second order hyperbolic equations application to dynamic contact problems the purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution the main application is dynamic contact problems the principle consists in the use of a singular mass matrix obtained by the mean of different discretizations of the solution and of its time derivative we prove that the semi discretized problem is well posed and energy conserving numerical experiments show that this is a crucial property to build stable numerical schemes

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

formulation and analysis of variational methods for time integration of linear elastodynamics abstract a general framework for variational formulations of linear elastodynamics is introduced variational formulations which originate from the principle of minimum potential energy the hellinger reissner principle and the hu washizu principle are considered they are characterized by the weak enforcement of the velocity displacement relation and of the initial displacement and velocity special cases are obtained by a priori enforcement of these conditions the time integration algorithms obtained discretizing in the space and time domains are studied with reference to accuracy stability and high frequency behaviour it is shown that some of these algorithms are very competitive with respect to classical finite difference methods the only drawback of variational methods seems to be the large size of the set of simultaneous equations which they generate effective solution procedures aiming at minimizing both the storage and the computational effort will be discussed in a separate paper

mixed interpretation and extensions of the equivalent mass matrix approach for elastodynamics with contact the present paper highlights the idea that the mass redistribution technique introduced by khenous and co workers 2006 17 18 for elastodynamics with impact can be reinterpreted as a mixed formulation in displacements and velocities in which a special compatibility condition is enforced such a formulation opens the route to various extensions and to variational integrators for impact problems potentially with variational time adaption those ideas are exemplified in the design of such integrators and various mass redistribution schemes

analysis of a space time discretization for dynamic elasticity problems based on mass free surface elements in this paper a new space time discretization is proposed which is based on a modified mass matrix the mass associated with a surface layer of elements is redistributed such that the inertia at the boundary is removed this approach is motivated by the observation that standard space time discretization schemes applied to dynamic contact problems yield spurious oscillations a widely used approach for the numerical simulation of these problems is based on lagrange multipliers which represent the contact stresses but the algebraic contact conditions in combination with the inertia volume terms often yield nonphysical results for the contact stresses and the stability of the algorithm can be lost our modified matrix is calculated via nonstandard quadrature formulas that require no extra computational effort in addition the conservation properties of the underlying algorithm are carried over to the modified method and the standard optimal a priori estimates are still satisfied numerical examples confirm the optimality of the approach and its stabilization effect applied to contact problems

wavelet theory demystified we revisit wavelet theory starting from the representation of a scaling function as the convolution of a b spline the regular part of it and a distribution the irregular or residual part this formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory including some new extensions for fractional orders n a self contained accessible fashion in particular we prove that the b spline component is entirely responsible for five key wavelet properties order of approximation reproduction of polynomials vanishing moments multiscale differentiation property and smoothness regularity of the basis functions we also investigate the interaction of wavelets with differential operators giving explicit time domain formulas for the fractional derivatives of the basis functions this allows us to specify a corresponding dual wavelet basis and helps us understand why the wavelet transform provides a stable characterization of the derivatives of a signal additional results include a new peeling theory of smoothness leading to the extended notion of wavelet differentiability in the l sub p sense and a sharper theorem stating that smoothness implies order