共查询到10条相似文献,搜索用时 93 毫秒
1.
Yan-feiWang Ya-xiangYuan 《计算数学(英文版)》2003,21(6):759-772
This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in many applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem.Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for ill-posed problems, Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising. 相似文献
2.
A new trust region algorithm for image restoration 总被引:1,自引:0,他引:1
WEN Zaiwen & WANG Yanfei State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China National Key Laboratory on Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(2):169-184
The image restoration problems play an important role in remote sensing and astronomical image analysis. One common method for the recovery of a true image from corrupted or blurred image is the least squares error (LSE) method. But the LSE method is unstable in practical applications. A popular way to overcome instability is the Tikhonov regularization. However, difficulties will encounter when adjusting the so-called regularization parameter a. Moreover, how to truncate the iteration at appropriate steps is also challenging. In this paper we use the trust region method to deal with the image restoration problem, meanwhile, the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method. We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded. The trust region method is very stable and robust, and it has the nice property of updating the trust region automatically. This releases us from tedious fi 相似文献
3.
In this work, a feasible direction method is proposed for computing the regularized solution of image restoration problems by simply using an estimate of the noise present on the data. The problem is formulated as an optimization problem with one quadratic constraint. The proposed method computes a feasible search direction by inexactly solving a trust region subproblem with the truncated Conjugate Gradient method of Steihaug. The trust region radius is adjusted to maintain feasibility and a line-search globalization strategy is employed. The global convergence of the method is proved. The results of image denoising and deblurring are presented in order to illustrate the effectiveness and efficiency of the proposed method. 相似文献
4.
In this paper, we consider an ill-posed image restoration problem with a noise contaminated observation, and a known convolution kernel. A special Hermitian and skew-Hermitian splitting (HSS) iterative method is established for solving the linear systems from image restoration. Our approach is based on an augmented system formulation. The convergence and operation cost of the special HSS iterative method for image restoration problems are discussed. The optimal parameter minimizing the spectral radius of the iteration matrix is derived. We present a detailed algorithm for image restoration problems. Numerical examples are given to demonstrate the performance of the presented method. Finally, the SOR acceleration scheme for the special HSS iterative method is discussed. 相似文献
5.
In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization problem leads to the generalized Sylvester matrix equation. For large-scale problems, we use the global-GMRES method which is an orthogonal projection method onto a matrix Krylov subspace. We present some theoretical results and give numerical tests in image restoration. 相似文献
6.
7.
For the solution of linear discrete ill-posed problems, in this paper we consider the Arnoldi-Tikhonov method coupled with the Generalized Cross Validation for the computation of the regularization parameter at each iteration. We study the convergence behavior of the Arnoldi method and its properties for the approximation of the (generalized) singular values, under the hypothesis that Picard condition is satisfied. Numerical experiments on classical test problems and on image restoration are presented. 相似文献
8.
G. Landi 《Computational Optimization and Applications》2008,39(3):347-368
In many science and engineering applications, the discretization of linear ill-posed problems gives rise to large ill-conditioned
linear systems with the right-hand side degraded by noise. The solution of such linear systems requires the solution of minimization
problems with one quadratic constraint, depending on an estimate of the variance of the noise. This strategy is known as regularization.
In this work, we propose a modification of the Lagrange method for the solution of the noise constrained regularization problem.
We present the numerical results of test problems, image restoration and medical imaging denoising. Our results indicate that
the proposed Lagrange method is effective and efficient in computing good regularized solutions of ill-conditioned linear
systems and in computing the corresponding Lagrange multipliers. Moreover, our numerical experiments show that the Lagrange
method is computationally convenient. Therefore, the Lagrange method is a promising approach for dealing with ill-posed problems.
This work was supported by the Italian FIRB Project “Parallel algorithms and Nonlinear Numerical Optimization” RBAU01JYPN. 相似文献
9.
In this paper, we show that minimization problems involving sublinear regularizing terms are ill-posed, in general, although numerical experiments in image processing give very good results. The energies studied here are inspired by image restoration and image decomposition. Rewriting the nonconvex sublinear regularizing terms as weighted total variations, we give a new approach to perform minimization via the well-known Chambolle's algorithm. The approach developed here provides an alternative to the well-known half-quadratic minimization one. 相似文献
10.
We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional trust-region subproblem, TRS, approach that makes use of the L-curve maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We apply a parameterized trust region approach to estimate the region of maximum curvature of the L-curve and find the regularized solution. This exploits the close connections between various parameters used to solve TRS. A MATLAB code for the algorithm is tested and a comparison to the conjugate gradient least squares, CGLS, approach is given and analysed. 相似文献