euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

on the dependence of analytic solutions of partial differential equations on the right hand side given a nonzero polynomial p z a m a0z0 on cn martineau proved in the 1960s that for each convex domain g of cn the partial differential operator p d f eai m aa0f c acting on the frechet space a g of all analytic functions on g is surective in the present paper it is investigated whether solutions f of the equation p d f g can be chosen as f r g with a continuous linear operator r a g a g for bounded g we give a necessary and sufficient condition for the existence of such an r

compressive sensing via nonlocal low rank regularization sparsity has been widely exploited for exact reconstruction of a signal from a small number of random measurements recent advances have suggested that structured or group sparsity often leads to more powerful signal reconstruction techniques in various compressed sensing cs studies in this paper we propose a nonlocal low rank regularization nlr approach toward exploiting structured sparsity and explore its application into cs of both photographic and mri images we also propose the use of a nonconvex log det x as a smooth surrogate function for the rank instead of the convex nuclear norm and justify the benefit of such a strategy using extensive experiments to further improve the computational efficiency of the proposed algorithm we have developed a fast implementation using the alternative direction multiplier method technique experimental results have shown that the proposed nlr cs algorithm can significantly outperform existing state of the art cs techniques for image recovery

l2 l filtering for stochastic systems driven by poisson processes and wiener processes this paper investigates the l2 l filtering problem for stochastic systems driven by poisson processes and wiener processes firstly this paper presents an approach to transform the expectation of stochastic integral with respect to poisson process into the expectation of lebesgue integral by the martingale theory then based on this a filter is designed to guarantee that the filtering error system is mean square asymptotically stable and its l2 l performance satisfies a prescribed level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

a versatile technique for the optimal approximation of random processes by functional quantization this paper presents the mathematical foundation of a novel and versatile technique for the approximation of random processes using the functional quantization concept in this approach random processes are represented by optimal quantizers that is finite collections of deterministic functions and corresponding probability masses that are carefully constructed to attain certain optimal properties although the computational cost of obtaining such optimal quantizers is not negligible their use in applications is simple and relatively inexpensive the paper has two objectives first we present an accessible overview of functional quantization theory second we introduce a novel methodology to compute optimal quantizers which is based on the classical lloyd s method and monte carlo simulation for validation purposes the proposed methodology is tested using two fundamental gaussian random processes brownian motion and fractional brownian motion for which optimal quantizers are known the results obtained compare very well with previous results reported in the literature then to demonstrate the unique versatility of the methodology the application to a non gaussian process is presented

adaptive multiregression in reproducing kernel hilbert spaces the multiaccess mimo channel case this paper introduces a wide framework for online i e time adaptive supervised multiregression tasks the problem is formulated in a general infinite dimensional reproducing kernel hilbert space rkhs in this context a fairly large number of nonlinear multiregression models fall as special cases including the linear case any convex continuous and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response the only requirement is the subgradient of the adopted loss function to be available in an analytic form to this end we demonstrate a way to calculate the subgradients of robust loss functions suitable for the multiregression task as it is by now well documented when dealing with online schemes in rkhs the memory keeps increasing with each iteration step to attack this problem a simple sparsification strategy is utilized which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters a convergence analysis of the technique based on arguments of convex analysis is also provided to demonstrate the capacity of the proposed method the multiregressor is applied to the multiaccess multiple input multiple output channel equalization task for a setting with poor resources and nonavailable channel information numerical results verify the potential of the method when its performance is compared with those of the state of the art linear techniques which in contrast use space time coding more antenna elements as well as full channel information

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

variance constrained h control for a class of nonlinear stochastic discrete time varying systems in this paper a general event triggered framework is set up to deal with the variance constrained h control problem for a class of discrete time varying systems with randomly occurring saturations stochastic nonlinearities and state multiplicative noises based on the relative error with respect to the measurement signal an event indicator variable is introduced and the corresponding event triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not the stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well studied nonlinearities a set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations stochastic nonlinearities and state dependent noises the purpose of the addressed multiobjective control problem is to design a set of time varying output feedback controller such that over a finite horizon the closed loop system achieves both the prescribed h noise attenuation level and the state covariance constraints a recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite horizon controllers and the analytical characterization of such controllers is also given simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme

reproducing kernel hilbert spaces and fractal interpolation reproducing kernel hilbert spaces rkhss are a very useful and powerful tool of functional analysis with application in many diverse paradigms such as multivariate statistics and machine learning fractal interpolation on the other hand is a relatively recent technique that generalizes traditional interpolation through the introduction of self similarity in this work we show that the functional space of any family of recurrent fractal interpolation functions r fifs constitutes an rkhs with a specific associated kernel function thus extending considerably the toolbox of known kernel functions and introducing fractals to the rkhs world we also provide the means for the computation of the kernel function that corresponds to any specific fractal rkhs and give several examples

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

brief paper non fragile h filter design for linear continuous time systems this paper studies the problem of non fragile h filter design for linear continuous time systems the filter to be designed is assumed to include additive gain variations which result from filter implementations a notion of structured vertex separator is proposed to approach the problem and exploited to develop sufficient conditions for the non fragile h filter design in terms of solutions to a set of linear matrix inequalities lmis the designs guarantee the asymptotic stability of the estimation errors and the h performance of the system from the exogenous signals to the estimation errors below a prescribed level a numerical example is given to illustrate the effect of the proposed method

h 2 and h_ infty robust filtering for discrete time linear systems this paper investigates robust filtering design problems in h2 and h infty spaces for discrete time systems subjected to parameter uncertainty which is assumed to belong to a convex bounded polyhedral domain it is shown that by a suitable change of variables both design problems can be converted into convex programming problems written in terms of linear matrix inequalities lmi the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h2 and h infty filters are proven to be of the same order as the order of the system comparisons with robust filters for systems subjected to norm bounded uncertainty are provided in both theoretical and practical settings in particular it is shown that under the same assumptions the results here are generally better as far as the minimization of a guaranteed cost expressed in terms of h2 or h infty norms is considered some numerical examples illustrate the theoretical results

image inpainting using reproducing kernel hilbert space and heaviside functions image inpainting a technique of repairing damaged images is an important topic in image processing in this paper we solve the problem from an intensity function estimation perspective we assume the underlying image is defined on a continuous domain and belongs to a space spanned by a basis of a reproducing kernel hilbert space and some variations of the heaviside function the reproducing kernel hilbert space is used to model the smooth component of the image while heaviside function variations are used to model the edges the coefficients of the redundant basis are computed by the discrete intensity at undamaged domain we test the proposed model through various images numerical experiments show the effectiveness of the proposed method especially in recovering edges

stochastic input to state stability and h filtering for a class of stochastic nonlinear systems in this paper an h filtering problem is considered for a class of stochastic nonlinear systems with time delay and exogenous disturbances sufficient conditions for stochastic input to state stability siss of the stochastic nonlinear systems are developed via lyapunov function method and linear matrix inequalities lmis technique the purpose of this work is to design a nonlinear filter to ensure both the siss and a prescribed h attenuation level for the corresponding filtering error system by using the siss results a set of sufficient conditions for the existence of h filter is given in the form of lmi when the lmi is feasible an explicit expression of a desired filter is presented finally some numerical and practical examples are employed to demonstrate the effectiveness of the proposed approaches

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

robust stabilization for uncertain saturated time delay systems a distributed delay dependent polytopic approach this technical note investigates the robust stabilization problem for uncertain linear systems with discrete and distributed delays under saturated state feedback different from the existing approaches a distributed delay dependent polytopic approach is proposed in this technical note and the saturation nonlinearity is represented as the convex combination of state feedback and auxiliary distributed delay feedback then by incorporating an appropriate augmented lyapunov krasovskii l k functional and some integral inequalities the less conservative stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities lmis the effectiveness and reduced conservatism of the proposed conditions are illustrated by numerical examples

h and l 2 l finite horizon filtering with randomly occurring gain variations and quantization effects this paper investigates the h and l 2 l filtering problem for discrete stochastic nonlinear system with randomly occurring gain variations and quantization effects over a finite horizon the system under consideration is subject to time varying parameters and exogenous signals a bernoulli distributed white sequence with a known conditional probability is introduced to describe the binary switching phenomenon between two types of nonlinear disturbances the randomly occurring filter gain variations are utilized to express the random change of filter parameters that is governed by a binary sequences taking values on 0 or 1 moreover the quantization effects of measurements are also taken into account where a form of logarithmic quantizer is applied by using the recursive linear matrix inequalities rlmis approach sufficient conditions are established for the existence of the desired finite horizon filter to guarantee the h and l 2 l performance specifications at the same time a numerical example is proposed to show the correctness and effectiveness of the proposed design method

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

finite time stability and stabilization of ito stochastic systems with markovian switching mode dependent parameter approach this technical note is concerned about the finite time stability and stabilization for ito stochastic systems with markovian switching a mode dependent parameter approach is proposed to give a sufficient condition for finite time stability and its superiority to common parameter approach is analyzed moreover the finite time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities a n mode algorithm is given for solving the obtained matrix inequalities arising from finite time stability stabilization finally an example is employed to illustrate the effectiveness of our obtained results

filling in by joint interpolation of vector fields and gray levels a variational approach for filling in regions of missing data in digital images is introduced the approach is based on joint interpolation of the image gray levels and gradient isophotes directions smoothly extending in an automatic fashion the isophote lines into the holes of missing data this interpolation is computed by solving the variational problem via its gradient descent flow which leads to a set of coupled second order partial differential equations one for the gray levels and one for the gradient orientations the process underlying this approach can be considered as an interpretation of the gestaltist s principle of good continuation no limitations are imposed on the topology of the holes and all regions of missing data can be simultaneously processed even if they are surrounded by completely different structures applications of this technique include the restoration of old photographs and removal of superimposed text like dates subtitles or publicity examples of these applications are given we conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow

symmetries and other transformations of the complex monge ampere equation on definit des transformations tangentes en utilisant la structure symplectique holomorphe du fibre cotangent holomorphe

feedback fuzzy control for quantized networked systems with random delays this paper investigates the problem of feedback fuzzy control design for networked systems involving both random measurement and actuation delays and subject to quantization and random packet dropout it is assumed that system state or output signal is quantized before being communicated the paper focuses initially on an observer based output feedback fuzzy controller design and then derives a state feedback controller as special case sufficient conditions for the existence of an admissible fuzzy controller are established to ensure the exponential stability of the resulting closed loop fuzzy system simulation experiments on a lab scale four tank system to demonstrate the applicability of the designed fuzzy control algorithm

inpainting of binary images using the cahn hilliard equation image inpainting is the filling in of missing or damaged regions of images using information from surrounding areas we outline here the use of a model for binary inpainting based on the cahn hilliard equation which allows for fast efficient inpainting of degraded text as well as super resolution of high contrast images

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

rapid image completion system using multiresolution patch based directional and nondirectional approaches this study presents a rapid image completion system comprising a training or analysis process and an image completion or synthesis process the proposed system adopts a multiresolution approach which not only improves the convergence rate of the synthesis process but also provides the ability to deal with large replaced regions in the training process a down sampling approach is applied to create a patch based texture eigenspace based on multiresolution background region information in the image completion process an up sampling approach is applied to synthesize the replaced foreground regions to ensure the continuity of the geometric texture structure between the original background scene regions and the replaced foreground regions directional and nondirectional image completion approaches are developed to reconstruct the global geometric structure and to enhance the local detailed features of the replaced foreground regions in the lower and higher resolution level images respectively moreover the synthesis priority order of the individual patches and the appropriate choice of completion scheme i e directional or nondirectional are both determined in accordance with a hessian matrix decision value hmdv parameter finally a texture refinement process is performed to optimize the resolution of the synthesized result

convex univalent functions and continuous linear right inverses abstract for surjective infinite order differential operators on the space of holomorphic functions on a convex domain g other than the entire complex plane we characterize when they admit a continuous linear right inverse the characterization is given by a smoothness condition on g which is phrased in terms of the boundary behavior of the riemann mapping of the unit disc onto g

robust nonfragile kalman filtering for uncertain linear systems with estimator gain uncertainty the note is concerned with the problem of a robust nonfragile kalman filter design for a class of uncertain linear systems with norm bounded uncertainties the designed state estimator can tolerate multiplicative uncertainties in the state estimator gain matrix the robust nonfragile state estimator designs are given in terms of solutions to algebraic riccati equations the designs guarantee known upper bounds on the steady state error covariance a numerical example is given to illustrate the results

trajectory based design of robust non fragile controllers for a class of uncertain linear continuous time systems this paper deals with a design problem of robust non fragile stabilizing controllers for a class of uncertain linear continuous time systems the proposed design approach of robust non fragile controllers is based on computation of the trajectory for the uncertain linear system and differs from the existing methods based on quadratic stabilization via lyapunov criterion in this paper we show that sufficient conditions for asymptotical stability of the linear system with uncertainties and controller gain variations and a lmi based design algorithm of a robust non fragile controller furthermore we extend the result to the design problem of decentralized robust non fragile controllers for a class of uncertain large scale interconnected systems finally the effectiveness of the proposed design scheme of robust non fragile controllers is shown through illustrative examples

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding