Continuous Piecewise Linear Approximation of BV Function

Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Yi, H. , Yu, T. , Chen, Z. and Zhu, J. (2014) Continuous Piecewise Linear Approximation of BV Function. Applied Mathematics, 5, 667-671. doi: 10.4236/am.2014.54063.

 [1] DeVore, R.A. and Lorentz, G.G. (1993) Constructive Approximation. Volume 303. Springer, Berlin. [2] DeVore, R.A. (1998) Nonlinear Approximation. In Acta Numerica, Cambridge University Press, Cambridge, 51-150. [3] Kahane, J.P. (1961) Teora Constructiva de Funciones, Volume 5. Universidad de Buenos Aires, Buenos Aires. [4] Zhang, T., Fan, Q. and Shu, H. (2009) Approximation of BV Function by Piecewise Constants and Its Application in Signal Denoising and Compression. 2nd International Congress on Image and Signal Processing, Tianjin, 17-19 October 2009, 1-5. [5] Donoho, D.L. and Johnstone, J.M. (1994) Ideal Spatial Adaptation by Wavelet Shrinkage. Biometrika, 81, 425-455. http://dx.doi.org/10.1093/biomet/81.3.425 [6] Donoho, D.L. and Johnstone, I.M. (1995) Adapting to Unknown Smoothness via Wavelet Shrinkage. Journal of the American Statistical Association, 90, 1200-1224. http://dx.doi.org/10.1080/01621459.1995.10476626 [7] Shi Y.Y. and Li, X.Y. (2010) Continuous Piecewise Linear Approximation Based on Haar Scale Transform. Journal of Liaoning Technical University (Natural Science), 3, 521-524.