GPR noise reduction by TVD and TVD-EMD

نوع مقاله : مقاله پژوهشی‌

نویسندگان

1 Ph.D student, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Associate Professor, Institute of Geophysics, University of Tehran, Tehran, Iran

3 Assistant Professor, Graduate University of advanced technology, Kerman, Iran

4 Assistant Professor, Payam Noor University of Parand, Tehran, Iran

چکیده

The existence of coherent and incoherent (random) noises including high-frequency electromagnetic inferences in the Ground Penetration Radar (GPR) signals is inevitable. Therefore, the elimination of noise from GPR data before performing any additional analysis is of great importance to increase the accuracy of the interpretations. We apply the Total Variation De-noising (TVD) and Savitzky-Golay (SG) filter on synthetic and real GPR datasets. For a better perception, the same trace of the data is compared after applying the mentioned methods. The results indicate that the TVD method is more effective than the common adaptive filtering in the time domain for reducing noise such as the SG filter which acts as a low-pass filter for smoothing data based on a polynomial least-squares approximation. However, due to the visibility of staircase artifacts using the TVD method, GPR data is first transferred to the Empirical Mode Decomposition (EMD) frame which is useful for non-linear and non-stationary signal processing, and then the TVD method is applied to it. Finally, noise reduction using TVD is compared in the time and EMD domains. The comparison of the outputs shows that the TVD algorithm in the EMD domain, based on the sequential extraction of the energy belonging to the different intrinsic time scales of the signal, provides better noise attenuation than the other algorithms. In addition, TVD-EMD improves the continuity in sections and preserves the event forms and signal forms.
 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

GPR noise reduction by TVD and TVD-EMD

نویسندگان [English]

  • Sadegh Moghaddam 1
  • Behrooz Oskooi 2
  • Alireza Goudarzi 3
  • Asghar Azadi 4
1 Ph.D student, Institute of Geophysics, University of Tehran, Tehran, Iran
2 Associate Professor, Institute of Geophysics, University of Tehran, Tehran, Iran
3 Assistant Professor, Graduate University of advanced technology, Kerman, Iran
4 Assistant Professor, Payam Noor University of Parand, Tehran, Iran
چکیده [English]

The existence of coherent and incoherent (random) noises including high-frequency electromagnetic inferences in the Ground Penetration Radar (GPR) signals is inevitable. Therefore, the elimination of noise from GPR data before performing any additional analysis is of great importance to increase the accuracy of the interpretations. We apply the Total Variation De-noising (TVD) and Savitzky-Golay (SG) filter on synthetic and real GPR datasets. For a better perception, the same trace of the data is compared after applying the mentioned methods. The results indicate that the TVD method is more effective than the common adaptive filtering in the time domain for reducing noise such as the SG filter which acts as a low-pass filter for smoothing data based on a polynomial least-squares approximation. However, due to the visibility of staircase artifacts using the TVD method, GPR data is first transferred to the Empirical Mode Decomposition (EMD) frame which is useful for non-linear and non-stationary signal processing, and then the TVD method is applied to it. Finally, noise reduction using TVD is compared in the time and EMD domains. The comparison of the outputs shows that the TVD algorithm in the EMD domain, based on the sequential extraction of the energy belonging to the different intrinsic time scales of the signal, provides better noise attenuation than the other algorithms. In addition, TVD-EMD improves the continuity in sections and preserves the event forms and signal forms.
 

کلیدواژه‌ها [English]

  • De-noising
  • Ground Penetrating Radar (GPR)
  • Empirical Mode Decomposition (EMD)
  • Savitzky-Golay (SG) filter
  • Total Variation De-noising (TVD)
Acharya, D., Rani, A., and Agarwal, S., 2016, Application of adaptive Savitzky-Golay filter for EEG signal processing: Perspectives in Science, doi 10.1016/j.pisc.2016.06.056.
Boudraa, A., Cexus, J., and Saidi, Z., 2007, EMD-based signal noise reduction: International Journal of Electronics and Communication Engineering, 1(2).
Chan, T. F., Osher, S., and Shen, J., 2001, The digital TV filter and nonlinear denoising: IEEE Transactions on Image Processing, 10(2), 231–241.
Chartrand, R., and Staneva, V., 2008, Total variation regularization of images corrupted by non-Gaussian noise using a quasi-Newton method: Image Processing, IET, 2(6), 295–303.
Ebrahimi, A., Gholami, A., and Nabi-Bidhendi, M., 2017, Sparsity-based GPR blind deconvolution and wavelet estimation: The Journal of Indian Geophysical Union, 21(1), 7-12.
Figueiredo, M., Bioucas-Dias, J., Oliveira, J. P., and Nowak, R. D., 2006, On total-variation de-noising: A new majorization-minimization algorithm and an experimental comparison with wavelet de-noising: Proceeding of IEEE International Conference of Image Processing.
Flandrin, P., Rilling, G., and Gonçalves, P., 2004, Empirical mode decomposition as a filter bank: IEEE Signal Processing Letters, 11(2), 112-114.
Han, J., and Van der Baan, M., 2013, Empirical mode decomposition for seismic time-frequency analysis: Geophysics, 78(2), 9-19.
Hansen, P. C.,1999, Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion, Philadelphia, SIAM.
Huang, N., Shen, Z., Long, S., Wu, M., Shin, H, Zheng, Q., Yen, N., Tung, C., and Liu, H., 1998, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis: Proceedings of the Royal Society of London A, 454, 903-995.
Jol, H., 2008, Ground Penetrating Radar Theory and Application: University of Wisconsin, Claire, USA, Elsevier Science.
Jose, A., Krishnan, S. R., and Seelamantula, C. S., 2013, Ridge detection using Savitzky-Golay filtering and steerable second-order Gaussian derivatives: Image Processing (ICIP) 2013 20th IEEE International Conference, 3059-3063.
Kennedy, H., 2015, Recursive digital filters with tunable lag and lead characteristics for proportional-differential control: IEEE Transactions on Control Systems Technology, 23(6), 2369-2374.
Krishnan, S. R., Magimai.-Doss, M., and Seelamantula, C. S., 2013, A Savitzky-Golay filtering perspective of dynamic feature computation: Signal Processing Letters, IEEE, 20, 281-284.
Liu, Y., Dang, B., Li, Y., Lin, H., and Ma, H., 2016, Applications of Savitzky-Golay filter for seismic random noise reduction: Acta Geophysica, 64(1), 101-124.
Liu, C., Song, C., and Lu, Q., 2017, Random noise de-noising and direct wave eliminating based on SVD method for ground penetrating radar signals: Journal of Applied Geophysics, 144(C), 125-133, doi 10.1016/j.jappgeo.2017.07.007.
Luo, J., Ying, K., He, P., and Bai, J., 2005, Properties of Savitzky-Golay digital differentiators: Digital Signal Processing, 15, 122-136.
Moghaddam, S., Oskooi, B., Goudarzi, A., and Azadi, A., 2019, The comparative sense of sparse deconvolution and least-squares deconvolution methods in increasing the temporal resolution of GPR data: Arabian Journal of Geosciences, 12(20), 1-10, doi 10.1007/s12517-019-4686-4.
Neelamani, R., Baurnstein, A. L., Gillard, D. G., Hadidi, M. T., and Soroka, W. L., 2008, Coherent and random noise attenuation using the curvelet transform: The Leading Edge, 27, 240-248, doi 10.1190/1.2840373.
Oskooi, B., Julayusefi, M., and Goudarzi, A., 2015, GPR noise reduction based on wavelet thresholdings: Arabian Journal of Geosciences, 8, 2937–2951.
Pakmanesh, P., Goudarzi, A., and Kourki, M., 2018, Hybrid Sparse Blind Deconvolution: an implementation of SOOT algorithm to real data: Journal of Geophysics and Engineering, 15(3), 621-626.
Press., W. H., and Teukolsky, S. A., 1990, Savitsky-Golay smoothing filters: Computers in Physics, 669-672.
Rudin, L., Osher, S., and Fatemi, E., 1992, Nonlinear total variation based noise removal algorithms: Physica D, 60, 259-268.
Sadeghi., M., and Fereidoon, B., 2018, Optimum window length of Savitzky-Golay filters with arbitrary order: Electrical Engineering and Systems Science, Signal processing, Working Paper, cite as arXiv:1808.10489.
Savitzky, A., and Golay, M., 1964, Smoothing and differentiation of data by simplified least squares procedures: Analytical Chemistry, 36, 1627-1639.
Selesnick, I., 2012, Total variation denoising (an MM algorithm): NYU Polytechnic School of Engineering Lecture Notes, 1-12.
Selesnick, I., and Chen, P., 2013, Total variation denoising with overlapping group sparsity: Acoustics, Speech and Signal Processing (ICASSP), IEEE International Conference, 5696-5700.
Wang, Y., Yang, J., Yin, W., and Zhang, Y., 2008, A new alternating minimization algorithm for total variation image reconstruction: SIAM Journal on Imaging Sciences, 1(3), 248–272.
Yin, W., Osher, S., Goldfarb, D., and Darbon, J., 2008, Bregman iterative algorithms for 1-minimization with applications to compressed sensing: SIAM Journal on Imaging Sciences, 1(1), 143–168.