Multiplicative Noise

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The Experts below are selected from a list of 15582 Experts worldwide ranked by ideXlab platform

Shengfan Zhou - One of the best experts on this subject based on the ideXlab platform.

Zhaojuan Wang - One of the best experts on this subject based on the ideXlab platform.

Chang Hwan Sung - One of the best experts on this subject based on the ideXlab platform.

Michael Basin - One of the best experts on this subject based on the ideXlab platform.

  • mean square data based controller for nonlinear polynomial systems with Multiplicative Noise
    Information Sciences, 2012
    Co-Authors: Michael Basin, Peng Shi, Pedro Soto
    Abstract:

    This paper presents the mean-square optimal data-based quadratic-Gaussian controller for stochastic nonlinear polynomial systems with a polynomial Multiplicative Noise, a linear control input, and a quadratic criterion over linear observations. The mean-square optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for stochastic nonlinear polynomial systems with a polynomial Multiplicative Noise, a linear control input, and a quadratic criterion. Performance of the obtained mean-square optimal data-based controller is verified in the illustrative example against the conventional LQG controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.

  • mean square optimal controller for stochastic polynomial systems with Multiplicative Noise
    American Control Conference, 2011
    Co-Authors: Michael Basin, Peng Shi, Pedro Soto
    Abstract:

    This paper presents the mean-square optimal quadratic-Gaussian controller for stochastic polynomial systems with a polynomial Multiplicative Noise, a linear control input, and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As an intermediate result, the paper gives a closed-form solution of the optimal regulator (control) problem for stochastic polynomial systems with a polynomial Multiplicative Noise, a linear control input, and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQG controller that is optimal for linearized systems. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.

  • optimal filtering for polynomial system states with polynomial Multiplicative Noise
    American Control Conference, 2006
    Co-Authors: Michael Basin, Jose P Perez, Mikhail Skliar
    Abstract:

    In this paper, the optimal filtering problem for polynomial system states with polynomial Multiplicative Noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial Multiplicative Noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear Multiplicative Noise and a bilinear state equation with bilinear Multiplicative Noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic Multiplicative Noise over linear observations against the optimal filter for a quadratic state with a state-independent Noise and a conventional extended Kalman-Bucy filter.

  • optimal filtering for polynomial system states with polynomial Multiplicative Noise
    International Journal of Robust and Nonlinear Control, 2006
    Co-Authors: Michael Basin, Jose P Perez, Mikhail Skliar
    Abstract:

    In this paper, the optimal filtering problem for polynomial system states with polynomial Multiplicative Noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial Multiplicative Noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of a linear state equation with linear Multiplicative Noise and a bilinear state equation with bilinear Multiplicative Noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic Multiplicative Noise over linear observations against the optimal filter for a quadratic state with a state-independent Noise and a conventional extended Kalman–Bucy filter. Copyright © 2006 John Wiley & Sons, Ltd.

Xu Yuesheng - One of the best experts on this subject based on the ideXlab platform.

  • Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm
    2020
    Co-Authors: Liu Xiaoxia, Lu Jian, Shen Lixin, Xu Chen, Xu Yuesheng
    Abstract:

    The goal of this paper is to develop a novel numerical method for efficient Multiplicative Noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to Multiplicative Noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex nonsmooth optimization problem having a patchwise data fidelity and a generalized nonlocal low-rank regularization term. To solve this optimization problem, we propose the PARM algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. A theoretical analysis of the proposed PARM algorithm is conducted to guarantee its global convergence to a critical point. Numerical experiments demonstrate that the proposed method for Multiplicative Noise removal significantly outperforms existing methods such as the benchmark SAR-BM3D method in terms of the visual quality of the deNoised images, and the PSNR (the peak-signal-to-Noise ratio) and SSIM (the structural similarity index measure) values

  • Multiplicative Noise Removal: Nonlocal Low-Rank Model and It\u27s Proximal Alternating Reweighted Minimization Algorithm
    ODU Digital Commons, 2020
    Co-Authors: Liu Xiaoxia, Lu Jian, Shen Lixin, Xu Chen, Xu Yuesheng
    Abstract:

    The goal of this paper is to develop a novel numerical method for efficient Multiplicative Noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to Multiplicative Noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex non-smooth optimization problem having a patchwise data fidelity and a generalized nonlocal low-rank regularization term. To solve this optimization problem, we propose the PARM algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. A theoretical analysis of the proposed PARM algorithm is conducted to guarantee its global convergence to a critical point. Numerical experiments demonstrate that the proposed method for Multiplicative Noise removal significantly outperforms existing methods, such as the benchmark SAR-BM3D method, in terms of the visual quality of the deNoised images, and of the peak-signal-to-Noise ratio (PSNR) and the structural similarity index measure (SSIM) values

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