Abstract
This paper presents a nonlinear method---total variation denoising (TVD) method, for impulse signals denoising. The basic idea of TVD is to solve a total variation function optimization problem. Experimental results suggest that the mean squared error (MSE) can not distinguish the results with some falsely identified impulses. Thus, a dual assessment criterion incorporating both MSE and false identification power (fid) is proposed. Numerical experiments have shown that the proposed approach outperforms the traditional wavelet denoising (WD) by using the dual assessment criterion.
Keyword: Denoise; total variation; impulse signals.
References
1. Y. S. Fan, and G. T. Zheng, “Research of high-resolution vibration signal detection technique and application to mechanical fault diagnosis,” Mechanical Systems and Signal Processing, 21, 2007, pp. 678-687.
2. S. Chen, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Transactions on Image Processing, 9, 2000, pp. 1532-1546.
.
3. S. Chen, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Transactions on Image Processing, 9, 2000, pp. 1522-1531.
4. J. Lin, M. Zuo, and K. Fyfe, “Mechanical fault detection based on the wavelet denoising technique,” ASME Journal of Vibration and Acoustics, 126, 2004, pp. 9-16.
5. A. Hyvarinen, “Sparse code shrinkage denoising of non-Gaussian data by maximum likelihood estimation,” Neural Computation, 11, 1999, pp. 739-1768.
6. Q. Xu, and Z. Li, “Recognition of wear mode using multi-variable synthesis approach based on wavelet packet and improved three-line method,” Mechanical Systems and Signal Processing, 21, 2007, pp. 3146-3166.
7. H. Hong, and M. Liang, “K-Hybrid: A kurtosis-based hybrid thresholding method for mechanical signal denoising,” Transactions of the ASME, 129, 2007, pp. 458-470.
8. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, 60, 1992, pp. 259-268.
9. D. C. Dobson, and C. R. Vogel, “Convergence of an iterative method for total variation denoising,” SIAM Journal on Numerical Analysis, 34, 1997, pp. 1779-1791.
10. Z. Xie, and J. Feng, “Blind source separation of continuous-time chaotic signals based on fast random search algorithm,” IEEE Transactions on Circuits and Systems II: Express Briefs, 57, 2010, pp. 461-465.
11. J. Nocedal, “Updating Quasi-Newton Matrices with Limited Storage,” Mathematics of Computation, 35, 1980, pp. 773-782.
12. D. C. Liu, and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Mathematical Programming, 45, 1989, pp. 503-528.
13. M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software Algorithms, New York, A.K. Peters, 1994.
作者簡介:
謝宗伯，博士，華南理工大學副研究員，IEEE/IEICE會員，主要研究方向為信號處理與機器學習。先后主持國家和省部級項目多項，在國際高水平期刊發表論文多篇。
馮久超，教授，博導，華南理工大學教授，IEEE會員，廣東省“珠江學者”特聘教授，主要研究方向為非線性系統理論。
