On the regularity of trust region-cg algorithm: With application to deconvolution problem
Deconvolution problem is a main topic in signal processing. Many practical applications are required to solve deconvolution problems. An important example is image reconstruction. Usually, researchers like to use regularization method to deal with this problem. But the cost of computation is high due to the fact that direct methods are used. This paper develops a trust region-cg method, a kind of iterative methods to solve this kind of problem. The regularity of the method is proved. Based on the special structure of the discrete matrix, FFT can be used for calculation. Hence combining trust region-cg method with FFT is suitable for solving large scale problems in signal processing.
Keywordsill- posed problems efficient implementation trust region- cg method regularity
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- 1.Guan Zhaozhi, Xu Wenyuan, Jia Peizhang et al., Signal Processing and Analysis (in Chinese), Beijing: Science Press, 1986.Google Scholar
- 2.Roggemann, M., Welsh, B., Roggemann, M. C. et al., Imaging through turbulence, Boca Raton, Florida: CRC Press, 1996.Google Scholar
- 3.Vogel, C. R., Computational methods for inverse problems, SIAM Frontiers in Applied Mathematics Series, No. 23, Philadelphia: SIAM, 2002.Google Scholar
- 4.Michael, K. Ng., Plemmons, R. J., Qiao, S. Z. et al., Regularized blind deconvolution using recursive inverse filtering, in Proc. HK97 Conference on Scientific Computation (eds. Golub, G., Liu, S., Luk, F. et al.), Berlin: Springer-Verlag, 1997.Google Scholar
- 7.Yuan Yaxiang, Problems on convergence of unconstrained optimization algorithms, in Numerical Linear Algebra and Optimization (ed. Yuan, Y. X.), Beijing/New York: Science Press, 1999, 95–107.Google Scholar
- 9.Kaltenbacher, B., On Broyden’s method for nonlinear ill-posed problems, Numer. Funct. Anal. Opt., 1998, 19.Google Scholar
- 12.Powell, M. J. D., Convergence properties of a class of minimization algorithms, in Nonlinear Programming (eds. Mangasarian, O. L., Meyer, R. R., Robinson, S. M.), New York: Academic Press, 1975, 2: 1–27.Google Scholar
- 13.Toint, Ph. L., Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses (ed. Duff, I.), Berlin: Academic Press, 1981, 57–88.Google Scholar
- 15.Hanke, M., Iterative regularization techniques in image reconstruction, Proceedings of the Conference Mathematical Methods in Inverse Problems for Partial Differential Equations, Mt. Holyoke: Springer-Verlag, 1998.Google Scholar