臺灣博碩士論文加值系統

In this paper we develope a new method based on the genetic algorithm to solve the total variation-based denoising problems. First, we briefly describe the genetic algorithm and some backgrounds of the total variation-based denoising problems. Second, we start to develope the genetic algorithm for the TV-based denoising problem. Finally we show some numerical results to demonstrate this method is fast.

Contents

1. Abstract 1
2. Introduction 2
3. Genetic Algorithm 4
4. Three Points Genetic Algorithm 10
4.1 Motivation 10
4.2 Algorithm 13
5. Numerical Results 15
6. A Genetic Algorithm for total variation denoising problem 18
7. Conclusion 27
8. Code 28
9. References 33

[1] D Ling, H. Y. Hsu, G Lin, S. H. Lee, Enhanced image-based coordinate measurement using a super-resolution method, Robotics and Computer-Integrated Manufacturing 21 (2005), pp. 579--588.

[2] A. Chambolle, An Algorithm for Total Variation Minimization and Applications, Journal of Mathematical Imaging and Vision 20(2004), pp. 89--97.

[3] F. Malgouyres, Minimizing the Total Variation Under a General Convex Constraint for Image Restoration, IEEE Trans. Image Processing, 11(2002), pp. 1450--1456.

[4] Y. Li, F. Santosa, A computational algorithm for minimizing total variation in image restoration, IEEE Trans. Image Processing, 5(1996), pp. 987--995.

[5] L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259--268.

[6] C. R. Vogel and M. E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput, 17 (1996), pp. 227--238.

[7] T. F. Chan, G. H. Golub, and P. Mulet, A nonlinear primal-dual method for total variationbased image restoration, SIAM J. Sci. Comput., 20 (1999), pp. 1964--1977.

[8] Q. Chang, I. L. Chern, Acceleration Methods for Total Variation-Based Image Denoising, SIAM J. Sci. Comput, 25(2003), pp. 982--994.

[9] Vogel C, Acar R, Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10 (1994) 1217-1229. Printed in the UK.

[10] Zbigniew Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs