Mobile robots are often subject to multiplicative noise in the target tracking tasks,where the multiplicative measurement noise is correlated with additive measurement noise.In this paper,first,a correlation multiplic...Mobile robots are often subject to multiplicative noise in the target tracking tasks,where the multiplicative measurement noise is correlated with additive measurement noise.In this paper,first,a correlation multiplicative measurement noise model is established.It is able to more accurately represent the measurement error caused by the distance sensor dependence state.Then,the estimated performance mismatch problem of Cubature Kalman Filter(CKF)under multiplicative noise is analyzed.An improved Gaussian filter algorithm is introduced to help obtain the CKF algorithm with correlated multiplicative noise.In practice,the model parameters are unknown or inaccurate,especially the correlation of noise is difficult to obtain,which can lead to a decrease in filtering accuracy or even divergence.To address this,an adaptive CKF algorithm is further provided to achieve reliable state estimation for the unknown noise correlation coefficient and thus the application of the CKF algorithm is extended.Finally,the estimated performance is analyzed theoretically,and the simulation study is conducted to validate the effectiveness of the proposed algorithm.展开更多
This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing an...This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.展开更多
The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the ...The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.展开更多
We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） an...We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.展开更多
This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon ap...This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.展开更多
Presented here is a new adaptive state filtering algorithm for systems with multiplicative noise. This algorithm estimates the vector state of the system and the statistics of noise when all the statistics of noise ar...Presented here is a new adaptive state filtering algorithm for systems with multiplicative noise. This algorithm estimates the vector state of the system and the statistics of noise when all the statistics of noise are unknown. This filtering algorithm is a simple recursive structure. A simulation example is presented which demonstrates the effectiveness of this filtering algorithm.展开更多
This paper studies the nonstationary filtering problem of Markov jump system under <span style="white-space:nowrap;"><i>l</i><sub>2</sub> - <i>l</i><sub>...This paper studies the nonstationary filtering problem of Markov jump system under <span style="white-space:nowrap;"><i>l</i><sub>2</sub> - <i>l</i><sub>∞</sub> </span>performance. Due to the difference in propagation channels, signal strength and phase will inevitably change randomly and cause the waste of signals resources. In response to this problem, a channel fading model with multiplicative noise is introduced. And then a nonstationary filter, which receives signals more efficiently is designed. Meanwhile Lyapunov function is constructed for error analysis. Finally, the gain matrix for filtering is obtained by solving the matrix inequality, and the results showed that the nonstationary filter converges to the stable point more quickly than the traditional asynchronous filter, the stability of the designed filter is verified.展开更多
This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks （MJSNNs） subject to mode-dependent time-varying interval delay and state-multiplicative noise....This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks （MJSNNs） subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality （LMI） format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.展开更多
A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is dev...A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is developed. The stochastic 2 D FMM Ⅱ with multiplicative noise can be reduced to a 1 D model, and the proposed optimal filtering algorithm for the stochastic 2 D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1 D systems. An example is given to illustrate the validity of this algorithm.展开更多
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motiva...Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.展开更多
In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm ...In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the展开更多
On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented K...On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.展开更多
This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in ...This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.展开更多
A decentralized parallel one-pass deconvolution algorithm for multisensor systems with multiplicative noises is proposed. Comparing with the conventional deconvolution algorithm, it avoids the computational overload a...A decentralized parallel one-pass deconvolution algorithm for multisensor systems with multiplicative noises is proposed. Comparing with the conventional deconvolution algorithm, it avoids the computational overload and the high storage requirement. The algorithm is optimal in the sense of linear minimum-variance. The simulation results illustrate the validity of the proposed algorithm.展开更多
The dynamical characters of a theoretical anti-tumor model under immune surveillance subjected to a pure multiplicative noise are investigated. The effects of pure multiplicative noise on the stationary probability di...The dynamical characters of a theoretical anti-tumor model under immune surveillance subjected to a pure multiplicative noise are investigated. The effects of pure multiplicative noise on the stationary probability distribution （SPD） and the mean first passage time （MFPT） are analysed based on the approximate Fokker-Planck equation of the system in detail. For the anti-tumor model, with the multiplieative noise intensity D increasing, the tumor population move towards to extinction and the extinction rate can be enhanced. Numerical simulations are carried out to check the approximate theoretical results. Reasonably good agreement is obtained.展开更多
This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a suffi...This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.展开更多
This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimiz...This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.展开更多
Multiplicative noise removal is a challenging problem in image denoising.In this paper,we develop a nonlocal matrix rank minimization method for the multiplicative noise removal problem.By utilizing the logarithm tran...Multiplicative noise removal is a challenging problem in image denoising.In this paper,we develop a nonlocal matrix rank minimization method for the multiplicative noise removal problem.By utilizing the logarithm transformation,we convert the problem into an additive noise removal problem and propose a maximum a posteriori(MAP)estimation-based matrix rank minimization model for this kind of additive noise removal.A proximal alternating algorithm is designed to solve the matrix rank minimization model.The convergence of the algorithm is demonstrated by the famous Kurdyka-Lojasiewicz property.Taking advantage of the proposed matrix rank minimization model and its proximal alternating algorithm,a multiplicative noise removal method is finally developed.Numerical experiments illustrate that the proposed method can remove multiplicative noise in images much better than the existing state-of-the-art methods in terms of both image recovered measure quantities and visual qualities.展开更多
This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （...This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61773147 and 62033010)Zhejiang Provincial Nature Science Foundation of China(Nos.LR17F030005 and LZ21F030004)Key-Area Research and Development Program of Guangdong Province,china(No.2018B010107002)。
文摘Mobile robots are often subject to multiplicative noise in the target tracking tasks,where the multiplicative measurement noise is correlated with additive measurement noise.In this paper,first,a correlation multiplicative measurement noise model is established.It is able to more accurately represent the measurement error caused by the distance sensor dependence state.Then,the estimated performance mismatch problem of Cubature Kalman Filter(CKF)under multiplicative noise is analyzed.An improved Gaussian filter algorithm is introduced to help obtain the CKF algorithm with correlated multiplicative noise.In practice,the model parameters are unknown or inaccurate,especially the correlation of noise is difficult to obtain,which can lead to a decrease in filtering accuracy or even divergence.To address this,an adaptive CKF algorithm is further provided to achieve reliable state estimation for the unknown noise correlation coefficient and thus the application of the CKF algorithm is extended.Finally,the estimated performance is analyzed theoretically,and the simulation study is conducted to validate the effectiveness of the proposed algorithm.
基金Sponsored by the National NSF (10901121, 10826091,10771074, and 10771139)NSF for Postdoctors in China (20090460952)+3 种基金NSF of Zhejiang Province (Y6080077)NSF of Guangdong Province (004020077)NSF of Wenzhou University (2008YYLQ01)Zhejiang youthteacher training project and Wenzhou 551 project
文摘This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.
基金supported by the National Natural Science Foundation of China (61174121,61121003)the National High Technology Researchand Development Program of China (863 Program) (2008AA121302)+1 种基金the National Basic Research Program of China (973 Program)(2009CB724000)the Research Fund for the Doctoral Program of Higher Education of China
文摘The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.
基金supported by China NSF(11271388)Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1400430)Basis and Frontier Research Project of Chongqing(cstc2014jcyj A00035)
文摘We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.
基金This work was supported by the Taishan Scholar Construction Engineering by Shandong Government and the National Natural Science Foundation of China （Nos. 61120106011, 61203029）.
文摘This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.
文摘Presented here is a new adaptive state filtering algorithm for systems with multiplicative noise. This algorithm estimates the vector state of the system and the statistics of noise when all the statistics of noise are unknown. This filtering algorithm is a simple recursive structure. A simulation example is presented which demonstrates the effectiveness of this filtering algorithm.
文摘This paper studies the nonstationary filtering problem of Markov jump system under <span style="white-space:nowrap;"><i>l</i><sub>2</sub> - <i>l</i><sub>∞</sub> </span>performance. Due to the difference in propagation channels, signal strength and phase will inevitably change randomly and cause the waste of signals resources. In response to this problem, a channel fading model with multiplicative noise is introduced. And then a nonstationary filter, which receives signals more efficiently is designed. Meanwhile Lyapunov function is constructed for error analysis. Finally, the gain matrix for filtering is obtained by solving the matrix inequality, and the results showed that the nonstationary filter converges to the stable point more quickly than the traditional asynchronous filter, the stability of the designed filter is verified.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006,60521003)the National High Technology Research and Development Program of China (863 Program) (Grant No 2006AA04Z183)+2 种基金the Natural Science Foundation of Liaoning Province of China (Grant No 20062018)973 Project (Grant No 2009CB320601)111 Project (Grant No B08015)
文摘This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks （MJSNNs） subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality （LMI） format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.
基金supported by NSFS Project for Tianyuan Mathematical Fund(No.A0324676)the Science&Technology Research Key Projects of the Ministry of Education of China(No.02131).
文摘A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is developed. The stochastic 2 D FMM Ⅱ with multiplicative noise can be reduced to a 1 D model, and the proposed optimal filtering algorithm for the stochastic 2 D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1 D systems. An example is given to illustrate the validity of this algorithm.
基金Project supported by the National Natural Science Foundation of China(Nos.11126160,11201475,11371183,and 11101356)
文摘In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
文摘Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.
基金supported by the National Natural Science Foundation of China(11101218)Natural Science Fouadation for Colleges and Universities in Jangsu Province(11KJB110009)the Scientific Research Foundation of NUPT(NY209025)
文摘In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the
基金supported by the National Natural Science Foundation of China (Grant No 60774067)the Natural Science Foundation of Fujian Province of China (Grant No 2006J0017)
文摘On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.
文摘This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.
基金This work was supported by the Science&Technology Research Key Projects of Ministry of Education of China.
文摘A decentralized parallel one-pass deconvolution algorithm for multisensor systems with multiplicative noises is proposed. Comparing with the conventional deconvolution algorithm, it avoids the computational overload and the high storage requirement. The algorithm is optimal in the sense of linear minimum-variance. The simulation results illustrate the validity of the proposed algorithm.
基金Supported by the Natural Science Foundation of China under Grant No.10865006the Science Foundation of the Education Bureau of Shaanxi Province under Grant No.09JK331the Science Foundation of Baoji University of Science and Arts of China under Grant No.Zk0725
文摘The dynamical characters of a theoretical anti-tumor model under immune surveillance subjected to a pure multiplicative noise are investigated. The effects of pure multiplicative noise on the stationary probability distribution （SPD） and the mean first passage time （MFPT） are analysed based on the approximate Fokker-Planck equation of the system in detail. For the anti-tumor model, with the multiplieative noise intensity D increasing, the tumor population move towards to extinction and the extinction rate can be enhanced. Numerical simulations are carried out to check the approximate theoretical results. Reasonably good agreement is obtained.
基金supported by the National Natural Science Foundation of China under Grants 61821004,62250056,62350710214,U23A20325,62350055the Natural Science Foundation of Shandong Province,China(ZR2021ZD14,ZR2021JQ24)+2 种基金High-level Talent Team Project of Qingdao West Coast New Area,China(RCTD-JC-2019-05)Key Research and Development Program of Shandong Province,China(2020CXGC01208)Science and Technology Project of Qingdao West Coast New Area,China(2019-32,2020-20,2020-1-4).
文摘This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.
文摘This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.
基金the researchers for providing the Matlab codes of the comparison methods.
文摘Multiplicative noise removal is a challenging problem in image denoising.In this paper,we develop a nonlocal matrix rank minimization method for the multiplicative noise removal problem.By utilizing the logarithm transformation,we convert the problem into an additive noise removal problem and propose a maximum a posteriori(MAP)estimation-based matrix rank minimization model for this kind of additive noise removal.A proximal alternating algorithm is designed to solve the matrix rank minimization model.The convergence of the algorithm is demonstrated by the famous Kurdyka-Lojasiewicz property.Taking advantage of the proposed matrix rank minimization model and its proximal alternating algorithm,a multiplicative noise removal method is finally developed.Numerical experiments illustrate that the proposed method can remove multiplicative noise in images much better than the existing state-of-the-art methods in terms of both image recovered measure quantities and visual qualities.
基金supported by National Natural Science Foundation of China under Grant Nos 60774020, 60736028,and 60821091
文摘This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.
