partition belief median filter based on dempster shafer theory for image processing a novel median type filter controlled by evidence fusion is proposed for removing noise from images the fusion of evidence based on the dempster shafer evidence theory providing a way to deal with the uncertainty in the evidence fusion indicates to what extent a noise is considered the filter proposed here is obtained as a weighted sum of the current pixel value and the output of the median filter and the weight is set based on the belief value of the input signal sequence the efficient step like function is used to partition the belief space and the least mean square lms algorithm is applied to obtain the optimal weight for each block moreover to improve the performance the new filter is recursively implemented experimental results have demonstrated that the proposed filter can outperform many well accepted median based filters in preserving image details while effectively suppressing impulsive noises and it also works satisfactorily in reducing gaussian as well as the mixture of gaussian and impulsive noise

relaxation limit and initial layer to hydrodynamic models for semiconductors abstract we study a relaxation limit of a solution to the initial boundary value problem for a hydrodynamic model to a drift diffusion model over a one dimensional bounded domain it is shown that the solution for the hydrodynamic model converges to that for the drift diffusion model globally in time as a physical parameter called a relaxation time tends to zero it is also shown that the solutions to the both models converge to the corresponding stationary solutions as time tends to infinity respectively here the initial data of electron density for the hydrodynamic model can be taken arbitrarily large in the suitable sobolev space provided that the relaxation time is sufficiently small because the drift diffusion model is a coupled system of a uniformly parabolic equation and the poisson equation since the initial data for the hydrodynamic model is not necessarily in momentum equilibrium an initial layer should occur however it is shown that the layer decays exponentially fast as a time variable tends to infinity and or the relaxation time tends to zero these results are proven by the decay estimates of solutions which are derived through energy methods

the relaxation of the hydrodynamic model for semiconductors to the drift diffusion equations abstract we establish the convergence and consistency of approximate solutions derived by the modified godunov scheme for the initial boundary value problem to a simplified one dimensional hydrodynamic model for semiconductors using the compensated compactness method the traces of weak solutions are introduced and then the weak solutions are proved to satisfy the natural boundary conditions the zero relaxation limit of the hydrodynamic model to the drift diffusion model is proved when the momentum relaxation time tends to zero

asymptotic behavior of solutions to euler poisson equations for bipolar hydrodynamic model of semiconductors abstract in this paper we study the cauchy problem for 1 d euler poisson system which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non flat doping profile different from the previous studies gasser et al 2003 7 huang et al 2011 12 huang et al 2012 13 for the case with two identical pressure functions and zero doping profile we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves steady state solutions rather than the diffusion waves furthermore we prove that when the flow is fully subsonic by means of a technical energy method with some new development the smooth solutions of the system are unique exist globally and time algebraically converge to the corresponding stationary solutions the optimal algebraic convergence rates are obtained

global existence and optimal decay rates for the timoshenko system the case of equal wave speeds abstract we first show the global existence and optimal decay rates of solutions to the classical timoshenko system in the framework of besov spaces due to the non symmetric dissipation the general theory for dissipative hyperbolic systems see 31 cannot be applied to the timoshenko system directly in the case of equal wave speeds we construct global solutions to the cauchy problem pertaining to data in the spatially besov spaces furthermore the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis consequently the optimal decay estimates of solution and its derivatives of fractional order are shown by time weighted energy approaches in terms of low frequency and high frequency decompositions as a by product the usual decay estimate of l 1 r l 2 r type is also shown

subsonic solutions to a one dimensional non isentropic hydrodynamic model for semiconductors the one dimensional stationary full hydrodynamic model for semiconductor devices with non isentropic pressure is studied this model consists of the equations for the electron density electron temperature and electric field in a bounded domain supplemented with boundary conditions the existence of a classical subsonic solution with positive particle density and positive temperature is shown in two situations non constant and constant heat conductivities moreover we prove uniqueness of a classical solution in the latter case the existence proofs are based on elliptic estimates stampacchia truncation methods and fixed point arguments

global quasi neutral limit of euler maxwell systems with velocity dissipation abstract we consider smooth solutions to the cauchy problem for an isentropic euler maxwell system with velocity dissipation and small physical parameters for initial data uniformly close to constant equilibrium states we prove the global in time convergence of the system as the parameters go to zero the limit systems are the e mhd system and the incompressible euler equations both with velocity dissipation the proof of the results relies on a single uniform energy estimate with respect to the time and the parameters together with compactness arguments for this purpose the classical energy estimates for the symmetrizable hyperbolic system are not sufficient we construct a lyapunov type energy by controlling the divergence and the curl of the velocity the electric and magnetic fields

efficient improvements on the bdnd filtering algorithm for the removal of high density impulse noise switching median filters are known to outperform standard median filters in the removal of impulse noise due to their capability of filtering candidate noisy pixels and leaving other pixels intact the boundary discriminative noise detection bdnd is one powerful example in this class of filters however there are some issues related to the filtering step in the bdnd algorithm that may degrade its performance in this paper we propose two modifications to the filtering step of the bdnd algorithm to address these issues experimental evaluation shows the effectiveness of the proposed modifications in producing sharper images than the bdnd algorithm

application of partition based median type filters for suppressing noise in images an adaptive median based filter is proposed for removing noise from images specifically the observed sample vector at each pixel location is classified into one of m mutually exclusive partitions each of which has a particular filtering operation the observation signal space is partitioned based an the differences defined between the current pixel value and the outputs of cwm center weighted median filters with variable center weights the estimate at each location is formed as a linear combination of the outputs of those cwm filters and the current pixel value to control the dynamic range of filter outputs a location invariance constraint is imposed upon each weighting vector the weights are optimized using the constrained lms least mean square algorithm recursive implementation of the new filter is then addressed the new technique consistently outperforms other median based filters in suppressing both random valued and fixed valued impulses and it also works satisfactorily in reducing gaussian noise as well as mixed gaussian and impulse noise

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

a switching median filter with boundary discriminative noise detection for extremely corrupted images a novel switching median filter incorporating with a powerful impulse noise detection method called the boundary discriminative noise detection bdnd is proposed in this paper for effectively denoising extremely corrupted images to determine whether the current pixel is corrupted the proposed bdnd algorithm first classifies the pixels of a localized window centering on the current pixel into three groups lower intensity impulse noise uncorrupted pixels and higher intensity impulse noise the center pixel will then be considered as uncorrupted provided that it belongs to the uncorrupted pixel group or corrupted for that two boundaries that discriminate these three groups require to be accurately determined for yielding a very high noise detection accuracy in our case achieving zero miss detection rate while maintaining a fairly low false alarm rate even up to 70 noise corruption four noise models are considered for performance evaluation extensive simulation results conducted on both monochrome and color images under a wide range from 10 to 90 of noise corruption clearly show that our proposed switching median filter substantially outperforms all existing median based filters in terms of suppressing impulse noise while preserving image details and yet the proposed bdnd is algorithmically simple suitable for real time implementation and application

diffusive relaxation limits of compressible euler maxwell equations abstract this work is concerned with compressible euler maxwell equations which take the form of euler equations for the conservation laws of mass density current density and energy density for electrons coupled to maxwell s equations for self consistent electromagnetic field we give a model hierarchy of non isentropic euler maxwell equations from the point of view of diffusive relaxation limits more precisely inspired by maxwell type iteration we construct new approximations and show that periodic initial value problems of a certain scaled euler maxwell equations have unique smooth solutions in a time interval independent of momentum relaxation time and energy relaxation time furthermore it is proved that smooth solutions converge to solutions of drift diffusion models and energy transport models in the process of combined diffusive relaxation limits and the corresponding convergence rates are also obtained

mixed noise removal by weighted encoding with sparse nonlocal regularization mixed noise removal from natural images is a challenging task since the noise distribution usually does not have a parametric model and has a heavy tail one typical kind of mixed noise is additive white gaussian noise awgn coupled with impulse noise in many mixed noise removal methods are detection based methods they first detect the locations of in pixels and then remove the mixed noise however such methods tend to generate many artifacts when the mixed noise is strong in this paper we propose a simple yet effective method namely weighted encoding with sparse nonlocal regularization wesnr for mixed noise removal in wesnr there is not an explicit step of impulse pixel detection instead soft impulse pixel detection via weighted encoding is used to deal with in and awgn simultaneously meanwhile the image sparsity prior and nonlocal self similarity prior are integrated into a regularization term and introduced into the variational encoding framework experimental results show that the proposed wesnr method achieves leading mixed noise removal performance in terms of both quantitative measures and visual quality

an explicit four step phase fitted method for the numerical integration of second order initial value problems abstract an explicit four step method with phase lag of infinite order is developed for the numerical integration of second order initial value problems extensive numerical testing indicates that this new method can be generally more efficient than other four step methods

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

a spectral solution of the sturm liouville equation comparison of classical and nonclassical basis sets abstract this paper considers a spectral method of solution of the sturm liouville equation and the associated schroedinger equation the main objective is to develop a collocation method based on quadrature collocation points generated from nonclassical polynomials the polynomials and associated quadrature points are calculated with gautschi s stieltjes procedure from some specified weight function the particular spectral method used here with nonclassical basis sets is referred to as the quadrature discretization method qdm the qdm and a related weighted qdm are applied to several sturm liouville and schroedinger equations and the results are compared with the traditional spectral methods based on chebyshev and legendre quadrature points the results are also compared with the results of other workers wherever available the qdm was found to give the most rapid convergence relative to other methods for the problems studied

asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors the present paper concerns the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a one dimensional heat conductive hydrodynamic model for semiconductors it is important to analyze thermal influence on the motion of electrons in semiconductor device to improve the reliability of devices by handling a hot carrier problem we show the unique existence of the stationary solution satisfying a subsonic condition by using the leray schauder and the schauder fixed point theorems then the asymptotic stability of the stationary solution is proved by deriving the a priori estimate uniformly in time here an energy form plays an essential role we also prove that the solution converges to the stationary solution exponentially fast as time tends to infinity

global solutions for the compressible quantum hydrodynamic model in a bounded domain abstract this paper concerns the existence of global smooth solutions to the initial boundary value problem for a three dimensional compressible quantum hydrodynamic model with damping and heat diffusion in a bounded domain in r 3 based on the continuation argument and the uniform a priori estimates with respect to the time we obtain the existence of global solutions in a bounded smooth domain provided that the initial perturbation around a constant state is small enough the key difficulty is to deal with the higher order quantum terms which do play an essential role in establishing the a priori estimates the boundary conditions finally adopted are the insulating boundary conditions

global existence of classical solutions of full euler maxwell equations abstract we prove the global existence and large time behavior of classical solutions to the full euler maxwell equations in chemin lerner spaces with critical regularity which generalizes those results on the isentropic euler maxwell equations

stability of steady states of the compressible euler poisson system in r 3 abstract we investigate the global existence and asymptotic behavior of smooth solutions near a non flat steady state to the compressible euler poisson system in r 3 using some concise energy estimates and an interpolation trick we refine the global existence and show that the solution converges to the stationary solution exponentially fast we assume that the h 3 norms of the initial density and velocity are small but the higher derivatives can be arbitrarily large in this sense our method simplifies the proof of hsiao et al 2003 17 and improves the results of it

a new adaptive center weighted median filter for suppressing impulsive noise in images in this work a new adaptive center weighted median acwm filter is proposed for improving the performance of median based filters preserving image details while effectively suppressing impulsive noise the proposed filter is an adaptive cwm filter with an adjustable central weight obtained by partitioning the observation vector space to obtain the optimal weight for each block the efficient scalar quantization sq method is used to partition the observation vector space the center weight within each block is obtained by using a learning approach based on the least mean square lms algorithm the noise filtering procedure is progressively applied through several iterations so that the mean square error of the output can be minimized experimental results have demonstrated that the proposed filter outperforms many well accepted median based filters in terms of both noise suppression and detail preservation the proposed new filter also provides excellent robustness at various percentages of impulsive noise

four step methods for y f x y abstract a systematic investigation is undertaken here on the possible practical consequences of the fact that the linear four step methods for y f x y form a family with a certain structure the mentioned property is found to be surprisingly rich in consequences and three of them are of particular importance i drastic reduction in the number of iterations at each step ii increased flexibility with respect to the start of integration and to the modification of the step size during the integration process iii possibility of direct and simple appraisal of the local truncation error

tuning the smoothness of the recursive median filter the median filter is a special case of nonlinear filters used for smoothing signals since the output of the median filter is always one of the input samples it is conceivable that certain signals could pass through the median filter unaltered these signals define the signature of a filter and are referred to as root signals median filters are known to possess the convergence property meaning that by repeating median filtering a root signal will be found starting from any input signal by associating the nonlinear operation of median filtering with a two terms cost function an optimization process that minimizes that function is obtained cost functions of the same type are associated with different recursive median filtering schemes by replacing the actual values inside the filter s window with the original signal the convergence behavior of these filters and their smoothness are studied by changing the positions of the replacements during filtering a tuning effect of the smoothness is obtained simulation results show that the proposed filtering schemes provide improved performance over the standard recursive median filter succeeding in preserving small details and fine textures

bifurcation analysis of the degond lucquin desreux morrow model for gas discharge abstract the main purpose of this paper is to investigate mathematically gas discharge townsend discovered and mechanisms which are essential for ionization of gas and then derived a threshold of voltage at which gas discharge can happen in this derivation he used some simplification such as discretization of time therefore it is an interesting problem to analyze the threshold by using the degond lucquin desreux morrow model and also to compare the results of analysis with townsend s theory note that gas discharge never happens in townsend s theory if mechanism is not taken into account in this paper we study an initial boundary value problem to the model with mechanism but no mechanism this problem has a trivial stationary solution of which the electron and ion densities are zero it is shown that there exists a threshold of voltage at which the trivial solution becomes unstable from stable then we conclude that gas discharge can happen for a voltage greater than this threshold even if mechanism is not taken into account it is also of interest to know the asymptotic behavior of solutions to this initial boundary value problem for the case that the trivial solution is unstable to this end we establish bifurcation of non trivial stationary solutions by applying crandall and rabinowitz s theorem and show the linear stability and instability of those non trivial solutions

initial boundary value problems for a quantum hydrodynamic model of semiconductors asymptotic behaviors and classical limits abstract the present paper proves the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a quantum hydrodynamic model of semiconductors over a one dimensional bounded domain we also discuss on a singular limit from this model to a classical hydrodynamic model without quantum effects precisely we prove that a solution for the quantum model converges to that for the hydrodynamic model as the planck constant tends to zero here we adopt a non linear boundary condition which means quantum effect vanishes on the boundary in the previous researches the existence and the asymptotic stability of a stationary solution are proved under the assumption that a doping profile is flat which makes the stationary solution also flat however the typical doping profile in actual devices does not satisfy this assumption thus we prove the above theorems without this flatness assumption firstly the existence of the stationary solution is proved by the leray schauder fixed point theorem secondly we show the asymptotic stability theorem by using an elementary energy method where the equation for an energy form plays an essential role finally the classical limit is considered by using the energy method again

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

a fuzzy impulse noise detection and reduction method removing or reducing impulse noise is a very active research area in image processing in this paper we describe a new algorithm that is especially developed for reducing all kinds of impulse noise fuzzy impulse noise detection and reduction method fidrm it can also be applied to images having a mixture of impulse noise and other types of noise the result is an image quasi without or with very little impulse noise so that other filters can be used afterwards this nonlinear filtering technique contains two separated steps an impulse noise detection step and a reduction step that preserves edge sharpness based on the concept of fuzzy gradient values our detection method constructs a fuzzy set impulse noise this fuzzy set is represented by a membership function that will be used by the filtering method which is a fuzzy averaging of neighboring pixels experimental results show that fidrm provides a significant improvement on other existing filters fidrm is not only very fast but also very effective for reducing little as well as very high impulse noise

universal impulse noise filter based on genetic programming in this paper we present a novel method for impulse noise filter construction based on the switching scheme with two cascaded detectors and two corresponding estimators genetic programming as a supervised learning algorithm is employed for building two detectors with complementary characteristics the first detector identifies the majority of noisy pixels the second detector searches for the remaining noise missed by the first detector usually hidden in image details or with amplitudes close to its local neighborhood both detectors are based on the robust estimators of location and scale median and mad the filter made by the proposed method is capable of effectively suppressing all kinds of impulse noise in contrast to many existing filters which are specialized only for a particular noise model in addition we propose the usage of a new impulse noise model the mixed impulse noise which is more realistic and harder to treat than existing impulse noise models the proposed model is the combination of commonly used noise models salt and pepper and uniform impulse noise models simulation results show that the proposed two stage gp filter produces excellent results and outperforms existing state of the art filters

global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source abstract in this paper a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation global existence to the cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established and the asymptotic behavior of these smooth solutions is investigated namely that the solutions converge to the general steady state solution exponentially fast as t is obtained moreover the existence and uniqueness of the stationary solutions are investigated

fuzzy random impulse noise reduction method a new two step fuzzy filter that adopts a fuzzy logic approach for the enhancement of images corrupted with impulse noise is presented in this paper the filtering method entitled as fuzzy random impulse noise reduction method frinr consists of a fuzzy detection mechanism and a fuzzy filtering method to remove random valued impulse noise from corrupted images based on the criteria of peak signal to noise ratio psnr and subjective evaluations we have found experimentally that the proposed method provides a significant improvement on other state of the art methods

relaxation limit in bipolar semiconductor hydrodynamic model with non constant doping profile abstract the relaxation limit from bipolar semiconductor hydrodynamic hd model to drift diffusion dd model is shown under the non constant doping profile assumption for both stationary solutions and global in time solutions which satisfy the general form of the ohmic contact boundary condition the initial layer phenomenon will be analyzed because the initial data is not necessarily in the momentum equilibrium due to the bipolar coupling structure the analysis is hard and different from the previous literature on unipolar model or bipolar model with zero doping profile restriction we first construct the non constant uniform stationary solutions by the operator method for both hd and dd models in a unified procedure then we prove the global existence of dd model and uniform global existence of hd model by the elementary energy method but with some new developments based on the above existence results we further calculate the convergence rates in relaxation limits

fuzzy two step filter for impulse noise reduction from color images a new framework for reducing impulse noise from digital color images is presented in which a fuzzy detection phase is followed by an iterative fuzzy filtering technique we call this filter the fuzzy two step color filter the fuzzy detection method is mainly based on the calculation of fuzzy gradient values and on fuzzy reasoning this phase determines three separate membership functions that are passed to the filtering step these membership functions will be used as a representation of the fuzzy set impulse noise one function for each color component our proposed new fuzzy method is especially developed for reducing impulse noise from color images while preserving details and texture experiments show that the proposed filter can be used for efficient removal of impulse noise from color images without distorting the useful information in the image

efficient impulse noise reduction via local directional gradients and fuzzy logic this paper proposes an efficient noise reduction method for image restoration a novel pixel classification method by using fuzzy logic and local gradients is first introduced to discriminate noise and noise free pixels from corrupted images then a switching filtering scheme is employed to noisy images the noise pixels will be filtered by a weighted median filter with adaptive weights when the noise free pixels are preserved in the filtered images both numerical comparisons and perceptual observations are demonstrated in the experimental simulations it is found that the proposed method achieves a fairly better performance than a number of other existing methods in noise reduction and image restoration

a hybrid neuro fuzzy filter for edge preserving restoration of images corrupted by impulse noise a new operator for restoring digital images corrupted by impulse noise is presented the proposed operator is a hybrid filter obtained by appropriately combining a median filter an edge detector and a neuro fuzzy network the internal parameters of the neuro fuzzy network are adaptively optimized by training the training is easily accomplished by using simple artificial images that can be generated in a computer the most distinctive feature of the proposed operator over most other operators is that it offers excellent line edge detail and texture preservation performance while at the same time effectively removing noise from the input image extensive simulation experiments show that the proposed operator may be used for efficient restoration of digital images corrupted by impulse noise without distorting the useful information in the image

fuzzy random impulse noise removal from color image sequences in this paper a new fuzzy filter for the removal of random impulse noise in color video is presented by working with different successive filtering steps a very good tradeoff between detail preservation and noise removal is obtained one strong filtering step that should remove all noise at once would inevitably also remove a considerable amount of detail therefore the noise is filtered step by step in each step noisy pixels are detected by the help of fuzzy rules which are very useful for the processing of human knowledge where linguistic variables are used pixels that are detected as noisy are filtered the others remain unchanged filtering of detected pixels is done by blockmatching based on a noise adaptive mean absolute difference the experiments show that the proposed method outperforms other state of the art filters both visually and in terms of objective quality measures such as the mean absolute error mae the peak signal to noise ratio psnr and the normalized color difference ncd

impulse noise removal from digital images by a detail preserving filter based on type 2 fuzzy logic a novel image filter based on type 2 fuzzy logic techniques is proposed for detail preserving restoration of digital images corrupted by impulse noise the performance of the proposed filter is evaluated for different test images corrupted at various noise densities and also compared with representative conventional as well as state of the art impulse noise filters from the literature experimental results show that the proposed filter exhibits superior performance over the competing operators and is capable of efficiently suppressing the noise in the image while at the same time effectively preserving thin lines edges texture and other useful information within the image

a detection statistic for random valued impulse noise this paper proposes an image statistic for detecting random valued impulse noise by this statistic we can identify most of the noisy pixels in the corrupted images combining it with an edge preserving regularization we obtain a powerful two stage method for denoising random valued impulse noise even for noise levels as high as 60 simulation results show that our method is significantly better than a number of existing techniques in terms of image restoration and noise detection

tri state median filter for image denoising a novel nonlinear filter called tri state median tsm filter is proposed for preserving image details while effectively suppressing impulse noise we incorporate the standard median sm filter and the center weighted median cwm filter into a noise detection framework to determine whether a pixel is corrupted before applying filtering unconditionally extensive simulation results demonstrate that the proposed filter consistently outperforms other median filters by balancing the tradeoff between noise reduction and detail preservation

the compressible euler equations in a bounded domain existence of solutions and the incompressible limit a short time existence theorem is proven for the euler equations for nonisentropic compressible fluid flow in a bounded domain and solutions with low mach number and almost incompressible initial data are shown to be close to corresponding solutions of the equations for incompressible flow

relaxation time limit and initial layer in the isentropic hydrodynamic model for semiconductors abstract this work is concerned with the relaxation time limit in the multidimensional isentropic hydrodynamic model for semiconductors in the critical besov space firstly we construct formal approximations of the initial layer solution to the nonlinear problem by the matched expansion method then assuming some regularity of the solution to the reduced problem and proves the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval

a fourth order bessel fitting method for the numerical solution of the schro dinger equation abstract a new fourth order method is developed for the numerical integration of the one dimensional radial schrodinger equation this method integrates bessel and neumann functions exactly it is shown that for large r this new formula is much more accurate and rapid than the bessel fitting method of second order which is developed by raptis and cash 1987 the benefit of using this new approach is demonstrated by considering some numerical examples based on the lenard jones potential

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

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

large time behavior of solutions to hyperbolic elliptic coupled systems we are concerned with the asymptotic behavior of a solution to the initial value problem for a system of hyperbolic conservation laws coupled with elliptic equations this kind of problem was first considered in our previous paper in the present paper we generalize the previous results to a broad class of hyperbolic elliptic coupled systems assuming the existence of the entropy function and the stability condition we prove the global existence and the asymptotic decay of the solution for small initial data in a suitable sobolev space then it is shown that the solution is well approximated for large time by a solution to the corresponding hyperbolic parabolic coupled system the first result is proved by deriving a priori estimates through the standard energy method the spectral analysis with the aid of the a priori estimate gives the second result

asymptotic convergence to planar stationary waves for multi dimensional unipolar hydrodynamic model of semiconductors abstract in this study we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of euler poisson equations based on the results that we have obtained in the first part huang et al 2011 16 for the 1 d case we can further show the stability of planar stationary waves in multi dimensional case utilizing the energy method we obtain the global existence of the solutions of high dimensional euler poisson equations for the unipolar hydrodynamic model and prove that the solutions converge to the planar stationary waves time exponentially

partition fuzzy median filter based on fuzzy rules for image restoration in this paper a novel adaptive median based filter called the partition fuzzy median pfm filter is proposed for improving the median based filter to preserve image details while effectively suppressing impulsive noises the proposed filter achieves its effect through a summation of the weighted output of the median filter and the related weighted input signal the weights are set in accordance with the fuzzy rules in order to design this weight function a method to partition of the observation vector space and a learning approach are proposed so that the mean square error of the filter output can be minimum based on the constrained least mean square algorithm an iterative learning procedure is derived and its convergence property is investigated as for the noise suppressing on both fixed and random valued impulses without degrading the quality of fine details extensive experimental results demonstrate that the proposed filter outperforms the other median based filters in the literature the new filter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples

steady hydrodynamic model of semiconductors with sonic boundary and transonic doping profile abstract as shown in 17 18 for the hydrodynamic model of semiconductors represented by euler poisson equations with sonic boundary and subsonic supersonic doping profile the structure of stationary solutions are very complicated it may possess various solutions like subsonic supersonic transonic flows in this paper we consider a more challenging case where the doping profile is transonic which is categorized into two types subsonic dominated and supersonic dominated in the subsonic dominated case we show that the system has a unique interior subsonic solution at least one interior supersonic solution and infinitely many transonic solutions under the suitable assumptions however the difference with the case of subsonic doping profile is that the interior subsonic solution and interior supersonic solution may not exist in special cases when the relaxation time is small in the supersonic dominated case the non existence and existence of all types of solutions are also obtained the approach adopted is the technical compactness analysis combining the green s function method here the results obtained perfectly develop the existing studies

relaxation time limits of non isentropic hydrodynamic models for semiconductors abstract this work deals with non isentropic hydrodynamic models for semiconductors with short momentum and energy relaxation times the high and low frequency decomposition methods are used to construct uniform global classical solutions to cauchy problems of a scaled hydrodynamic model in the framework of critical besov spaces furthermore it is rigorously justified that the classical solutions strongly converge to that of a drift diffusion model as two relaxation times both tend to zero as a by product global existence of weak solutions to the drift diffusion model is also obtained

a four step method for the numerical solution of the schro dinger equation abstract a new four step exponentially fitted method is developed in this paper the expressions for the coefficients of the method are found such as to ensure the optimal approximation to the eigenvalue schrodinger equation i e equivalent to positive energy

a family of four step exponentially fitted predictor corrector methods for the numerical integration of the schro dinger equation a family of predictor corrector exponential four step methods is developed for the numerical integration of the one dimensional schrodinger equation the formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions the new methods integrate more exponential functions and are very simple compared with the well known sixth algebraic order runge kutta type methods numerical results indicate that the new method is much more accurate than other exponentially fitted methods

energy transport and drift diffusion limits of nonisentropic euler poisson equations abstract two relaxation limits in critical spaces for the scaled nonisentropic euler poisson equations with the momentum relaxation time and energy relaxation time are considered as the first step of this justification the uniform global classical solutions to the cauchy problem in chemin lerner s spaces with critical regularity are constructed furthermore by the compactness argument it is rigorously justified that the scaled classical solutions converge to the solutions of energy transport equations and drift diffusion equations respectively with respect to different time scales

pde based random valued impulse noise removal based on new class of controlling functions this paper is concerned with partial differential equation pde based image denoising for random valued impulse noise we introduce the notion of eni the abbreviation for edge pixels noisy pixels and interior pixels that denotes the number of homogeneous pixels in a local neighborhood and is significantly different for edge pixels noisy pixels and interior pixels we redefine the controlling speed function and the controlling fidelity function to depend on eni according to our two controlling functions the diffusion and fidelity process at edge pixels noisy pixels and interior pixels can be selectively carried out furthermore a class of second order improved and edge preserving pde denoising models is proposed based on the two new controlling functions in order to deal with random valued impulse noise reliably we demonstrate the performance of the proposed pdes via application to five standard test images corrupted by random valued impulse noise with various noise levels and comparison with the related second order pde models and the other special filtering methods for random valued impulse noise our two controlling functions are extended to automatically other pde models

cognition and removal of impulse noise with uncertainty uncertainties are the major inherent feature of impulse noise this fact makes image denoising a difficult task understanding the uncertainties can improve the performance of image denoising this paper presents a novel adaptive detail preserving filter based on the cloud model cm to remove impulse noise it is called the cm filter first an uncertainty based detector identifies the pixels corrupted by impulse noise then a weighted fuzzy mean filter is applied to remove the noise candidates the experimental results show that compared with the traditional switching filters the cm filter makes a great improvement in image denoising even at a noise level as high as 95 the cm filter still can restore the image with good detail preservation

a universal denoising framework with a new impulse detector and nonlocal means impulse noise detection is a critical issue when removing impulse noise and impulse gaussian mixed noise in this paper we propose a new detection mechanism for universal noise and a universal noise filtering framework based on the nonlocal means nl means the operation is carried out in two stages i e detection followed by filtering for detection first we propose the robust outlyingness ratio ror for measuring how impulselike each pixel is and then all the pixels are divided into four clusters according to the ror values second different decision rules are used to detect the impulse noise based on the absolute deviation to the median in each cluster in order to make the detection results more accurate and more robust the from coarse to fine strategy and the iterative framework are used in addition the detection procedure consists of two stages i e the coarse and fine detection stages for filtering the nl means are extended to the impulse noise by introducing a reference image then a universal denoising framework is proposed by combining the new detection mechanism with the nl means ror nlm finally extensive simulation results show that the proposed noise detector is superior to most existing detectors and the ror nlm produces excellent results and outperforms most existing filters for different noise models unlike most of the other impulse noise filters the proposed ror nlm also achieves high peak signal to noise ratio and great image quality by efficiently removing impulse gaussian mixed noise