A novel wavelet seismic denoising method using type II fuzzy

Graphical abstractDisplay Omitted HighlightsWe have found that wavelet coefficients of seismic signal contain vagueness.Hence for the first time, we have proposed using fuzzy concept in wavelet denoising.We have found that fuzzy schemes are insufficient to handle the vagueness.Hence type II fuzzy thresholder is being proposed as a new thresholder.The results show promising improvements, when compared to other landmark methods. Wavelet based denoising of the observed non stationary time series earthquake loading has become an important process in seismic analysis. The process of denoising ensures a noise free seismic data, which is essential to extract features accurately (max acceleration, max velocity, max displacement, etc.). However, the efficiency of wavelet denoising is decided by the identification of a crucial factor called threshold. But, identification of optimal threshold is not a straight forward process as the signal involved is non-stationary. i.e. The information which separates the wavelet coefficients that correspond to the region of interest from the noisy wavelet coefficients is vague and fuzzy. Existing works discount this fact. In this article, we have presented an effective denoising procedure that uses fuzzy tool. The proposal uses type II fuzzy concept in setting the threshold. The need for type II fuzzy instead of fuzzy is discussed in this article. The proposed algorithm is compared with four current popular wavelet based procedures adopted in seismic denoising (normal shrink, Shannon entropy shrink, Tsallis entropy shrink and visu shrink).It was first applied on the synthetic accelerogram signal (gaussian waves with noise) to determine the efficiency in denoising. For a gaussian noise of sigma=0.075, the proposed type II fuzzy based denoising algorithm generated 0.0537 root mean square error (RMSE) and 16.465 signal to noise ratio (SNR), visu shrink and normal shrink could be able to give 0.0682 RMSE with 14.38 SNR and 0.068 RMSE with 14.2 SNR, respectively. Also, Shannon and Tsallis generated 0.0602 RMSE with 15.47 SNR and 0.0610 RMSE with 15.35 SNR, respectively. The proposed method is then applied to real recorded time series accelerograms. It is found that the proposal has shown remarkable improvement in smoothening the highly noisy accelerograms. This aided in detecting the occurrence of 'P' and 'S' waves with lot more accuracy. Interestingly, we have opened a new research field by hybriding fuzzy with wavelet in seismic denoising.

[1]  A. Pazos,et al.  Non-linear filter, using the wavelet transform, applied to seismological records , 2003 .

[2]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[3]  Nikhil R. Pal,et al.  Fuzzy divergence, probability measure of fuzzy events and image thresholding , 1992, Pattern Recognit. Lett..

[4]  Vicente Alarcón Aquino,et al.  A comparative simulation study of wavelet based denoising algorithms , 2005, 15th International Conference on Electronics, Communications and Computers (CONIELECOMP'05).

[5]  Hamid R. Tizhoosh,et al.  Image thresholding using type II fuzzy sets , 2005, Pattern Recognit..

[6]  A. K. Ray,et al.  Segmentation using fuzzy divergence , 2003, Pattern Recognit. Lett..

[7]  Sankar K. Pal,et al.  Index of area coverage of fuzzy image subsets and object extraction , 1990, Pattern Recognit. Lett..

[8]  Hong Yan,et al.  Fuzzy Algorithms: With Applications to Image Processing and Pattern Recognition , 1996, Advances in Fuzzy Systems - Applications and Theory.

[9]  Frank Scherbaum,et al.  Of Poles and Zeros: Fundamentals of Digital Seismology , 2013 .

[10]  A. Sayman Application of Kalman filter to synthetic seismic traces , 1992 .

[11]  Steven D. Glaser,et al.  Wavelet denoising techniques with applications to experimental geophysical data , 2009, Signal Process..

[12]  Dong Wang,et al.  Entropy-Based Wavelet De-noising Method for Time Series Analysis , 2009, Entropy.

[13]  C. V. Jawahar,et al.  Investigations on fuzzy thresholding based on fuzzy clustering , 1997, Pattern Recognit..

[14]  Kwang Baek Kim,et al.  Nucleus Extraction of Uterine Cervical Pap-Smears Using Marker Information and Watershed Algorithm , 2014 .

[15]  Brij N. Singh,et al.  Optimal selection of wavelet basis function applied to ECG signal denoising , 2006, Digit. Signal Process..

[16]  M. M. Mustafa,et al.  Comparing the performance of Fourier decomposition and Wavelet decomposition for seismic signal analysis , 2009 .

[17]  Hamid R. Tizhoosh,et al.  Enhancement and associative restoration of electronic portal images in radiotherapy , 1998, Int. J. Medical Informatics.

[18]  Asadollah Noorzad,et al.  Correction of highly noisy strong motion records using a modified wavelet de-noising method , 2010 .

[19]  P. Morettin Wavelets in Statistics , 1997 .

[20]  Paul S. Addison,et al.  The Illustrated Wavelet Transform Handbook , 2002 .

[21]  S. Pal,et al.  Fuzzy geometry in image analysis , 1992 .

[22]  J. J. Giner,et al.  De-Noising of Short-Period Seismograms by Wavelet Packet Transform , 2003 .

[23]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[24]  Mao-Jiun J. Wang,et al.  Image thresholding by minimizing the measures of fuzzines , 1995, Pattern Recognit..

[25]  J. Mohanalin,et al.  Wavelet based seismic signal de-noising using Shannon and Tsallis entropy , 2012, Comput. Math. Appl..

[26]  Shang-Jeng Tsai,et al.  Heuristic wavelet shrinkage for denoising , 2011, Appl. Soft Comput..

[27]  Anuja Nair,et al.  Choosing the optimal mother wavelet for decomposition of radio-frequency intravascular ultrasound data for characterization of atherosclerotic plaque lesions , 2005, SPIE Medical Imaging.

[28]  Brian L. Hughes,et al.  Nonconvexity of the capacity region of the multiple-access arbitrarily varying channel subject to constraints , 1995, IEEE Trans. Inf. Theory.

[29]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[30]  Azriel Rosenfeld,et al.  Image enhancement and thresholding by optimization of fuzzy compactness , 1988, Pattern Recognit. Lett..

[31]  J. Douglas,et al.  High-frequency filtering of strong-motion records , 2011 .

[32]  C. V. Jawahar,et al.  Analysis of fuzzy thresholding schemes , 2000, Pattern Recognit..

[33]  J. Mohanalin,et al.  Denoising Performance of Complex Wavelet Transform with Shannon Entropy and its Impact on Alzheimer Disease EEG Classification Using Neural Network , 2014 .

[34]  Mihailo D. Trifunac,et al.  Common problems in automatic digitization of strong motion accelerograms , 1999 .