PDE-based signal quantization

被引：0
作者：
Belahmidi A. [1 ]
机构：
[1] CEREMADE, Université de Paris Dauphine
来源：
J. Appl. Math. Comp. | 2006年 / 3卷 / 117-132期
关键词：
numerical approximation; partial differential equations; reactiondiffusion model; Signal quantization; signal restoration; variational methods;
D O I：
10.1007/BF02832041
中图分类号：
学科分类号：
摘要：
We present a new method for signal restoration/quantization based on diffusion reaction model with memory term. We prove that the model is stable, with the existence and uniqueness results. We also propose a numerical approximation that we prove the convergence and present some experiments on noisy signals. © 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.
引用
收藏
页码：117 / 132
页数：15
相关论文
共 14 条
[1]  
Alvarez L., Esclarin J., Image quantization using reaction-diffusion equations, SIAM J. Appl. Math., 57, 1, pp. 153-175, (1997)
[2]  
Belahmidi A., Solvability of a coupled system arising in image and signal processing, African Diaspora Journal of Mathematics, 3, 1, pp. 45-61, (2005)
[3]  
Belahmidi A., Chambolle A., Time-delay regularization of anisotropic diffusion and image processing, Mathematical Modelling and Numerical Analysis, 39, 2, pp. 231-251, (2005)
[4]  
Brezis H., Analyse Fonctionnelle. Théorie et Application, (1987)
[5]  
Catte F., Lions P.L., Morel J.M., Coll T., Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29, 1, pp. 182-193, (1992)
[6]  
Cottet G.-H., Germain L., Image processing through reaction combined with nonlinear diffusion, Math. Comp., 61, 204, pp. 659-673, (1993)
[7]  
Hollig K., Nohel J.A., A diffusion equation with a nonmonotone consititutive function, Systems of nonlinear partial differential equations, Proc. on Systems of Nonlinear PDEs, pp. 409-422, (1983)
[8]  
Kawohl B., Kutev N., Maximum and comparison principle for one-dimensional anisotropic diffusion, Math. Ann., 311, 1, pp. 107-123, (1998)
[9]  
Kichenassamy S., The Perona-Malik paradox, SIAM J. Appl. Math., 57, 5, pp. 1343-1372, (1997)
[10]  
Lloyd S.P., Least squares quantization in PCM, IEEE Trans. Information Theory, 3, 28, pp. 29-137, (1982)
12