The Experts below are selected from a list of 67395 Experts worldwide ranked by ideXlab platform
Yu Bin Zhou - One of the best experts on this subject based on the ideXlab platform.
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Tikhonov Regularization Method for a backward problem for the time-fractional diffusion equation
Applied Mathematical Modelling, 2013Co-Authors: Jungang Wang, Ting Wei, Yu Bin ZhouAbstract:Abstract This paper is devoted to solve a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain by the Tikhonov Regularization Method. Based on the eigenfunction expansion of the solution, the backward problem for searching the initial data is changed to solve a Fredholm integral equation of the first kind. The conditional stability for the backward problem is obtained. We use the Tikhonov Regularization Method to deal with the integral equation and obtain the series expression of solution. Furthermore, the convergence rates for the Tikhonov regularized solution can be proved by using an a priori Regularization parameter choice rule and an a posteriori Regularization parameter choice rule. Two numerical examples in one-dimensional and two-dimensional cases respectively are investigated. Numerical results show that the proposed Method is effective and stable.
Jungang Wang - One of the best experts on this subject based on the ideXlab platform.
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Tikhonov Regularization Method for a backward problem for the time-fractional diffusion equation
Applied Mathematical Modelling, 2013Co-Authors: Jungang Wang, Ting Wei, Yu Bin ZhouAbstract:Abstract This paper is devoted to solve a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain by the Tikhonov Regularization Method. Based on the eigenfunction expansion of the solution, the backward problem for searching the initial data is changed to solve a Fredholm integral equation of the first kind. The conditional stability for the backward problem is obtained. We use the Tikhonov Regularization Method to deal with the integral equation and obtain the series expression of solution. Furthermore, the convergence rates for the Tikhonov regularized solution can be proved by using an a priori Regularization parameter choice rule and an a posteriori Regularization parameter choice rule. Two numerical examples in one-dimensional and two-dimensional cases respectively are investigated. Numerical results show that the proposed Method is effective and stable.
Feng Dong - One of the best experts on this subject based on the ideXlab platform.
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L1-L2 Spatial Adaptive Regularization Method for Electrical Tomography
2019 Chinese Control Conference (CCC), 2019Co-Authors: Ziqi Liu, Feng DongAbstract:Regularization is an effective Method for the ill-posed problem of inverse problems in electrical tomography(ET). Traditional Regularization Methods utilize fixed Regularization terms which neglect the spatial characteristics of the field. In this paper, a novel Regularization Method was proposed which combines selection of the Regularization terms with spatial information such as electrical parameters that obtained from iterative result of each step. L1 or L2 norm is chosen as the Regularization term according to the distribution of electrical properties. The simulation results have verified that this proposed Method can effectively improve the imaging resolution and enhance the noise immunity of the inverse problem compared with the traditional Regularization Methods such as L2 Regularization and L1 Regularization.
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A new Regularization Method for electrical impedance tomography
2017 IEEE International Conference on Imaging Systems and Techniques (IST), 2017Co-Authors: Bing Han, Feng DongAbstract:Regularization Methods are good ways to address the ill-posed problem of the inverse problem of electrical impedance tomography (EIT). Common Regularization Methods such as Tikhonov, L1 norm and total variation (TV) Regularization Methods have their own inescapable problems, such as the over smoothness of reconstructed edges and the unstable solution due to measurement noise. In this paper, a new Regularization Method was proposed, which utilizes the total differences of conductivities of neighbored pixels (TDN) as penalty term. This Method performed strong robustness against the boundary measurement noise, good ability to reserve the sharp edges as well as special capacity to reconstruct the accurate shape of square objects.
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a hybrid Regularization Method combining tikhonov with total variation for electrical resistance tomography
Flow Measurement and Instrumentation, 2015Co-Authors: Xizi Song, Feng DongAbstract:Abstract Electrical resistance tomography (ERT) is a promising measurement technique in industrial process imaging. However, image reconstruction in ERT is an ill-posed inverse problem. Regularization Methods have been developed to solve the ill-posed inverse problem. Since the penalty term is a form of L2-norm, Tikhonov Regularization Method guarantees the stability of the solution, but it always makes the image edge oversmoothed. Total variation (TV) Regularization Method has good ability of preserving image edges. A hybrid Regularization Method, which combines Tikhonov with TV Regularization Method, is proposed to get better reconstructed images. The choice of the adaptive weighted parameter between TV and Tikhonov penalty term has been discussed in detail. In the proposed hybrid Regularization Method, the function of conductivity gradients is used as the adaptive weighted parameter to control automatically the weighting between the penalty terms from TV and Tikhonov Regularization. For the model with sharp edges, the proportion of the penalty term from TV Regularization is increased to preserve the edges, while for the model with smooth edges, the proportion of penalty term from Tikhonov Regularization is increased to make the solution stable and robust to noise. Both simulation and experimental results of Tikhonov, TV and hybrid Regularization Method are shown respectively, which indicates that the hybrid Regularization Method can improve the reconstruction quality with sharp edges and is more robust to noise, and it is applicable for models with different edge characteristic.
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A spatially adaptive total variation Regularization Method for electrical resistance tomography
Measurement Science and Technology, 2015Co-Authors: Xizi Song, Feng DongAbstract:The total variation (TV) Regularization Method has been used to solve the ill-posed inverse problem of electrical resistance tomography (ERT), owing to its good ability to preserve edges. However, the quality of the reconstructed images, especially in the flat region, is often degraded by noise. To optimize the Regularization term and the Regularization factor according to the spatial feature and to improve the resolution of reconstructed images, a spatially adaptive total variation (SATV) Regularization Method is proposed. A kind of effective spatial feature indicator named difference curvature is used to identify which region is a flat or edge region. According to different spatial features, the SATV Regularization Method can automatically adjust both the Regularization term and Regularization factor. At edge regions, the Regularization term is approximate to the TV functional to preserve the edges; in flat regions, it is approximate to the first-order Tikhonov (FOT) functional to make the solution stable. Meanwhile, the adaptive Regularization factor determined by the spatial feature is used to constrain the Regularization strength of the SATV Regularization Method for different regions. Besides, a numerical scheme is adopted for the implementation of the second derivatives of difference curvature to improve the numerical stability. Several reconstruction image metrics are used to quantitatively evaluate the performance of the reconstructed results. Both simulation and experimental results indicate that, compared with the TV (mean relative error 0.288, mean correlation coefficient 0.627) and FOT (mean relative error 0.295, mean correlation coefficient 0.638) Regularization Methods, the proposed SATV (mean relative error 0.259, mean correlation coefficient 0.738) Regularization Method can endure a relatively high level of noise and improve the resolution of reconstructed images.
Ting Wei - One of the best experts on this subject based on the ideXlab platform.
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Tikhonov Regularization Method for a backward problem for the time-fractional diffusion equation
Applied Mathematical Modelling, 2013Co-Authors: Jungang Wang, Ting Wei, Yu Bin ZhouAbstract:Abstract This paper is devoted to solve a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain by the Tikhonov Regularization Method. Based on the eigenfunction expansion of the solution, the backward problem for searching the initial data is changed to solve a Fredholm integral equation of the first kind. The conditional stability for the backward problem is obtained. We use the Tikhonov Regularization Method to deal with the integral equation and obtain the series expression of solution. Furthermore, the convergence rates for the Tikhonov regularized solution can be proved by using an a priori Regularization parameter choice rule and an a posteriori Regularization parameter choice rule. Two numerical examples in one-dimensional and two-dimensional cases respectively are investigated. Numerical results show that the proposed Method is effective and stable.
I. V. Konnov - One of the best experts on this subject based on the ideXlab platform.
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Partial Regularization Method for nonmonotone variational inequalities
Computational Mathematics and Mathematical Physics, 2008Co-Authors: D. A. Dyabilkin, I. V. KonnovAbstract:A variational inequality with a nonmonotone mapping is considered in a Euclidean space. A Regularization Method with respect to some of the variables is proposed for its solution. The convergence of the Method is proved under a coercivity-type condition. The Method is applied to an implicit optimization problem with an arbitrary perturbing mapping. The solution technique combines partial Regularization and the dual descent Method.
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On the convergence of a Regularization Method for variational inequalities
Computational Mathematics and Mathematical Physics, 2006Co-Authors: I. V. KonnovAbstract:For variational inequalities in a finite-dimensional space, the convergence of a Regularization Method is examined in the case of a nonmonotone basic mapping. It is shown that a fairly general sufficient condition for the existence of solutions to the original problem also guarantees the convergence and existence of solutions to perturbed problems. Examples of applications to problems on order intervals are presented.