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A Novel Fractional Fourier Domain Filter Design Based on Time–Frequency Image Edge Detection

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 246)

Abstract

To realize the lossless recovery of non-stationary signal in complicated noise environment, a novel design method of fractional Fourier domain filter is proposed assisted by time–frequency image edge detection. The time–frequency distribution of observed signal is obtained by Gabor-Wigner transform, and based on technique of image edge detection and selection algorithm, adjacent edge information of the different regions of in the time–frequency plane are obtained, which can be used to build support vector machine (SVM) training set. Respectively, for the two cases of linearly separable and inseparable signal and noise distribution, the separating line is drawn by the SVM separating algorithm and then the parameters of filter can be determined by the parameters of separating line. Simulation results show that without any prior knowledge of signal and noise, the design process can ensure the optimal performance of the filter and higher signal noise ratio is reached. Furthermore, an undistorted signal recovery is achieved even in the case of strong coupling between signal and noise, which proves the reliability, versatility and effectiveness of our filter design.

Keywords

Time–frequency filtering Fractional Fourier transform Gabor-Wigner transform Image edge detection Support vector machine 

Notes

Acknowledgments

This work is supported by the National Natural Science Fund of China (61271069).

References

  1. 1.
    Almeida LB (1994) The fractional Fourier transform and time-frequency representations. IEEE Trans Signal Process 42(11):3084–3091CrossRefGoogle Scholar
  2. 2.
    Suba RS, Bingo WL, Apostolos G (2012) Filtering in Rotated Time-Frequency domains with unknown noise statistics. IEEE Trans Signal Process 60(1):489–493CrossRefMathSciNetGoogle Scholar
  3. 3.
    Zalevsky Z, Mendlovic D (1996) Fractional Wiener filter. Appl Opt 35(20):3930–3936CrossRefGoogle Scholar
  4. 4.
    Kutay MA, Ozaktas HM, Onural L et al (1997) Optimal filtering in fractional Fourier domains. IEEE Trans Signal Process 45(5):1129–1143CrossRefGoogle Scholar
  5. 5.
    Erden MF, Kutay MA, Ozaktas HM (1999) Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration. IEEE Trans Signal Process 47(5):1458–1462CrossRefGoogle Scholar
  6. 6.
    Pei SC, Ding JJ (2007) Relations between Gabor transforms and fractional Fourier transforms and their applications for signal processing. IEEE Trans Signal Process 55(10):4839–4850CrossRefMathSciNetGoogle Scholar
  7. 7.
    Pei SC, DING JJ (2000) Closed-form discrete fractional and affine Fourier transforms. IEEE Trans Signal Process 48(5):1338–1353CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Ding L, Goshtasby A (2001) On the Canny edge detector. Pattern Recognit 34(3):721–725CrossRefMATHGoogle Scholar
  9. 9.
    Cortes C, Vapni C (1995) Support-vector networks. Mach Learn 20(3):273–297MATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jiexiao Yu
    • 1
  • Kaihua Liu
    • 1
  • Xiangdong Huang
    • 1
  • Ge Yan
    • 1
  1. 1.School of Electronic Information EngineeringTianjin UniversityTianjinChina

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