inverse formulation for geometrically exact stress resultant shells the inverse elastostatics method tackles a class of problems in which the deformed geometry and the applied load are known while the initial geometry and the stress in the deformed state are to be determined the method is imperative for many biomechanics applications particularly for image based stress analysis of living organs as the geometry captured by imaging often correspond to a pre deformed configuration 3 4 the computational aspects of inverse elastostatics i e the inverse formulations have been established for general elastic solids 1 2 3 in this work the inverse formulation of thin walled structures modeled as geometrically exact stress resultant shell 5 is presented the inverse formulation builds on a fundamental assumption of the elastic media that the stress depends on local relative motion of the body if either the reference or the deformed configuration is given the other can be found from the elastostatic equilibrium the shell formulation follows the same logic albeit involving shell kinematics and kinetics regardless of the additional assumptions introduced in the shell theory the fundamental premise underlying inverse analysis remains the same in the proposed formulation the inverse problem is solved by using the standard week form of shell balance equations which are yet parameterized and linearized in terms of the inverse motion to facilitate an effective numerical computation an invariant approached is used to formulate the constitutive equations a consistent reduction from 3d energy function is also introduced numerical examples involving both isotopic and anisotropic materials are provided for validating the formulation applications to several biological thin walled structures demonstrate the practical utility of the method

muntz galerkin methods and applications to mixed dirichlet neumann boundary value problems solutions for many problems of interest exhibit singular behaviors at domain corners or points where the boundary condition changes type for these types of problems direct spectral methods with the usual polynomial basis functions do not lead to a satisfactory convergence rate we develop in this paper a muntz galerkin method which is based on specially tuned muntz polynomials to deal with the singular behaviors of the underlying problems by exploring the relations between jacobi polynomials and muntz polynomials we develop efficient implementation procedures for the muntz galerkin method and provide optimal error estimates as an example of applications we consider the poisson equation with mixed dirichlet neumann boundary conditions whose solution behaves like o r 1 2 near the singular point and demonstrate that the muntz galerkin method greatly improves the rates of convergence of the usual spectral method

fuzzy selection filters for image restoration with neural learning a novel class of nonlinear filters called rank conditioned fuzzy selection rcfs filters is proposed to improve the filtering capability of rank conditioned rank selection filters in contrast to the selection filters the output of rcfs filters is obtained from the center gravity of a selected fuzzy set of the observation samples

the method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities babuska and oh have introduced a new approach called the method of auxiliary mapping mam to deal with elliptic boundary value problems with singularities they showed that for the laplace equation with corner singularities in the context of the p version of the finite element method mam yielded an exponential rate of convergence at virtually no extra cost in this paper those results are extended by showing the exponential convergence of mam for homogeneous laplace equations with boundary singularities and helmholtz equations with both corner and boundary singularities in addition a convergence result is developed for mam as applied to the h p version of the finite element method to clarify the power of mam a series of benchmark runs are made for three examples using our implementation mapfem comparisons are made with two h version finite element codes pltmg6 and fesop both of which use adaptive meshes the finite difference code ellpack and the recent singular element code isbfm the examples include the well known motz problem and both homogeneous and nonhomogeneous helmholtz equations

dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition abstract the dual formulation of the multiple reciprocity method mrm is employed to solve the acoustic mode of a cavity with a thin partition in order to avoid the spurious eigenvalues and non uniqueness of the solution in the case of zero thickness for the partition the hypersingular equation for mrm is considered to determine the invariant quantity of influence coefficients more efficiently an objectivity concept i e a frame of indifference is used by means of co ordinate transformation a generalized eigenvalue problem is derived and transformed into a standard eigenvalue problem through the state space formulation the spurious roots in mrm are examined and filtered out by using the hypersingular formulation three examples including finite thickness of the partition zero thickness and no partition are shown to check the validity of the proposed method also the analytical solution if available the fem results obtained by petyt and by abaqus and experimental measurements are compared with those of the proposed method and it is found that the agreement between them is very good

solution of nonlinear elliptic equations with boundary singularities by an integral equation method a boundary integral equation bie formulation is presented for the numerical solution of certain two dimensional nonlinear elliptic equations subject to nonlinear boundary conditions by applying the kirchoff transformation all nonlinear aspects are first transferred to the boundary of the solution domain then the accurate solution of problems in which there are boundary singularities is demonstrated by including the analytic nature of the singular solution in only those regions nearest the singularity because of this only a minor modification of the classical nonlinear bie is required and this results in a substantial improvement in the accuracy of the numerical results throughout the entire solution domain

application of the rbf meshless method to the solution of the radiative transport equation in this paper we introduce a radial basis function collocation method for computing solutions to the time dependent radiative transfer equation for these computations we use finite differences to discretize the time coordinate a discrete ordinate method to discretize the directional variable and an expansion in radial basis functions to approximate the spatial dependence of the solution the main advantages of the rbf method are that it does not require any mesh or grid achieves spectral accuracy in multi dimensions for arbitrary node layouts and it is extremely simple to implement

theoretical analysis of the max median filter median filtering has been used successfully for extracting features from noisy one dimensional signals however the extension of the one dimensional case to higher dimensions has not always yielded satisfactory results although noise suppression is obtained too much signal distortion is introduced and many features of interest are lost in this paper we introduce a multidimensional filter based on a combination of one dimensional median estimates it is shown that threshold decomposition holds for this class of filters making the deterministic analysis simpler invariant signals to the filter called root signals consist of very low resolution features making this filter much more attractive than conventional median filters

colored l l filters and their application in speech pitch detection this paper develops colored l l filters with tap bias and evaluates their performance in nonlinear system modeling and speech pitch detection l l filters are nonlinear weighted sum based filters that jointly exploit the temporal and rank orderings of observation samples the use of joint ordering allows l l filters to effectively process nonstationary signals with heavy tailed distributions utilizing this method of incorporating temporal and rank order information however requires n sup 2 parameters to describe a window size n filter this polynomial growth in the number of filter parameters limits the use of l l filters to applications that can be satisfactorily addressed with moderate sized windows it is shown here that performance increases in temporal rank order filters can often be achieved by expanding the window size a method for reducing the l l filter parameter space and thus relaxing the window size limitations is developed through the use of group theory based coloring or quantization of rank order information additionally the modeling ability of colored l l filters is improved through the simple inclusion of tap biases optimization procedures are developed for determining filter tap weights and biases as well as the rank order coloring it is shown that the window size rank order quantization tradeoff has advantages in many applications and that the inclusion of tap bias results in improved nonlinear system modeling finally a method for utilizing colored l l filters in the determination of glottal closure instants gcis for speech pitch period identification is developed results presented show that this method is a more accurate gci indicator than a commonly used wavelet approach and requires less processing time

a new class of detail preserving filters for image processing a new class of median type filters for image processing is proposed in the filters linear fir substructures are used in conjunction with the median operation the root signals and noise attenuation properties of the fir median hybrid filters are analyzed and compared to representative edge preserving filtering operations the concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the fir median hybrid filters in the multilevel filters there exists a tradeoff between noise attenuation and detail preservation the analysis and examples indicate that fir median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the k nearest neighbor averaging filters

a universal noise removal algorithm with an impulse detector we introduce a local image statistic for identifying noise pixels in images corrupted with impulse noise of random values the statistical values quantify how different in intensity the particular pixels are from their most similar neighbors we continue to demonstrate how this statistic may be incorporated into a filter designed to remove additive gaussian noise the result is a new filter capable of reducing both gaussian and impulse noises from noisy images effectively which performs remarkably well both in terms of quantitative measures of signal restoration and qualitative judgements of image quality our approach is extended to automatically remove any mix of gaussian and impulse noise

boundary knot method based on geodesic distance for anisotropic problems the radial basis function rbf collocation techniques for the numerical solution of partial differential equation problems are increasingly popular in recent years thanks to their striking merits being inherently meshless integration free and highly accurate however the rbf based methods have markedly been limited to handle isotropic problems due to the use of the isotropic euclidean distance this paper makes the first attempt to use the geodesic distance with the rbf based boundary knot method bkm to solve 2d and 3d anisotropic helmholtz type and convection diffusion problems this approach is mathematically simple and easy to implement and spectral convergence is numerically observed for problems under complex shaped boundary numerical results show that the bkm based on the geodesic distance can produce highly accurate solutions of anisotropic problems with a relatively small number of knots this study provides a promising strategy for the rbf based methods to effectively solve anisotropic problems

singularities in 2d anisotropic potential problems in multi material corners real variable approach an analysis of singular solutions at corners consisting of several different homogeneous wedges is presented for anisotropic potential theory in plane the concept of transfer matrix is applied for a singularity analysis first of single wedge problems and then of multi material corner problems explicit forms of eigenequations for evaluation of singularity exponent in the case of multi material corners are derived both for all combinations of homogeneous neumann and dirichlet boundary conditions at faces of open corners and for multi material planes with singular interior points perfect transmission conditions at wedge interfaces are considered in both cases it is proved that singularity exponents are real for open anisotropic multi material corners and a sufficient condition for the singularity exponents to be real for anisotropic multi material planes is deduced a case of a complex singularity exponent for an anisotropic multi material plane is reported apparently for the first time in potential theory simple expressions of eigenequations are presented first for open bi material corners and bi material planes and second for a crack terminating at a bi material interface as examples of application of the theory developed here analytical solutions of these eigenequations are presented for interface cracks with any combination of homogeneous boundary conditions along the interface crack faces and also for a special case of a crack perpendicular to a bi material interface a numerical study of variation of the singularity exponent as a function of inclination of a crack terminating at a bi material interface is presented

lum filters a class of rank order based filters for smoothing and sharpening a new class of rank order based filters called lower upper middle lum filters is introduced the output of these filters is determined by comparing a lower and an upper order statistic to the middle sample in the filter window these filters can be designed for smoothing and sharpening or outlier rejection the level of smoothing done by the filter can range from no smoothing to that of the median filter this flexibility allows the lum filter to be designed to best balance the tradeoffs between noise smoothing and signal detail preservation lum filters for enhancing edge gradients can be designed to be insensitive to low levels of additive noise and to remove impulsive noise furthermore lum filters do not cause overshoot or undershoot some statistical and deterministic properties of the lum filters are developed and a number of experimental results are presented to illustrate the performance these experiments include applications to 1d signals and to images

a new efficient approach for the removal of impulse noise from highly corrupted images a new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank ordered pixels in a sliding window as part of this framework several algorithms are examined each of which is applicable to fixed and random valued impulse noise models first a simple two state approach is described in which the algorithm switches between the output of an identity filter and a rank ordered mean rom filter the technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter for a small additional cost in memory this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and rom filter in which the weighting coefficients can be optimized using image training data extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40 impulse noise corruption moreover the method can effectively restore images corrupted with gaussian noise and mixed gaussian and impulse noise finally the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise

determining the finite elasticity reference state from a loaded configuration there are a number of situations where the deformed configuration of a body is known and it is necessary to determine the reference state previous methods developed to calculate the reference state involve the formulation of the finite elasticity equations in terms of the deformed configuration this paper demonstrates that the undeformed reference state can be accurately determined from a deformed configuration and the associated loading conditions by using conventional finite elasticity balance equations together with a solution procedure that treats the reference configuration as the unknowns the mathematical theory behind the solution method is described validated with an analytical solution and verified using experimental studies on gel phantoms the practical utility of this method is then demonstrated in the field of breast biomechanics copyright 2007 john wiley sons ltd

switching bilateral filter with a texture noise detector for universal noise removal in this paper we propose a switching bilateral filter sbf with a texture and noise detector for universal noise removal operation was carried out in two stages detection followed by filtering for detection we propose the sorted quadrant median vector sqmv scheme which includes important features such as edge or texture information this information is utilized to allocate a reference median from sqmv which is in turn compared with a current pixel to classify it as impulse noise gaussian noise or noise free the sbf removes both gaussian and impulse noise without adding another weighting function the range filter inside the bilateral filter switches between the gaussian and impulse modes depending upon the noise classification result simulation results show that our noise detector has a high noise detection rate as well as a high classification rate for salt and pepper uniform impulse noise and mixed impulse noise unlike most other impulse noise filters the proposed sbf achieves high peak signal to noise ratio and great image quality by efficiently removing both types of mixed noise salt and pepper with uniform noise and salt and pepper with gaussian noise in addition the computational complexity of sbf is significantly less than that of other mixed noise filters

finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity this paper introduces a finite element model for the inverse design of pieces with large displacements in the elastic range the problem consists in determining the initial shape of the piece such that it attains the designed shape under the effect of service loads the model is particularly focused on the design of parts with a markedly anisotropic behavior like laminated turbine blades although the formulation expresses equilibrium on the distorted configuration it uses a standard constitutive equations library that is expressed as usual for measures attached to the undistorted configuration in this way the modifications to a standard finite elements code are limited to the routines for the computation of the finite element internal forces and tangent matrix two examples are given the first one for validation purposes while the second is an application which has industrial interest for the design of turbine blades copyright 2007 john wiley sons ltd

xfem based crack detection scheme using a genetic algorithm a new computational tool is developed for the accurate detection and identification of cracks in structures to be used in conjunction with non destructive testing of specimens it is based on the solution of an inverse problem based on some measurements typically along part of the boundary of the structure that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies the goal is to estimate whether the structure contains a crack and if so to find the parameters location size orientation and shape of the crack that produces a response closest to the given measurement data in some chosen norm the inverse problem is solved using a genetic algorithm ga the ga optimization process requires the solution of a very large amount of forward problems the latter are solved via the extended finite element method xfem this enables one to employ the same regular mesh for all the forward problems performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane various computational aspects of the method are discussed including the a priori estimation of the ill posedness of the crack identification problem copyright 2007 john wiley sons ltd

representation of digital image by fuzzy neural network a multilayer feedforward fuzzy neural network fnn by which the predetermined fuzzy system can be realized is constructed to express a given two dimensional 2 d digital image it is shown that such a network is universal approximator the fnn approach provides us with the representation model of the 2 d discrete image in noise environment some given fuzzy numbers are employed to describe gray levels of a digital image and the deviation of corrupted image to its noise free one a class of fuzzy rules for removing impulse noise in degraded image are presented the corresponding fnn may work as a filter which improves the performances of median and rank conditioned rank selection filters especially such a filter may to a greatest extent maintain the fine structure of the image under the minimum mean absolute error criterion the membership functions of fuzzy numbers are adaptively adjusted and an optimal fnn for image representation is derived in noise environment simultaneously some real image examples are systemically analyzed to show that the fnn may result in higher quality global restoration

numerical solution of the cauchy problem for steady state heat transfer in two dimensional functionally graded materials the application of the method of fundamental solutions to the cauchy problem for steady state heat conduction in two dimensional functionally graded materials fgms is investigated the resulting system of linear algebraic equations is ill conditioned and therefore regularization is required in order to solve this system of equations in a stable manner this is achieved by employing the zeroth order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for both smooth and piecewise smooth geometries the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

scattering by a hybrid asymptotic finite element method abstract we describe a hybrid asymptotic finite element method with application to the solution of the helmholtz equation for large wavenumber thus this method is suitable to compute the acoustic field radiated or scattered by acoustically large objects the method is based on patching a short wavelength asymptotic expansion of the outer field to an fem interpolation of the inner field the patching takes place on an artificial boundary continuity of the field and its normal derivative across the artificial boundary is enforced weakly in a variational setting the variational principle is described as is an element like implementation strategy two example applications are included diffraction by a truncated wedge and radiation by a source on a wave bearing surface

permutation filters a class of nonlinear filters based on set permutations introduces and analyzes a new class of nonlinear filters that have their roots in permutation theory the authors show that a large body of nonlinear filters proposed to date constitute a proper subset of permutation filters spl pscr filters in particular rank order filters weighted rank order filters and stack filters embody limited permutation transformations of a set indeed by using the full potential of a permutation group transformation one can design very efficient estimation algorithms permutation groups inherently utilize both rank order and temporal order information thus the estimation of nonstationary processes in gaussian nongaussian environments with frequency selection can be effectively addressed an adaptive design algorithm that minimizes the mean absolute error criterion is described as well as a more flexible adaptive algorithm that attains the optimal permutation filter under a deterministic least normed error criterion simulation results are presented to illustrate the performance of permutation filters in comparison with other widely used filters

image denoising a nonlinear robust statistical approach nonlinear filtering techniques based on the theory of robust estimation are introduced some deterministic and asymptotic properties are derived the proposed denoising methods are optimal over the huber spl epsi contaminated normal neighborhood and are highly resistant to outliers experimental results showing a much improved performance of the proposed filters in the presence of gaussian and heavy tailed noise are analyzed and illustrated

an efficient wave based method for 2d acoustic problems containing corner singularities abstract the wave based method is an efficient alternative prediction technique based on a trefftz approach which as compared to element based methods can be applied in a wider frequency range at a reasonable cost this paper discusses the use of this method for the particular case of 2d acoustic problems where singularities are present in the corners of the acoustic domain the conventional set of expansion functions used to approximate the dynamic pressure field is extended with special purpose functions that incorporate the singular behaviour in the region around the singular corners this enrichment comes with a beneficial convergence rate while only a small increase of computational effort is incurred this is illustrated for various problem settings including different combinations of both homogeneous and non homogeneous boundary conditions and bounded as well as unbounded problems are considered

the boundary element solution of the cauchy steady heat conduction problem in an anisotropic medium in this paper the iterative algorithm proposed by kozlov et al for the cauchy problem for the laplace equation is extended in order to solve the cauchy steady state heat conduction problem in an anisotropic medium the iterative algorithm is numerically implemented using the boundary element method bem the convergence and the stability of the numerical method as well as various types of accuracy convergence and stopping criteria are investigated the numerical results obtained confirm that provided an appropriate stopping regularization criterion is imposed then the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularization criterion to cease the iterative process is proposed and the rate of convergence of the algorithm is improved by using various relaxation procedures between iterations a new concept of a variable relaxation factor is proposed analytical formulae for the coefficients of the matrices resulting from the direct application of the bem in an anisotropic medium are also presented copyright 2000 john wiley sons ltd

a simple neuro fuzzy impulse detector for efficient blur reduction of impulse noise removal operators for digital images a new impulse noise detector based on neuro fuzzy methods is presented the proposed detector comprises two identical neuro fuzzy subdetectors combined with a decision maker the internal parameters of the subdetectors are adaptively adjusted by training training of the subdetectors is accomplished by using a simple computer generated artificial image the detector can be combined with any impulse noise removal operator the operation of the detector is completely independent of the noise removal operator and it has no influence on the filtering behavior of the operator experimental results show that the proposed detector significantly reduces the distortion effects of any impulse noise removal operator even if the operator already has its own noise detector

the method of fundamental solutions for inverse boundary value problems associated with the steady state heat conduction in anisotropic media in this paper the method of fundamental solutions is applied to solve some inverse boundary value problems associated with the steady state heat conduction in an anisotropic medium since the resulting matrix equation is severely ill conditioned a regularized solution is obtained by employing the truncated singular value decomposition while the optimal regularization parameter is chosen according to the l curve criterion numerical results are presented for both two and three dimensional problems as well as exact and noisy data the convergence and stability of the proposed numerical scheme with respect to increasing the number of source points and the distance between the fictitious and physical boundaries and decreasing the amount of noise added into the input data respectively are analysed a sensitivity analysis with respect to the measure of the accessible part of the boundary and the distance between the internal measurement points and the boundary is also performed the numerical results obtained show that the proposed numerical method is accurate convergent stable and computationally efficient and hence it could be considered as a competitive alternative to existing methods for solving inverse problems in anisotropic steady state heat conduction copyright 2005 john wiley sons ltd

computational methods for inverse deformations in quasi incompressible finite elasticity this paper presents a formulation for incorporating quasi incompressibility in inverse design problems for finite elastostatics where deformed configurations and cauchy tractions are known in the recent paper of govindjee and mihalic 1996 comput methods appl mech engng 136 47 57 a method for solving this class of inverse problems was presented for compressible materials here we extend this work to the important case of nearly incompressible materials a displacement pressure mixed formulation is combined with a penalty method to enforce the quasi incompressible constraint without locking numerical examples are presented and compared to known solutions further examples present practical applications of this research to active problems in elastomeric component design 1998 john wiley sons ltd

fast adaptation and performance characteristics of fir wos hybrid filters fast adaptive algorithms are developed for training weighted order statistic wos filters and fir wos hybrid fwh filters under the mean absolute error mae criterion these algorithms are based on the threshold decomposition of real valued signals introduced in this paper with this method an n length wos filter can be implemented by thresholding the input signals at most n times independent of the accuracy used beside saving in computations the proposed algorithms can be applied to process arbitrary real valued signals directly performance characteristics of fwh filters in 1 d and 2 d signal restoration are investigated through computer simulations we show that both in restoration of signals containing edges and in the case of heavy tailed nongaussian noise considerable improvement in performance can be achieved with fwh filters over wos filters ll filters and adaptive linear filters two new fwh filter design strategies are found for removal of impulsive noise and for restoration of a square wave respectively

the use of neural network approximation models to speed up the optimisation process in electrical impedance tomography a reduced approximation model technique based on neural networks is developed in order to increase the rate of convergence of an evolution strategy es used for solving a non destructive evaluation problem the inverse problem investigated consists of identifying the geometry of discontinuities in a conductive material from cauchy data measurements taken on the boundary in this study we use neural network nn approximation models in order to increase the rate of convergence of the optimisation algorithm and to efficiently detect from a computational time point of view a subsurface cavity such as a circle the algorithm developed by combining evolution strategies and neural networks is found to be a robust fast and efficient method for detecting the size and location of subsurface cavities

the numerical solution of plane potential problems by improved boundary integral equation methods abstract a modified boundary integral bie method which facilitates accurate solution of laplacian boundary value problems is presented this method is designed specifically for treatment of problems in which singularities occur on the interface between two regions with different physical properties and is illustrated by application to two physical problems analytic expressions for the integrals arising in the piecew se linear and piecewise quadratic bie approximations are also presented these analytical expressions afford an appreciable reduction in computational time when compared with previously employed quadrature formulae

extended permutation filters and their application to edge enhancement extended permutation ep filters are defined and analyzed in particular we focus on extended permutation rank selection eprs filters these filters are constrained to output an order statistic from an extended observation vector this extended vector includes n observation samples and k statistics that are functions of the observation samples the rank permutations from selected samples in this extended observation vector are used as the basis for selecting an order statistic output we show that by including the sample mean in the extended observation vector the filters exhibit excellent edge enhancement properties we also show that several previously defined classes of rank order based edge enhancers cs lum and wmmr sharpeners can be formulated as subclasses of eprs filters these sharpening subclasses are in addition to the smoothing subclasses which include rank conditioned rank selection permutation stack and weighted order statistic filters thus this novel class of filters provides a broad framework within which many rank order based smoothers and edge enhancers can be unified edge enhancement properties are developed and an l sub n norm eprs filter optimization procedure is presented finally extensive computer simulation results are presented comparing the performance of eprs and other sharpening filters in edge enhancement applications

fuzzy rank lum filters the rank information of samples is widely utilized in nonlinear signal processing algorithms recently developed fuzzy transformation theory introduces the concept of fuzzy ranks which incorporates sample spread or sample diversity information into the sample ranking framework thus the fuzzy rank reflects a sample s rank as well as its similarity to the other sample namely joint rank order and spread and can be utilized to improve the performance of the conventional rank order based filters in this paper the well known lower upper middle lum filters are generalized utilizing the fuzzy ranks yielding the class of fuzzy rank lum f lum filters statistical and deterministic properties of the f lum filters are derived showing that the f lum smoothers have similar impulsive noise removal capability to the lum smoothers while preserving the image details better the f lum sharpeners are capable of enhancing strong edges while simultaneously preserving small variations the performance of the f lum filters are evaluated for the problems of image impulsive noise removal sharpening and edge detection preprocessing the experimental results show that the f lum smoothers can achieve a better tradeoff between noise removal and detail preservation than the lum smoothers the f lum sharpeners are capable of sharpening the image edges without amplifying the noise or distorting the fine details the joint smoothing and sharpening operation of the general f lum filters also showed superiority in edge detection preprocessing application in conclusion the simplicity and versatility of the f lum filters and their advantages over the conventional lum filters are desirable in many practical applications this also shows that utilizing fuzzy ranks in filter generalization is a promising methodology

computational method of inverse elastostatics for anisotropic hyperelastic solids the paper presents a computational method for predicting the initial geometry of a finitely deforming anisotropic elastic body from a given deformed state the method is imperative for a class of problem in stress analysis particularly in biomechanical applications while the basic idea has been established elsewhere comput methods appl mech eng 1996 136 47 57 int j numer meth engng 1998 43 821 838 the implementation in general anisotropic solids is not a trivial exercise but comes after a systematic development of eulerian representations of constitutive equations in this paper we discuss the general representation in the context of fibrous hyperelastic solids and provide explicit stress functions for some commonly used soft tissue models including the fung model and the holzapfel model a three field mixed formulation is introduced to enforce quasi incompressibility constraints the practical utility of this method is demonstrated using an example of aneurysm stress analysis copyright 2006 john wiley sons ltd

high stability awfm filter for signal restoration and its hardware design abstract an adaptive weighted fuzzy mean awfm filter with high stability is proposed for signal restoration in this paper awfm is an extension of weighted fuzzy mean wfm filter by linking a fuzzy detector and a dynamic selection procedure to wfm in order to overcome the drawback of wfm in fine signal preservation the fuzzy detector detects the amplitude of impulse noise which will be used as the argument of the dynamic selection procedure by referring to two fuzzy intervals and the wfm filtered outputs then the dynamic selection procedure applies four heuristic decision rules to determine the final filtering output awfm not only preserves the high performance of wfm on removing heavy additive impulse noise but also improves the performance of wfm on light additive impulse noise moreover it results in a high stability on the full range of noise occurrence probability compared with the other filters awfm exhibits better performance in the criteria of mean absolute error mae and mean square error mse on the subjective evaluation of those filtered images awfm also results in a higher quality of global restoration for the dedicated hardware implementation the kernel of awfm filter wfm is synthesized with the generic lr fuzzy cells which realize high speed fuzzy inference the hardware complexity is much simpler than the conventional median filter and simulation result exhibits that up to 6 6m pixels per second can be filtered by a wfm filter with small chip area

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

recycling krylov subspaces for efficient large scale electrical impedance tomography electrical impedance tomography eit captures images of internal features of a body electrodes are attached to the boundary of the body low intensity alternating currents are applied and the resulting electric potentials are measured then based on the measurements an estimation algorithm obtains the three dimensional internal admittivity distribution that corresponds to the image one of the main goals of medical eit is to achieve high resolution and an accurate result at low computational cost however when the finite element method fem is employed and the corresponding mesh is refined to increase resolution and accuracy the computational cost increases substantially especially in the estimation of absolute admittivity distributions therefore we consider in this work a fast iterative solver for the forward problem which was previously reported in the context of structural optimization we propose several improvements to this solver to increase its performance in the eit context the solver is based on the recycling of approximate invariant subspaces and it is applied to reduce the eit computation time for a constant and high resolution finite element mesh in addition we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver the numerical results show the effectiveness of our approach the proposed algorithm is faster than the preconditioned conjugate gradient cg algorithm the results also show that even on a standard pc without parallelization a high mesh resolution more than 150 000 degrees of freedom can be used for image estimation at a relatively low computational cost

fuzzy stack filters their definitions fundamental properties and application in image processing a new fuzzy filter called fuzzy stack filter fsf is proposed to extend the filtering capability of conventional stack filter sf which is based on the positive boolean function pbf as its window operator we fuzzify the onset and off set of a given pbf to obtain two types of fuzzy pbfs then we adopt the architecture of threshold decomposition to develop this new fuzzy filter with a fuzzy pbf as its window operator each fuzzy pbf is associated with a set of control parameters therefore the original pbf can be estimated from above and below by two fuzzy pbfs with appropriate control parameters furthermore we can apply the fuzzy modifiers to modify the fuzzy pbfs such that the pbfs can be completely estimated by the fuzzy pbfs hence the stack filter is a special case of fuzzy stack filter since some control parameters are added in this new filter the neural learning algorithms can be easily developed under the flexibility of the given control parameters we first propose the fuzzy m n rank order filter to test our proposed learning algorithm in this simple learning algorithm we can remove the noise corrupted images very well in contrast to the filtering behavior of rank order filters we believe that the results presented will lead to more fruitful research on more advanced and powerful learning algorithms dedicated to the appropriate applications

an integrated approach to shape optimization and mesh adaptivity based on material residual forces abstract this contribution is concerned with the coupling of finite element based shape optimization to methods of mesh adaptivity therein the nodal points of a finite element mesh serve as design variables in an optimization problem that aims to minimize a cost functional with respect to different constraints in order to avoid the occurrence of oscillating boundaries in the optimal design trials we generate the respective design updates through solving a series of fictitious boundary value problems on an updated lagrangian configuration the design update process is accompanied by adaptive mesh refinement to obtain more accurate results for the structural analysis and the design sensitivity analysis for the mesh adaptation process we consider r adaptive node relocation h adaptive mesh refinement and a combination of both approaches in each case the derivations rest upon the notion of material residual forces induced by finite element discretization and the coupling of shape optimization and mesh adaptivity is of intermittent type i e mesh adaptivity is invoked once a certain number of design updates has been generated we examine the benefits of the proposed method on the basis of some numerical examples in comparison to the same shape optimization method not involving adaptive mesh refinement where we evaluate the corresponding numerical costs the gain in accuracy and the effects on the optimal shapes being obtained

stack filters the median and other rank order operators possess two properties called the threshold decomposition and the stacking properties the first is a limited superposition property which leads to a new architecture for these filters the second is an ordering property which allows an efficient vlsi implementation of the threshold decomposition architecture motivated by the success of rank order filters in a wide variety of applications and by the ease with which they can now be implemented we consider in this paper a new class of filters called stack filters they share the threshold decomposition and stacking properties of rank order filters but are otherwise unconstrained they are shown to form a very large class of easily implemented nonlinear filters which includes the rank order operators as well as all compositions of morphological operators the convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters the results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals the output distribution for these filters is also found all the stack filters of window width 3 are determined along with their convergence properties among these filters are found two which we have named asymmetric median filters they share all the properties of median filters except that they remove impulses of one sign only that is one removes only positive going edges the other removes only negative going edges while the median filter removes impulses of both signs this investigation of the properties of stack filters thus produces several new useful and easily implemented filters

multiresolution permutation filter implementations based on acyclic connected graphs permutation filters are a broad class of nonlinear selection filters that utilize the complete spatial and rank order information of observation samples this use of joint spatial rank information has proven useful in numerous applications the application of permutation filters however is limited by the factorial growth in the number of spatial rank orderings although m permutation filters have been developed to address the growth in orderings their a priori uniform selection of samples is not appropriate in most cases permutation filter implementations based on acyclic connected graphs provide a more general approach that allows the level of ordering information utilized to automatically adjust to the problem at hand in addition to developing and analyzing graph implementations of permutation filters this paper presents a lne based optimization of the graph structure and filter operation simulation results illustrating the performance of the optimization technique and the advantages of the graph implementation are presented

state description for the root signal set of median filters median filtering is a simple digital technique for smoothing signals one main characteristic of the filter is that it maps the input signal space into a root signal space where signals invariant to median filters are called roots of the signal in this paper we develop the theory for the root signal set of median filters a tree structure for the root signal set is obtained for binary signals the number of roots r n for a signal of length n and window size filter 2s 1 is exactly represented by the difference equation r n r n 1 r n s a general solution is obtained in a z domain approach finally a method for faster one dimensional median filter operation is introduced

iterative truncated arithmetic mean filter and its properties the arithmetic mean and the order statistical median are two fundamental operations in signal and image processing they have their own merits and limitations in noise attenuation and image structure preservation this paper proposes an iterative algorithm that truncates the extreme values of samples in the filter window to a dynamic threshold the resulting nonlinear filter shows some merits of both the fundamental operations some dynamic truncation thresholds are proposed that guarantee the filter output starting from the mean to approach the median of the input samples as a by product this paper unveils some statistics of a finite data set as the upper bounds of the deviation of the median from the mean some stopping criteria are suggested to facilitate edge preservation and noise attenuation for both the long and short tailed distributions although the proposed iterative truncated mean itm algorithm is not aimed at the median it offers a way to estimate the median by simple arithmetic computing some properties of the itm filters are analyzed and experimentally verified on synthetic data and real images

rank conditioned rank selection filters for signal restoration a class of nonlinear filters called rank conditioned rank selection rcrs filters is developed and analyzed in this paper the rcrs filters are developed within the general framework of rank selection rs filters which are filters constrained to output an order statistic from the observation set many previously proposed rank order based filters can be formulated as rs filters the only difference between such filters is in the information used in deciding which order statistic to output the information used by rcrs filters is the ranks of selected input samples hence the name rank conditioned rank selection filters the number of input sample ranks used is referred to as the order of the rcrs filter the order can range from zero to the number of samples in the observation window giving the filters valuable flexibility low order filters can give good performance and are relatively simple to optimize and implement if improved performance is demanded the order can be increased but at the expense of filter simplicity in this paper many statistical and deterministic properties of the rcrs filters are presented a procedure for optimizing over the class of rcrs filters is also presented finally extensive computer simulation results that illustrate the performance of rcrs filters in comparison with other techniques in image restoration applications are presented

the fuzzy transformation and its applications in image processing the spatial and rank sr orderings of samples play a critical role in most signal processing algorithms the recently introduced fuzzy ordering theory generalizes traditional or crisp sr ordering concepts and defines the fuzzy spatial samples fuzzy order statistics fuzzy spatial indexes and fuzzy ranks here we introduce a more general concept the fuzzy transformation fzt which refers to the mapping of the crisp samples order statistics and sr ordering indexes to their fuzzy counterparts we establish the element invariant and order invariant properties of the fzt these properties indicate that fuzzy spatial samples and fuzzy order statistics constitute the same set and under commonly satisfied membership function conditions the sample rank order is preserved by the fzt the fzt also possesses clustering and symmetry properties which are established through analysis of the distributions and expectations of fuzzy samples and fuzzy order statistics these properties indicate that the fzt incorporates sample diversity into the ordering operation which can be utilized in the generalization of conventional filters here we establish the fuzzy weighted median fwm fuzzy lower upper middle flum and fuzzy identity filters as generalizations of their crisp counterparts the advantage of the fuzzy generalizations is illustrated in the applications of dct coded image deblocking impulse removal and noisy image sharpening

numerical analysis of singularities in two dimensions part 1 computation of eigenpairs a numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second order elliptic partial differential equations in two dimensions in the vicinity of singular points the singularities may be caused by re entrant corners and abrupt changes in boundary conditions or material properties such singularities are of great interest from the point of view of failure initiation the eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes for this reason failure theories directly or indirectly involve the eigenpairs and their amplitudes this paper addresses the problem of determining the eigenpairs numerically on the basis of the steklov formulation numerical results are presented for several cases importantly the method is applicable to three dimensional cases

detail preserving ranked order based filters for image processing the theoretical analysis of multistage median filters is developed it is shown that multistage median filters are a combination of max median and min median filters since multistage median filters belong to the class of two dimensional stack filters they have threshold decomposition attributes making their theoretical analysis simple statistical threshold decomposition is applied to derive the statistical characteristics of these filters and the results are used to evaluate the performance of these two types of multistage filters finally a quantitative and qualitative comparison of the multistage filters and of other efficient detail preserving filters is presented the comparisons are made using the mean squared error and the mean absolute error criteria

boundary infinite elements for the helmholtz equation in exterior domains a novel approach to the development of infinite element formulations for exterior problems of time harmonic acoustics is presented this approach is based on a functional which provides a general framework for domain based computation of exterior problems special cases include non reflecting boundary conditions such as the dtn method a prominent feature of this formulation is the lack of integration over the unbounded domain simplifying the task of discretization the original formulation is generalized to account for derivative discontinuities across infinite element boundaries typical of standard infinite element approximations continuity between finite elements and infinite elements is enforced weakly precluding compatibility requirements various infinite element approximations for two dimensional configurations with circular interfaces are presented implementation requirements are relatively simple numerical results demonstrate the good performance of this scheme 1998 john wiley sons ltd

efficient boundary element analysis of sharp notched plates the present paper further develops the boundary element singularity subtraction technique to provide an efficient and accurate method of analysing the general mixed mode deformation of two dimensional linear elastic structures containing sharp notches the elastic field around sharp notches is singular because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields these singularities are subtracted out of the original elastic field using the first term of the williams series expansion this regularization procedure introduces the stress intensity factors as additional unknowns in the problem hence extra conditions are required to obtain a solution extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the williams solution the procedure can take into account any number of terms of the series expansion the standard boundary element method is modified to handle additional unknowns and extra boundary conditions analysis of plates with symmetry boundary conditions is shown to be straightforward with the modified boundary element method in the case of non symmetrical plates the singular tip tractions are not primary boundary element unknowns the boundary element method must be further modified to introduce the boundary integral stress equations of an internal point approaching the notch tip as primary unknowns in the formulation the accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed mode problems new results are presented for the mixed mode analysis of a non symmetrical configuration of a single edge notched plate

stack filters and the mean absolute error criterion a method to determine the stack filter which minimizes the mean absolute error between its output and a desired signal given noisy observations of this desired signal is presented specifically an optimal window width b stack filter can be determined with a linear program with o b2 sup b variables this algorithm is efficient since the number of different inputs to a window width b filter is m sup b if the filter has m valued input and the number of stack filters grows faster than 2 raised to the 2 sup b 2 power it is shown that optimal stack filtering under the mean absolute error criterion is analogous to optimal linear filtering under the mean squared error criterion both linear filters and stack filters are defined by superposition properties both classes are implementable and both have tractable procedures for finding the optimal filter under an appropriate error criterion

on the computation of stress fields on polygonal domains with v notches the interior stress problem is solved numerically for a single edge notched specimen under uniaxial load the algorithm is based on a modification of a fredholm second kind integral equation with compact operators due to muskhelishvili several singular basis functions for each of the seven corners in the geometry enable high uniform resolution of the stress field with a modest number of discretization points as a consequence notch stress intensity factors can be computed directly from the solution this is an improvement over other procedures where the stress field is not resolved in the corners and where notch stress intensity factors are computed in a roundabout way via a path independent integral numerical examples illustrate the superior stability and economy of the new scheme less

inverse motion based form finding for quasi incompressible finite electroelasticity this work deals with inverse motion based form finding for electroelasticity the inverse motion problem is formulated for the electroelastic case and the resulting equations are implemented within a finite element framework a four field variational approach is adopted taking into consideration the typically incompressible behavior of the elastomer materials commonly used in electromechanical applications by means of numerical simulations the inverse motion based form finding makes it possible to design the referential configuration so that a given set of loads and boundary conditions results in a prespecified deformed configuration the computational finite element framework established in this work allows for such numerical simulations and testing and thereby the possibility to improve the design and accuracy in electroelastic applications such as grippers sensors and seals less

on referential and spatial formulations of inverse elastostatic analysis abstract there are two families of element formulation for inverse elastostatic analysis in the literature they employ different computation procedures at the element and material levels it has been suggested that one of them can preserve material library while the other requires redeveloping the material functions in this article we show that these two formulations are completely equivalent under certain conditions both can preserve the material library while under other conditions neither can we show that the modification of material functions is caused by the need of updating material symmetry in the inverse solution process several theoretical results were obtained while establishing the equivalence including an identity relating the inverse and forward tangent tensors for isotropic materials a comprehensive documentation of these two formulations is provided

an alternating iterative algorithm for the cauchy problem associated to the helmholtz equation in this paper the iterative algorithm proposed by kozlov et al comput maths math phys 31 1991 45 for obtaining approximate solutions to the ill posed cauchy problem for the helmholtz equation is analysed the technique is then numerically implemented using the boundary element method bem the numerical results confirm that the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularising criterion is also proposed

analysis of the properties of median and weighted median filters using threshold logic and stack filter representation the deterministic properties of weighted median wm filters are analyzed threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering the authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive boolean function because the cascade of wm filters can always be expressed as a single stack filter this allows expression of the cascade of wm filters as a single wm filter a direct application is the computation of the output distribution of a cascade of wm filters the same method is used to find a nonrecursive expansion of a recursive wm filter as applications of theoretical results several interesting deterministic and statistical properties of wm filters are derived

treatment of singularities in helmholtz type equations using the boundary element method abstract in many engineering problems boundaries with sharp corners or abrupt changes in the boundary conditions and or the material properties give rise to singularities of various types which tend to slow down the rate of convergence with respect to decreasing the mesh size of any standard numerical method used for obtaining the solution in this paper in order to develop a method which overcomes this difficulty the singular solutions of isotropic and anisotropic helmholtz type equations with homogeneous dirichlet and or neumann boundary conditions in the neighbourhood of a singular point are derived the standard boundary element method bem is then modified to take account of the form of singularity without an appreciable increase in the computational effort and at the same time keeping a uniform discretization three examples are carefully investigated and the numerical results presented show an excellent performance of the approach developed

singularities in anisotropic steady state heat conduction using a boundary element method in many heat conduction problems boundaries with sharp corners or abrupt changes in the boundary conditions give rise to singularities of various types which tend to slow down the rate of convergence with decreasing mesh size of any standard numerical method used for obtaining the solution in this paper it is shown how this difficulty may be overcome in the case of an anisotropic medium by a modified boundary element method the standard boundary element method is modified to take account of the form of the singularity without appreciably increasing the amount of computation involved two test examples the first with a singularity caused by an abrupt change in a boundary condition and the second with a singularity caused by a sharp re entrant corner are investigated and numerical results are presented copyright 2002 john wiley sons ltd

inverse elastostatic stress analysis in pre deformed biological structures demonstration using abdominal aortic aneurysms in stress analysis of membrane like biological structures the geometry constructed from in vivo image which often corresponds to a deformed state is routinely taken as the initial stress free geometry in this paper we show that this limitation can be completely removed using an inverse elastostatic approach namely a method for finding the initial geometry of an elastic body from a given deformed state we demonstrate the utility of the inverse approach using a patient specific abdominal aortic aneurysm model and identify the scope of error in stress estimation in the conventional approach within a realistic range of material parameter variations

thermal generalized stress intensity factors in 2 d domains lately methods that are capable of predicting failure initiation and propagation in structural components subjected to thermal loads have been sought it is postulated as in the theory of linear elastic fracture mechanics that the methods should correlate experimental observed failures to parameters characterizing the thermoelastic stress field in the vicinity of failure initiation points failures due to thermal loading occur for example in integrated circuits which are assemblages of dissimilar materials with different thermal and mechanical properties addressed in chapter 9 the mismatch of elastic constants and thermal expansion coefficients causes stress intensification at corners of interfaces and may lead to mechanical failure

two dimensional root structures and convergence properties of the separable median filter the root signals invariant to filtering structures of the two dimensional separable median filter are derived and presented in addition it is proved that with rare exception after repetitive passes of the separable median filter any two dimensional signal will be reduced to a signal containing only root structures

coupling of spectral methods and the p version of the finite element method for elliptic boundary value problems containing singularities in this paper we study a coupling of spectral methods and the p version finite element methods for elliptic boundary value problems containing singularities the method of auxiliary mapping which is a recent development to deal with domain singularities in the p version of the finite element method is employed to remove the pollution effect caused by singularities an iterative interfacial coupling between spectral methods and the p version of the finite element method is used and investigated numerically the advantages of such an approach are demonstrated by the high accuracy of spectral methods for the smooth part of solutions and the flexibility of the p version of the finite element method for dealing with singularities and irregular domains the efficiency of the coupling method is also evaluated by comparing results obtained by this method with those obtained by the full finite element algorithm

optimization of partition based weighted sum filters and their application to image denoising partition based weighted sum p ws filtering is an effective method for processing nonstationary signals especially those with regularly occurring structures such as images p ws filters were originally formulated as hard partition weighted sum hp ws filters and were successfully applied to image denoising this formulation relied on intuitive arguments to generate the filter class here we present a statistical analysis that justifies the use of weighted sum filters after observation space partitioning unfortunately the hp ws filters are nondifferentiable and an analytical solution for their global optimization is therefore difficult to obtain a two stage suboptimal training procedure has been reported in the literature but prior to this research no evaluation on the optimality of this approach has been reported here a genetic algorithm ga hp ws optimization procedure is developed that in simulations shows that the simpler two stage training procedure yields near optimal results also developed in this paper are soft partition weighted sum sp ws filters the sp ws filters utilize soft or fuzzy partitions that yield a differentiable filtering operation enabling the development of gradient based optimization procedures image denoising simulation results are presented comparing hp ws and sp ws filters their optimization procedures and wavelet based image denoising these results show that p ws filters in general outperform traditional and wavelet based image filters and sp ws filters utilizing soft partitioning not only allow for simple optimization but also yields improved performance

the method of fundamental solutions and condition number analysis for inverse problems of laplace equation this paper investigates the applications of the method of fundamental solutions together with the conditional number analysis to solve various inverse 2d laplace problems involving under specified and or over specified boundary conditions through the method of fundamental solutions and the condition number analysis it is numerically found that solutions of inverse laplace problems can be obtained without iteration or regularization for small noise levels since the method of fundamental solutions is a boundary type meshless numerical method that can automatically satisfy the governing equation however for larger values of noise levels regularization is still necessary to obtain promising result the present paper mainly focuses on the two types of numerical predictions of inverse 2d laplace problems 1 cauchy problem and 2 shape identification problem good quantitative agreement with the analytical solutions and other numerical methods for small perturbed boundary data is observed by using present meshless numerical scheme

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

boundary element analysis for the helmholtz eigenvalue problems with a multiply connected domain for a helmholtz eigenvalue problem with a multiply connected domain the boundary integral equation approach as well as the boundary element method is shown to yield spurious eigenvalues even if the complex valued kernel is used in such a case it is found that spurious eigenvalues depend on the geometry of the inner boundary demonstrated as an analytical case the spurious eigenvalue for a multiply connected problem with its inner boundary as a circle is studied analytically by using the degenerate kernels and circulants an annular case can be studied analytically in a discrete system and can be treated as a special case the proof for the general boundary instead of the circular boundary is also derived the burton miller method is employed to eliminate spurious eigenvalues in the multiply connected case moreover a modified method considering only the real part formulation is provided five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary good agreement between analytical prediction and numerical results are found

a computational method to assess the in vivo stresses and unloaded configuration of patient specific blood vessels in the modelling process of cardiovascular diseases one often comes across the numerical simulation of the blood vessel wall when the vessel geometry is patient specific and is obtained in vivo via medical imaging the stress distribution throughout the vessel wall is unknown however simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall in this work a computational method is formulated to restore the zero pressure geometry of patient specific blood vessels and to recover the in vivo stress field of the loaded structures at the moment of imaging the proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations as only an update of the mesh is required the formulation of this method allows for a straightforward implementation in combination with existing structural solvers even if the structural solver is a black box

a finite element method for laplace and helmholtz type boundary value problems with singularities laplace and helmholtz type boundary value problems with singularities are considered a sequence of approximations to the exact boundary conditions at an artificial boundary is given then the original problem is reduced to a boundary value problem in a domain away from the singularities furthermore finite element approximations are applied to this problem and error estimates are obtained finally some numerical examples show the effectiveness of this method

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

partition based weighted sum filters for image restoration we develop the concept of partitioning the observation space to build a general class of filters referred to as partition based weighted sum pws filters in the general framework each observation vector is mapped to one of m partitions comprising the observation space and each partition has an associated filtering function we focus on partitioning the observation space utilizing vector quantization and restrict the filtering function within each partition to be linear in this formulation a weighted sum of the observation samples forms the estimate where the weights are allowed to be unique within each partition the partitions are selected and weights tuned by training on a representative set of data it is shown that the proposed data adaptive processing allows for greater detail preservation when encountering nonstationarities in the data and yields superior results compared to several previously defined filters optimization of the pws filters is addressed and experimental results are provided illustrating the performance of pws filters in the restoration of images corrupted by gaussian noise

numerical treatment of acoustic problems with boundary singularities by the singular boundary method abstract the singular boundary method sbm is a novel boundary type meshless method based on the fundamental solution of the given governing equation the sbm employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions in this paper we investigate the acoustic problems with boundary singularities using the sbm this is achieved by combining the sbm with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution the singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities then the regular solution is obtained by the sbm numerical examples show the excellent performance of the proposed technique

cluster based differential energy detection for spectrum sensing in multi carrier systems this paper presents a novel differential energy detection scheme for multi carrier systems which can form fast and reliable decision of spectrum availability even in very low signal to noise ratio snr environment for example the proposed scheme can reach 90 in probability of detection pd and 10 in probability of false alarm pfa for the snrs as low as 21 db while the observation length is equivalent to 2 multi carrier symbol duration the underlying initiative of the proposed scheme is applying order statistics on the clustered differential energy spectral density esd in order to exploit the channel frequency diversity inherent in high data rate communications specifically to enjoy a good frequency diversity the clustering operation is utilized to group uncorrelated subcarriers while the differential operation applied onto each cluster can effectively remove the noise floor and consequently overcome the impact of noise uncertainty while exploiting the frequency diversity more importantly the proposed scheme is designed to allow robustness in terms of both time and frequency offsets in order to analytically evaluate the proposed scheme pfa and pd for rayleigh fading channel are derived the closed form expressions show a clear relationship between the sensing performance and the cluster size which is an indicator of the diversity gain moreover we are able to observe up to 10 db gain in the performance compared to the state of the art spectrum sensing schemes

analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation abstract the antiplane strain problem of two dissimilar anisotropic composite wedges of arbitrary angles that are bonded together along a common edge is considered the surfaces of the wedges can be subjected to traction traction traction displacement or displacement displacement boundary conditions the dependence of the order of the stress singularity on the wedge angles and material constants is studied the angular distribution of stresses at the apex and the exact full field stress solutions are also investigated explicit solutions for the order of stress singularity are obtained for some special cases it is found that the order of the stress singularity is always real for the antiplane dissimilar anisotropic wedge problem this is quite different from the in plane case in which the complex type of stress singularity might exist

a finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear a finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading the displacement field of the sectorial element is quadratic in the angular co ordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura14 for in plane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries

adaptive stack filtering under the mean absolute error criterion an adaptive filter algorithm is developed for the class of stack filters which is a class of nonlinear filters obeying a weak superposition property the adaptation algorithm can be interpreted as a learning algorithm for a group of decision making units the decisions of which are subject to a set of constraints called the stacking constraints under a rather weak statistical assumption on the training inputs the decision strategy adopted by the group which evolves according to the proposed learning algorithm is shown to converge to an optimal strategy in the sense that it corresponds to an optimal stack filter under the mean absolute error criterion this adaptive algorithm requires only increment decrement and comparison operations and only local interconnections between the learning units implementation of the algorithm in hardware is therefore very feasible an example is provided to show how the adaptive stack filtering algorithm can be used in an application in image processing

the bitonic filter linear filtering in an edge preserving morphological framework a new filter is presented which has better edge and detail preserving properties than a median noise reduction capability similar to a gaussian and is applicable to many signal and noise types it is built on a definition of signal as bitonic i e containing only one local maxima or minima within the filter range this definition is based on data ranking rather than value hence the bitonic filter comprises a combination of non linear morphological and linear operators it has no data level sensitive parameters and can locally adapt to the signal and noise levels in an image precisely preserving both smooth and discontinuous signals of any level when there is no noise but also reducing noise in other areas without creating additional artifactual noise both the basis and the performance of the filter are examined in detail and it is shown to be a significant improvement on the gaussian and median it is also compared over various noisy images to the image guided filter anisotropic diffusion non local means the grain filter and self dual forms of leveling and rank filters in terms of signal to noise the bitonic filter outperforms all these except non local means and sometimes anisotropic diffusion however it gives good visual results in all circumstances with characteristics which make it appropriate particularly for signals or images with varying noise or features at varying levels the bitonic has very few parameters does not require optimization nor prior knowledge of noise levels does not have any problems with stability and is reasonably fast to implement despite its non linearity it hence represents a very practical operation with general applicability

an integral equation method for the solution of singular slow flow problems a biharmonic boundary integral equation bbie method is used to solve a two dimensional contained viscous flow problem in order to achieve a greater accuracy than is usually possible in this type of method analytic expressions are used for the piecewise integration of all the kernel functions rather than the more time consuming method of gaussian quadrature