an efficient two phase rm l 1 tv method for restoring blurred images with impulse noise a two phase image restoration method based upon total variation regularization combined with an l1 data fitting term for impulse noise removal and deblurring is proposed in the first phase suitable noise detectors are used for identifying image pixels contaminated by noise then in the second phase based upon the information on the location of noise free pixels images are deblurred and denoised simultaneously for efficiency reasons in the second phase a superlinearly convergent algorithm based upon fenchel duality and inexact semismooth newton techniques is utilized for solving the associated variational problem numerical results prove the new method to be a significantly advance over several state of the art techniques with respect to restoration capability and computational efficiency

aspects of total variation regularized l1 function approximation the total variation based image denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 has been generalized and modified in many ways in the literature one of these modifications is to use the l1 norm as the fidelity term we study the interesting consequences of this modification especially from the point of view of geometric properties of its solutions it turns out to have interesting new implications for data driven scale selection and multiscale image decomposition

stability radii of positive linear difference equations under affine parameter perturbations in this paper we study stability radii of positive linear difference equations under arbitrary affine parameter perturbations it is shown that real and complex stability radii of positive equations coincide for block diagonal disturbances moreover for these stability radii estimates and computable formulae are derived which generalize to positive linear difference equations known results obtained earlier for positive linear discrete time systems of the form x k 1 ax k email protected n some illustrative examples are given

decision based order statistic filters the authors propose two adaptive order statistic filters which generate outputs based on the results of hypothesis tests to reduce edge shifting of the median filter a modified median filter mmf is proposed first a hypothesis test is applied to detect the edge location then whenever an edge is detected the mmf generates the output by modifying the median output based on a comparison of median value to the current input value the mmf can retain more fine details than the median filter with the same window size as well as reduce the output mean square error which is caused mainly by edge shifting to suppress nonimpulsive noise as well as impulsive noise an l type structure is combined with the mmf the proposed filter generates the output by using asymmetric alpha trimming on the mmf output in addition to noise suppression it can enhance the gradient of blurred edges provided that the size of the window is greater than the transition width of the blurred edges experimental results for one and two dimensional signals are presented

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

the treatment of lubrication forces in boundary integral equations despite their many advantages over other numerical methods boundary integral formulations still fail to provide accurate predictions of mesoscale motion in dense suspensions of rigid particles because the nearly singular flow between surfaces in close proximity cannot be resolved accurately a procedure for incorporating analytical solutions for the lubrication flow within a large scale boundary integral equation method is shown although the method is applied to the case of spherical particles in conjunction with the completed double layer boundary integral equation it can be developed further to treat more complex geometries and can be adapted to other numerical techniques in contrast to other apparently similar approaches the present method does not resort to effective medium approximations and in principle retains all the advantages typical of boundary integral approaches the framework also allows for forces other than those due to hydrodynamic lubrication between particles provided that they are a linear function of the relative velocity or at least can be linearized for example forces due to sub continuum fluid behaviour or forces resulting from surface chemistry it is shown using several benchmarks that the relative motion between two particles in various flows is captured accurately both statically and dynamically in situations where uncorrected simulations fail moreover the computational effort is reduced substantially by the application of the method

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

robust d stability for linear uncertain discrete time delay systems we propose criteria which guarantee robust pole location within a specified circular region for a linear uncertain discrete time delay system the perturbations are treated with structured and unstructured information examples are given to demonstrate the result

a new weighted mean filter with a two phase detector for removing impulse noise abstract this paper proposes a new weighted mean filter with a two phase noise detector for image denoising operations are carried out by the detection followed by filtering strategy for detection a two phase noise detector is presented to detect impulse noise in in the first phase a rank ordered difference of road rod road scheme is introduced for detecting noise candidates different from most of the existing in detectors the proposed detector identifies a pixel by a fuzzy rule that matches the stochastic nature of in and greatly improves the denoising performance in the second phase a local image statistic minimum edge pixels difference mepd is proposed to identify edge pixels from noise candidates this preserves edges from being wrongly detected as noise therefore improves the detection accuracy for filtering we design a new weighted mean filter wmf that is more suitable for in to suppress the detected noisy pixels finally an iterative denoising algorithm is presented by combining the proposed two phase noise detector and the new wmf the proposed method is accessible and easy to implement experimental results show that the proposed method outperforms all the tested state of the art denoising methods with respect to the visual effects and quantitative measure results

pole assignment robustness in a specified disk abstract a sufficient condition is proposed to guarantee robust pole location within a specified circular region for a linear uncertain system the explicit bounds on linear time invariant perturbations with highly structured information are obtained under these allowable highly structured perturbations both stability robustness and certain performance robustness will thus be ensured the merit of the proposed new approach is demonstrated by a given example where the results achieved are much better than the ones reported recently

fast impulsive noise removal a generic n dimensional filter with the primary purpose of eliminating impulsive like noise is presented this recursive nonlinear filter is composed of two conditional rules which are applied independently in any order one after the other it identifies noisy items by inspection of their surrounding neighborhood and afterwards it replaces their values with the most conservative ones out of their neighbors values in this way no new values are introduced and the histogram distribution range is conserved this n dimensional filter can be decomposed recursively to a lower dimensional space each time generating two sets of n n 1 dimensional filters this study which focuses on the case of two dimensional signals gray scale images explores one possible implementation of this new filter and orients the evaluation of its performance toward the median filter as this filter is the basis of many more sophisticated filters for impulsive noise reduction tests were carried out using both real and artificial images we found this new filter to be much faster than the median filter while performing comparably in terms of both image information conservation and noise reduction which suggests that it could replace the median filter for the preliminary processing included in state of the art noise removal filters this new filter should either eliminate or attenuate most noisy pixels in synthetic and natural images not excessively contaminated it has a slight smoothing effect on nonnoisy image regions in addition it is scalable easily implemented and adaptable to specific applications

noise reduction by fuzzy image filtering a new fuzzy filter is presented for the noise reduction of images corrupted with additive noise the filter consists of two stages the first stage computes a fuzzy derivative for eight different directions the second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values both stages are based on fuzzy rules which make use of membership functions the filter can be applied iteratively to effectively reduce heavy noise in particular the shape of the membership functions is adapted according to the remaining noise level after each iteration making use of the distribution of the homogeneity in the image a statistical model for the noise distribution can be incorporated to relate the homogeneity to the adaptation scheme of the membership functions experimental results are obtained to show the feasibility of the proposed approach these results are also compared to other filters by numerical measures and visual inspection

statistical based impulsive noise removal in digital radiography a new filter to restore radiographic images corrupted by impulsive noise is proposed it is based on a switching scheme where all the pulses are first detected and then corrected through a median filter the pulse detector is based on the hypothesis that the major contribution to image noise is given by the photon counting process with some pixels corrupted by impulsive noise such statistics is described by an adequate mixture model the filter is also able to reliably estimate the sensor gain its operation has been verified on both synthetic and real images the experimental results demonstrate the superiority of the proposed approach in comparison with more traditional methods

orthogonal rational functions for system identification numerical aspects recently there has been a growing interest in the use of orthogonal rational functions orfs in system identification there are many advantages over more classical techniques probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 the so called malmquist basis the attention has been on the development of methods using this basis however for some discrete identification problems this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved in this note we give an algorithm based on a more general system of orf to overcome the numerical problem and which allows for a fast order update of the estimate

generalised nonlocal image smoothing we propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches one of such dissimilarity measures is the weighted l 2 distance between patches in such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain it can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels but also the similarity of their corresponding neighbours this leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure by slightly modifying the way the similarities are computed we obtain two related filters the nl means filter of buades et al siam multiscale model simul 4 2 490 530 2005b and the nds filter of mrazek et al geometric properties for incomplete data computational imaging and vision vol 31 pp 335 352 springer dordrecht 2006 in fact the proposed approach can be considered as a generalisation of the latter filter to the space of patches we also provide novel insights into relations of the nds filter with diffusion regularisation methods as well as with some recently proposed graph regularisation techniques we evaluate our method for the task of denoising greyscale and colour images degraded with gaussian and salt and pepper noise demonstrating that it compares very well to other more sophisticated approaches

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

a nonconvex l1 l1 l2 model for image restoration with impulse noise abstract in this paper we propose a model for image restoration with blur and impulse noise it is composed of l 1 data fitting term and a nonconvex regularization term which is the weighted difference of l 1 norm and l 2 norm based on wavelet frame the combined model is difficult to solve by the corresponding euler lagrangian equations here we solve it by alternating direction method of multipliers admm we describe the detailed process of the algorithm and establish the convergence of the algorithm the experimental outcomes on different blurs and different impulse noises demonstrate that the proposed approach is better than those existing methods in terms of standard signal to noise ratio psnr relative error reerr and visual quality

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

a new impulse detection and filtering method for removal of wide range impulse noises a new impulse detection and filtering algorithm is proposed for restoration of images that are highly corrupted by impulse noise it is based on the minimum absolute value of four convolutions obtained by one dimensional laplacian operators the proposed algorithm can effectively remove the impulse noise with a wide range of noise density and produce better results in terms of the qualitative and quantitative measures of the images even at noise density as high as 90 extensive simulations show that the proposed algorithm provides better performance than many of the existing switching median filters in terms of noise suppression and detail preservation

framelet algorithms for de blurring images corrupted by impulse plus gaussian noise this paper studies a problem of image restoration that observed images are contaminated by gaussian and impulse noise existing methods for this problem in the literature are based on minimizing an objective functional having the l1 fidelity term and the mumford shah regularizer we present an algorithm on this problem by minimizing a new objective functional the proposed functional has a content dependent fidelity term which assimilates the strength of fidelity terms measured by the l1 and l2 norms the regularizer in the functional is formed by the l1 norm of tight framelet coefficients of the underlying image the selected tight framelet filters are able to extract geometric features of images we then propose an iterative framelet based approximation sparsity deblurring algorithm ifasda for the proposed functional parameters in ifasda are adaptively varying at each iteration and are determined automatically in this sense ifasda is a parameter free algorithm this advantage makes the algorithm more attractive and practical the effectiveness of ifasda is experimentally illustrated on problems of image deblurring with gaussian and impulse noise improvements in both psnr and visual quality of ifasda over a typical existing method are demonstrated in addition fast ifasda an accelerated algorithm of ifasda is also developed

real stability radii of linear time invariant time delay systems in this paper the real stability radii for perturbed linear differential equations of the retarded and neutral type are investigated we present the corresponding readily computable formulae with respect to an arbitrary stability region in the complex plane the results are further extended to the case of linear discrete time delay systems

using uncorrupted neighborhoods of the pixels for impulsive noise suppression with anfis in this paper a novel adaptive network based fuzzy inference system anfis based filter abf is presented for the restoration of images corrupted by impulsive noise in the abf is performed in two steps in the first step impulse detection is realized by using statistical tools in the second step a nonlinear filtering scheme based on anfis is performed for only the corrupted pixels detected in the first step to demonstrate the effectivity of abf at the removal of high level in extensive simulations were realized for abf and nine different comparison filters empirical results indicate that the proposed filter achieves a better performance than the comparison filters in terms of noise suppression and detail preservation even when the images are highly corrupted by in

the barzilai and borwein gradient method for the large scale unconstrained minimization problem the barzilai and borwein gradient method for the solution of large scale unconstrained minimization problems is considered this method requires few storage locations and very inexpensive computations furthermore it does not guarantee descent in the objective function and no line search is required recently the global convergence for the convex quadratic case has been established however for the nonquadratic case the method needs to be incorporated in a globalization scheme in this work a nonmonotone line search strategy that guarantees global convergence is combined with the barzilai and borwein method this strategy is based on the nonmonotone line search technique proposed by grippo lampariello and lucidi siam j numer anal 23 1986 pp 707 716 numerical results to compare the behavior of this method with recent implementations of the conjugate gradient method are presented these results indicate that the global barzilai and borwein method may allow some significant reduction in the number of line searches and also in the number of gradient evaluations

finite element techniques for removing the mixture of gaussian and impulsive noise the finite element method has become a very powerful and popular tool to solve boundary value problems coming from science and engineering here we consider a scattered data fitting method based on the finite element method and apply the method to remove the mixture of gaussian and impulsive noise from an image numerical results show the performance of the approach

a fast integral equation method for solid particles in viscous flow using quadrature by expansion boundary integral methods are advantageous when simulating viscous flow around rigid particles due to the reduction in number of unknowns and straightforward handling of the geometry in this work

an efficient algorithm for finding the d stability bound of discrete singularly perturbed systems with multiple time delays in this paper we present an original work on the d stabilization problem of discrete singularly perturbed systems with multiple time delays a new robust d stability criterion in terms of stability radius is first derived to guarantee that all poles of the discrete multiple time delay systems remain inside the specific disk d alpha r uncertainties then by using the technique of time scale separation we derive the corresponding slow and fast subsystems of a discrete multiple time delay singularly perturbed system the state feedback controls for the d stabilization of the slow and the fast subsystems are separately designed and a composite state feedback control for the original system is subsequently synthesized from these state feedback controls thereafter we derive a frequency domain epsilon dependent dstability criterion for the original discrete multiple time delay singularly perturbed system under the composite state feedback control if any one of the conditions of this criterion is fulfilled

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

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

an efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise we extend the alternating minimization algorithm recently proposed in y wang j yang w yin and y zhang siam j imag sci 1 2008 pp 248 272 j yang w yin y zhang and y wang siam j imag sci 2 2009 pp 569 592 to the case of recovering blurry multichannel color images corrupted by impulsive rather than gaussian noise the algorithm minimizes the sum of a multichannel extension of total variation and a data fidelity term measured in the ell 1 norm and is applicable to both salt and pepper and random valued impulsive noise we derive the algorithm by applying the well known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and q linear convergence rate under periodic boundary conditions the main computational requirements of the algorithm are fast fourier transforms and a low complexity gaussian elimination procedure numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm in addition it is numerically compared to the least absolute deviation method h y fu m k ng m nikolova and j l barlow siam j sci comput 27 2006 pp 1881 1902 and the two phase method j f cai r chan and m nikolova aims j inverse problems and imaging 2 2008 pp 187 204 for recovering grayscale images we also present results of recovering multichannel images

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

a weighted dictionary learning model for denoising images corrupted by mixed noise this paper proposes a general weighted l2 l0 norms energy minimization model to remove mixed noise such as gaussian gaussian mixture impulse noise and gaussian impulse noise from the images the approach is built upon maximum likelihood estimation framework and sparse representations over a trained dictionary rather than optimizing the likelihood functional derived from a mixture distribution we present a new weighting data fidelity function which has the same minimizer as the original likelihood functional but is much easier to optimize the weighting function in the model can be determined by the algorithm itself and it plays a role of noise detection in terms of the different estimated noise parameters by incorporating the sparse regularization of small image patches the proposed method can efficiently remove a variety of mixed or single noise while preserving the image textures well in addition a modified k svd algorithm is designed to address the weighted rank one approximation the experimental results demonstrate its better performance compared with some existing methods

minimizers of cost functions involving nonsmooth data fidelity terms application to the processing of outliers we present a theoretical study of the recovery of an unknown vector x in mathbb r p such as a signal or an image from noisy data y in mathbb r q by minimizing with respect to x a regularized cost function cal f x y psi x y alpha phi x where psi is a data fidelity term phi is a smooth regularization term and alpha 0 is a parameter typically psi x y ax y 2 where a is a linear operator the data fidelity terms psi involved in regularized cost functions are generally smooth functions only a few papers make an exception to this and they consider restricted situations nonsmooth data fidelity terms are avoided in image processing in spite of this we consider both smooth and nonsmooth data fidelity terms our goal is to capture essential features exhibited by the local minimizers of regularized cost functions in relation to the smoothness of the data fidelity term in order to fix the context of our study we consider psi x y sum i psi a i tx y i where a i t are the rows of a and psi is cal c m on mathbb r setminus 0 we show that if psi 1 0 psi 1 0 then typical data y give rise to local minimizers hat x of cal f y which fit exactly a certain number of the data entries there is a possibly large set hat h of indexes such that a i t hat x y i for every i in hat h in contrast if psi is smooth on mathbb r for almost every y the local minimizers of cal f y do not fit any entry of y thus the possibility that a local minimizer fits some data entries is due to the nonsmoothness of the data fidelity term this is a strong mathematical property which is useful in practice by way of application we construct a cost function allowing aberrant data outliers to be detected and to be selectively smoothed our numerical experiments advocate the use of nonsmooth data fidelity terms in regularized cost functions for special purposes in image and signal processing

integral equation methods for stokes flow and isotropic elasticity in the plane we present a class of integral equation methods for the solution of biharmonic boundary value problems with applications to two dimensional stokes flow and isotropic elasticity the domains may be multiply connected and finite infinite or semi infinite in extent our analytic formulation is based on complex variables and our fast multipole based iterative solution procedure requireso n operations wherenis the number of nodes in the discretization of the boundary the performance of the methods is illustrated with several large scale numerical examples

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

weighted couple sparse representation with classified regularization for impulse noise removal many impulse noise in reduction methods suffer from two obstacles the improper noise detectors and imperfect filters they used to address such issue in this paper a weighted couple sparse representation model is presented to remove in in the proposed model the complicated relationships between the reconstructed and the noisy images are exploited to make the coding coefficients more appropriate to recover the noise free image moreover the image pixels are classified into clear slightly corrupted and heavily corrupted ones different data fidelity regularizations are then accordingly applied to different pixels to further improve the denoising performance in our proposed method the dictionary is directly trained on the noisy raw data by addressing a weighted rank one minimization problem which can capture more features of the original data experimental results demonstrate that the proposed method is superior to several state of the art denoising methods

robustness of discrete systems under structured uncertainties we give a sufficient condition for the robust stability of the discrete system x k 1 f e x k where the perturbation e is bounded e u a necessary and sufficient condition is derived in the case where f is a positive or a negative matrix and u f the stability of interval matrices is also considered numerical examples are given for illustration

d stability of continuous time delay systems subjected to a class of highly structured perturbations the d stability testing problem for continuous time delay systems subjected to a class of highly structured parametric perturbations is addressed in this note by means of the lyapunov stability theorem razumikhin type theorem gersgorin theorem concept of spectral radius and norm and matrix measure techniques the author has developed several new sufficient conditions for guaranteeing that all characteristic roots of the above systems are located inside a specified disk d spl alpha r with center at spl alpha j0 and radius r in the left half complex plane for the present results it is not necessary to solve any lyapunov equation which may be unsolvable though the lyapunov stability theorem is utilized

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

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

the idude framework for grayscale image denoising we present an extension of the discrete universal denoiser dude specialized for the denoising of grayscale images the original dude is a low complexity algorithm aimed at recovering discrete sequences corrupted by discrete memoryless noise of known statistical characteristics it is universal in the sense of asymptotically achieving without access to any information on the statistics of the clean sequence the same performance as the best denoiser that does have access to such information the dude however is not effective on grayscale images of practical size the difficulty lies in the fact that one of the dude s key components is the determination of conditional empirical probability distributions of image samples given the sample values in their neighborhood when the alphabet is relatively large as is the case with grayscale images even for a small sized neighborhood the required distributions would be estimated from a large collection of sparse statistics resulting in poor estimates that would not enable effective denoising the present work enhances the basic dude scheme by incorporating statistical modeling tools that have proven successful in addressing similar issues in lossless image compression instantiations of the enhanced framework which is referred to as idude are described for examples of additive and nonadditive noise the resulting denoisers significantly surpass the state of the art in the case of salt and pepper s p and ary symmetric noise and perform well for gaussian noise

an lmi approach to d stability and d stabilization of linear discrete singular systems with state delay abstract the problems of d stability and d stabilization for linear discrete singular systems with state delay are addressed in this paper by using the state augmentation technique a necessary and sufficient d stability condition and a sufficient d stabilization condition for linear discrete singular time delay systems are firstly proposed then based on these conditions quadratic d stability and d stabilization conditions for linear discrete singular time delay systems with norm bounded uncertainties and interval uncertainties are obtained respectively both the d stability and d stabilization conditions are proposed in terms of linear matrix inequalities finally illustrative examples show that the proposed conditions are effective to check the d stability and to design the d stabilizing controller for linear discrete singular time delay systems

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

robust controller design for uncertain linear systems with circular pole constraints in this paper the problem of robust controller design for uncertain linear continuous and discrete time systems with circular pole constraints is considered the problem we address is the design of robust state feedback controllers such that all poles of the closed loop systems are placed within a prescribed circular region sufficient conditions for the existence of the desired controllers are given based on the generalized inverse theory the analytical expression of the set of desired controllers is also presented it is emphasized that when the uncertainties are absent the results include the characterization of all state feedback controllers achieving the specified circular pole constraints an illustrative example is given to show the applicability of the proposed design procedure accepted in final revised form 7 february 1996 communicated by professor h kimura

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

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

fast multilevel algorithm for a minimization problem in impulse noise removal an effective 2 phase method for removing impulse noise was recently proposed its phase 1 identifies noisy pixel candidates by using median type filters then in phase 2 it restores only the noisy pixel candidates by some variational methods the resulting method can handle salt and pepper noise and random valued impulse noise at a level as high as 90 and 60 respectively the aim of this paper is to generalize a fast multilevel method for gaussian denoising to solving the minimization problem arising in phase 2 of the 2 phase method the multilevel algorithm gives better images than standard optimization methods such as the newton method or the conjugate gradient method also it can handle more general regularization functionals than the smooth ones previously considered supporting numerical experiments on two dimensional gray scale images are presented

an improved recursive median filtering scheme for image processing in a recent publication it was shown that median filtering is an optimization process in which a two term cost function is minimized based on this functional optimization property of the median filtering process a new approach for designing the recursive median filter for image processing applications is introduced in this paper we prove that the new approach is guaranteed to converge to root within a finite number of iterations the new method is applied to process a real image corrupted by pseudorandom impulsive noise and the results show that the new scheme provides improved mean square error rise performance over the standard recursive median filters

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

low rank prior in single patches for nonpointwise impulse noise removal this paper introduces a low rank prior in small oriented noise free image patches considering an oriented patch as a matrix a low rank matrix approximation is enough to preserve the texture details in the optimally oriented patch based on this prior we propose a single patch method within a generalized joint low rank and sparse matrix recovery framework to simultaneously detect and remove nonpointwise random valued impulse noise e g very small blobs a weighting matrix is incorporated in the framework to encode an initial estimate of the spatial noise distribution an accelerated proximal gradient method is adapted to estimate the optimal noise free image patches experiments show the effectiveness of our framework in detecting and removing nonpointwise random valued impulse noise

robust scale space filter using second order partial differential equations this paper describes a robust scale space filter that adaptively changes the amount of flux according to the local topology of the neighborhood in a manner similar to modeling heat or temperature flow in physics the robust scale space filter is derived by coupling fick s law with a generalized continuity equation in which the source or sink is modeled via a specific heat capacity the filter plays an essential part in two aspects first an evolution step size is adaptively scaled according to the local structure enabling the proposed filter to be numerically stable second the influence of outliers is reduced by adaptively compensating for the incoming flux we show that classical diffusion methods represent special cases of the proposed filter by analyzing the stability condition of the proposed filter we also verify that its evolution step size in an explicit scheme is larger than that of the diffusion methods the proposed filter also satisfies the maximum principle in the same manner as the diffusion our experimental results show that the proposed filter is less sensitive to the evolution step size as well as more robust to various outliers such as gaussian noise impulsive noise or a combination of the two

stokes flow around cylinders in a bounded two dimensional domain using multipole accelerated boundary element methods the multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from o n2 iterative solvers or o n3 gaussian elimination to o n log n or o n where n is the number of nodes in the discretized system such a reduction in the growth of the calculation time and data storage is crucial in applications where n is large such as when modelling the macroscopic behaviour of suspensions of particles in such cases a minimum of 1000 particles is needed to obtain statistically meaningful results leading to systems with n of the order of 10 000 for the smallest problems when only boundary velocities are known the indirect boundary element formulation for stokes flow results in fredholm equations of the second kind which generally produce a well posed set of equations when discretized a necessary requirement for iterative solution methods the direct boundary element formulation on the other hand results in fredholm equations of the first kind which upon discretization produce ill conditioned systems of equations the model system here is a two dimensional wide gap couette viscometer where particles are suspended in the fluid between the cylinders this is a typical system that is efficiently modelled using boundary element method simulations the multipolar technique is applied to both direct and indirect formulations it is found that the indirect approach is sufficiently well conditioned to allow the use of fast multipole methods the direct approach results in severe ill conditioning to a point where application of the multipole method leads to non convergence of the solution iteration copyright 1999 john wiley sons ltd

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

noise adaptive soft switching median filter existing state of the art switching based median filters are commonly found to be nonadaptive to noise density variations and prone to misclassifying pixel characteristics at high noise density interference this reveals the critical need of having a sophisticated switching scheme and an adaptive weighted median filter we propose a novel switching based median filter with incorporation of fuzzy set concept called the noise adaptive soft switching median nasm filter to achieve much improved filtering performance in terms of effectiveness in removing impulse noise while preserving signal details and robustness in combating noise density variations the proposed nasm filter consists of two stages a soft switching noise detection scheme is developed to classify each pixel to be uncorrupted pixel isolated impulse noise nonisolated impulse noise or image object s edge pixel no filtering or identity filter standard median sm filter or our developed fuzzy weighted median fwm filter will then be employed according to the respective characteristic type identified experimental results show that our nasm filter impressively outperforms other techniques by achieving fairly close performance to that of ideal switching median filter across a wide range of noise densities ranging from 10 to 70

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

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

d stability robustness for linear discrete uncertain singular systems with delayed perturbations in this paper the robust d stability problem i e the robust eigenvalue clustering in a specified circular region problem of linear discrete singular systems with both structured elemental parameter uncertainties and delayed perturbations is investigated under the assumptions that the linear discrete nominal singular system is regular and causal and has all its finite eigenvalues lying inside a specified circular region by using the maximum modulus principle and the spectral radius of matrices a new sufficient condition is proposed to preserve the assumed properties when both structured parameter uncertainties and delayed perturbations are added into the linear discrete nominal singular system when all the finite eigenvalues lie inside the unit circle of the z plane the proposed criterion will become the stability robustness criterion the proposed criterion is mathematically proved and numerically shown respectively to be less conservative than the existing ones reported recently

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

a robust hidden markov gauss mixture vector quantizer for a noisy source noise is ubiquitous in real life and changes image acquisition communication and processing characteristics in an uncontrolled manner gaussian noise and salt and pepper noise in particular are prevalent in noisy communication channels camera and scanner sensors and medical mri images it is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images for example hidden markov gauss mixture models hmgmm have been shown to perform well in image segmentation applications but they are quite sensitive to image noise we propose a modified hmgmm procedure specifically designed to improve performance in the presence of noise the key feature of the proposed procedure is the adjustment of covariance matrices in gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion mdi in adjusting covariance matrices we expand or shrink their elements based on the noisy image while most results reported in the literature assume a particular noise type we propose a framework without assuming particular noise characteristics without denoising the corrupted source we apply our method directly to the segmentation of noisy sources we apply the proposed procedure to the segmentation of aerial images with salt and pepper noise and with independent gaussian noise and we compare our results with those of the median filter restoration method and the blind deconvolution based method respectively we show that our procedure has better performance than image restoration based techniques and closely matches to the performance of hmgmm for clean images in terms of both visual segmentation results and error rate

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

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

d stability analysis for discrete systems with a time delay this paper first discusses the d pole placement problem of discrete time delay systems some criteria are proposed to ensure that all the closed loop eigenvalues of discrete systems with a time delay are located inside a specific disk d r centered at 0 with radius r then several sufficient conditions for guaranteeing the d stability of discrete time delay systems subjected to parametric perturbations are presented both unstructured and highly structured parametric perturbations are considered by these sufficient conditions the tolerable parametric perturbation bounds that ensure all the closed loop poles of discrete time delay perturbed systems to remain inside the desired disk d r can be estimated finally illustrative examples are given for demonstration

selective removal of impulse noise based on homogeneity level information we propose a decision based signal adaptive median filtering algorithm for removal of impulse noise our algorithm achieves accurate noise detection and high snr measures without smearing the fine details and edges in the image the notion of homogeneity level is defined for pixel values based on their global and local statistical properties the cooccurrence matrix technique is used to represent the correlations between a pixel and its neighbors and to derive the upper and lower bound of the homogeneity level noise detection is performed at two stages noise candidates are first selected using the homogeneity level and then a refining process follows to eliminate false detections the noise detection scheme does not use a quantitative decision measure but uses qualitative structural information and it is not subject to burdensome computations for optimization of the threshold values empirical results indicate that our scheme performs significantly better than other median filters in terms of noise suppression and detail preservation

pole assignment in a specified disk the problem of assigning all poles of a closed loop system in a specified disk by state feedback is considered for both continuous and discrete systems a state feedback control law is determined by using a discrete riccati equation this kind of pole assignment problem is named d pole assignment and its relation to the optimal control problem and its robustness properties are discussed the gain and phase margins for all closed loop poles to stay inside the specified disk d are determined for the proposed control

probabilistic tensor canonical polyadic decomposition with orthogonal factors tensor canonical polyadic decomposition cpd which recovers the latent factor matrices from multidimensional data is an important tool in signal processing in many applications some of the factor matrices are known to have orthogonality structure and this information can be exploited to improve the accuracy of latent factors recovery however existing methods for cpd with orthogonal factors all require the knowledge of tensor rank which is difficult to acquire and have no mechanism to handle outliers in measurements to overcome these disadvantages in this paper a novel tensor cpd algorithm based on the probabilistic inference framework is devised in particular the problem of tensor cpd with orthogonal factors is interpreted using a probabilistic model based on which an inference algorithm is proposed that alternatively estimates the factor matrices recovers the tensor rank and mitigates the outliers simulation results using synthetic data and real world applications are presented to illustrate the excellent performance of the proposed algorithm in terms of accuracy and robustness

image deblurring in the presence of impulsive noise consider the problem of image deblurring in the presence of impulsive noise standard image deconvolution methods rely on the gaussian noise model and do not perform well with impulsive noise the main challenge is to deblur the image recover its discontinuities and at the same time remove the impulse noise median based approaches are inadequate because at high noise levels they induce nonlinear distortion that hampers the deblurring process distinguishing outliers from edge elements is difficult in current gradient based edge preserving restoration methods the suggested approach integrates and extends the robust statistics line process half quadratic and anisotropic diffusion points of view we present a unified variational approach to image deblurring and impulse noise removal the objective functional consists of a fidelity term and a regularizer data fidelity is quantified using the robust modified l 1 norm and elements from the mumford shah functional are used for regularization we show that the mumford shah regularizer can be viewed as an extended line process it reflects spatial organization properties of the image edges that do not appear in the common line process or anisotropic diffusion this allows to distinguish outliers from edges and leads to superior experimental results

technical communique d stability and d stabilization of linear discrete time delay systems with polytopic uncertainties sufficient conditions for d stability and d stabilization of linear discrete time delay systems with polytopic uncertainties are proposed in this paper the results are based on parameter dependent lyapunov functions obtained from the feasibility of a set of linear matrix inequalities defined at the vertices of polytopic systems these conditions guarantee all the poles of a corresponding system in a specified circular region finally an illustrative example shows that the proposed conditions are effective to check the d stability and to design the d stabilizing controller for linear discrete time delay systems

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

a robust bi sparsity model with non local regularization for mixed noise reduction sparse representation model srm has been widely used in many image processing and computer vision tasks however the conventional srm usually neglects the prior knowledge about similar signals considering the fact that similar signals also have subtle differences in this paper we propose a robust bi sparsity model rbsm to effectively exploit the prior knowledge about the similarities and the distinctions of signals in rbsm similar signals are encouraged to be coded on the same sub dictionary but the distinctiveness of similar signals is also addressed by imposing the l0 norm regularization on the difference between each coefficient and its non local means in addition a weight vector is incorporated into the loss function to make the proposed model robust to outliers we apply rbsm for mixed noise reduction and experimental results show that our proposed model is superior to several state of the art mixed noise removal methods