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Citation:
 Yifei Zou,Xiukun Li,Ge Yu.Adaptive WVD Cross-Term Removal Method Based on Multidimensional Property Differences[J].Journal of Marine Science and Application,2025,(4):774-788.[doi:10.1007/s11804-024-00469-4]
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Adaptive WVD Cross-Term Removal Method Based on Multidimensional Property Differences

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Title:
Adaptive WVD Cross-Term Removal Method Based on Multidimensional Property Differences
Author(s):
Yifei Zou123 Xiukun Li123 Ge Yu123
Affilations:
Author(s):
Yifei Zou123 Xiukun Li123 Ge Yu123
1. National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China;
2. Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China;
3. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
Keywords:
Cross-term removalMultidimensional propertyApproximate entropyRényi entropySeeded region growing
分类号:
-
DOI:
10.1007/s11804-024-00469-4
Abstract:
Wigner–Ville distribution (WVD) is widely used in the field of signal processing due to its excellent time–frequency (TF) concentration. However, WVD is severely limited by the cross-term when working with multicomponent signals. In this paper, we analyze the property differences between auto-term and cross-term in the one-dimensional sequence and the two-dimensional plane and approximate entropy and Rényi entropy are employed to describe them, respectively. Based on this information, we propose a new method to achieve adaptive cross-term removal by combining seeded region growing. Compared to other methods, the new method can achieve cross-term removal without decreasing the TF concentration of the auto-term. Simulation and experimental data processing results show that the method is adaptive and is not constrained by the type or distribution of signals. And it performs well in low signal-to-noise ratio environments.

References:

[1] Adams R, Bishof L (1994) Seeded region growing. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(6): 641-647. https://doi.org/10.1109/34.295913
[2] ANS, BIO, AVS (2016) Optimization of quadratic time-frequency distributions using the local Rényi entropy information-ScienceDirect. Signal Processing 129: 17-24. https://doi.org/10.1016/j.sigpro
[3] Baraniuk RG, Flandrin P, Janssen AJEM, Michel OJJ (2001) Measuring time-frequency information content using the Renyi entropies. IEEE Transactions on Information Theory 47(4): 1391-1409. https://doi.org/10.1109/18.923723
[4] Baraniuk RG, Jones DL (1994) A signal-dependent time-frequency representation: fast algorithm for optimal kernel design. IEEE Transactions on Signal Processing 42(1): 134-146. https://doi.org/10.1109/78.258128
[5] Barbarossa S (1995) Analysis of multicomponent LFM signals by a combined Wigner-Hough transform. IEEE Transactions on Signal Processing 43(6): 1511-1515. https://doi.org/10.1109/78.388866
[6] Campbell LL (1965) A coding theorem and Rényi’s entropy. Information & Control 8(4): 423-429. https://doi.org/10.1016/S0019-9958(65)90332-3
[7] Carvalho EA, Ushizima DM, Medeiros, FNS, Martins CIO, Marques RCP, Oliveira INS (2010) Sar imagery segmentation by statistical region growing and hierarchical merging. Digital Signal Processing 20(5): 1365-1378. https://doi.org/10.1016/j.dsp.2009.10.014
[8] Choi HI, Williams WJ (1989) Improved time-frequency representation of multicomponent signals using exponential kernels. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(6): 862-871. https://doi.org/10.1109/ASSP.1989.28057
[9] Cohen L (1995) Time-frequency analysis: Theory and application. Englewood Cliffs: Prentice Hall Press, NJ, USA, 25-27
[10] Fu XQ, Yu J, Dai LY, Liu JF, Huang JG, Ren WB (2022) Cross-term suppression method for time-frequency spectrum of engineering blasting signals. Journal of Testing and Evaluation 50(1): 205-224. https://doi.org/10.1520/JTE20210094
[11] Guo JT, Wang HY (2008) Optimal kernel design and time-frequency analysis for frequency hopping signal using entropy measure. 2008 International Conference on Information and Automation, Changsha, China, 1168-1171. https://doi.org/10.1109/ICINFA.2008.4608176
[12] Hao GC, Tan F, Hu XY, Bai YX, Lv YW (2019) A matching pursuit-based method for cross-term suppression in WVD and its application to the ENPEMF. IEEE Geoscience and Remote Sensing Letters 16(8): 1304-130. https://doi.org/10.1109/LGRS.2019.2894223
[13] Jeong J, Williams WJ (1992) Mechanism of the cross-terms in spectrograms. IEEE Transactions on Signal Processing 40(10): 2608-2613. https://doi.org/10.1109/78.157305
[14] Jones DL, Baraniuk RG (1995) An adaptive optimal-kernel time-frequency representation. IEEE Transactions on Signal Processing 43(10): 2361-2371. https://doi.org/10.1109/78.469854
[15] Khan NA, Sandsten M (2016) Time-frequency image enhancement based on interference suppression in Wigner-Ville distribution. Signal Processing 127: 80-85. https://doi.org/10.1016/j.sigpro.2016.02.027
[16] Kumar R, Sumathi P, Kumar A (2015) Analysis of frequency shifting in seismic signals using Gabor-Wigner transform. Earthquake Engineering & Engineering Vibration 14(4): 715-724. https://doi.org/10.1007/s11803-015-0056-8
[17] Li XK, Liu MY, Jiang S (2015) Morphological research on geometrical scattering waves of an underwater target. Journal of Marine Science and Application 14(2): 208-214. https://doi.org/10.1007/s11804-015-1293-y
[18] Liu NH, Wang JY, Yang Y, Li Z, Gao JH (2023) WVD net: Time-frequency analysis via semi-supervised learning. IEEE Signal Processing Letters 30: 55-59. https://doi.org/10.1109/LSP.2023.3235646
[19] Liu WY, Han JG, Jiang JL (2013) A novel ball bearing fault diagnosis approach based on auto term window method. Measurement 46(10): 4032-4037. https://doi.org/10.1016/j.measurement.2013.07.039
[20] Moghadasian SS, Gazor S (2020) Sparsely localized time-frequency energy distributions for multi-component LFM signals. IEEE Signal Processing Letters 27: 6-10. https://doi.org/10.1109/LSP.2019.2951467
[21] Narasimhan SV, Kumar BKS (2004) Harmonic wavelet transform signal decomposition and modified group delay for improved Wigner-Ville distribution. 2004 International Conference on Signal Processing and Communications, Bangalore, India, 354-358. https://doi.org/10.1109/SPCOM.2004.1458417
[22] Pachori RB, Nishad A (2016) Cross-terms reduction in the Wigner-Ville distribution using tunable-Q wavelet transform. Signal Processing 120: 288-304. https://doi.org/10.1016/j.sigpro.2015.07.026
[23] Qiao Z, He YB, Liao CR, Zhu RH (2023) Noise-boosted weak signal detection in fractional nonlinear systems enhanced by increasing potential-well width and its application to mechanical fault diagnosis. Chaos, Solitons & Fractals 175: 113960. https://doi.org/10.1016/j.chaos.2023.11396
[24] Qiao Z, Shu XD (2021) Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery. Chaos Solitons & Fractals 145: 110813. https://doi.org/10.1016/j.chaos.2021.110813
[25] Ren H, Ren A, Li Z (2016) A new strategy for the suppression of cross-terms in pseudo-Wigner-Ville distribution. Signal Image & Video Processing 10(1): 139-144. https://doi.org/10.1007/s11760-014-0713-9
[26] Sampaio DL, Nicoletti R (2016) Detection of cracks in shafts with the Approximated Entropy algorithm. Mechanical Systems & Signal Processing 72: 286-302. https://doi.org/10.1016/j.ymssp.2015.10.026
[27] Sang TH, Williams WJ (1995) Renyi information and signal-dependent optimal kernel design. 1995 International Conference on Acoustics, Speech, and Signal Processing, Detroit, USA, 997-1000. https://doi.org/10.1109/ICASSP.1995.480344
[28] Sattar F, Salomonsson G (1999) The use of a filter bank and the Wigner-Ville distribution for time-frequency representation. IEEE Transactions on Signal Processing 47(6): 1776-1783. https://doi.org/10.1109/78.765169
[29] Singh VK, Pachori RB (2021) Sliding eigenvalue decomposition-based cross-term suppression in Wigner-Ville distribution. Journal of Computational Electronics 20(6): 2245-2254. https://doi.org/10.1007/s10825-021-01781-w
[30] Staniovi? L (2001) A measure of some time-frequency distributions concentration. Signal Processing 81(3): 621-631. https://doi.org/10.1016/S0165-1684(00)00236-X
[31] Sucic V, Saulig N, Boashash B (2014) Analysis of local time-frequency entropy features for nonstationary signal components time supports detection. Digital Signal Processing 34: 56-66. https://doi.org/10.1016/j.dsp.2014.07.013
[32] Vaillancourt DE (2010) Approximate entropy. In: Katie Kompoliti and Leo Verhagen Metman (Eds.). Encyclopedia of Movement Disorders, Chicago, USA, 54-56. https://doi.org/10.1016/B978-0-12-374105-9.00434-2
[33] Vedran J (2024) Local Rényi entropy-based Gini index for measuring and optimizing sparse time-frequency distributions. Digital Signal Processing 147: 104401. https://doi.org/10.1016/j.dsp.2024.104401
[34] Wacker M, Witte H (2011) Adaptive phase extraction: Incorporating the Gabor transform in the matching pursuit algorithm. IEEE Transactions on Biomedical Engineering 58(10): 2844-2851. https://doi.org/10.1109/TBME.2011.2160636
[35] Wang XJ, Cai YP, Lin XZ (2014) ICE fault diagnosis method based on mutual information and WVD time-frequency analysis. Applied Mechanics and Materials 525: 741-745. https://doi.org/10.4028/www.scientific.net/AMM.525.741
[36] Wigner EP (1932) On the quantum correction for thermodynamic equilibrium. Phy Rev 40(40): 749-759. https://doi.org/10.1103/PhysRev.40.749
[37] Williams WJ, Brown ML, Hero AO (1991) Uncertainty, information, and time-frequency distributions. SPIE’s 1994 International Symposium on Optics, Imaging, and Instrumentation, San Diego, United States, 144-156. https://doi.org/10.1117/12.49818
[38] Wood JC, Barry DT (1992) Radon transformation of time-frequency distributions for analysis of multicomponent signals. IEEE Transactions on Signal Processing 42(11): 3166-3177. https://doi.org/10.1109/78.330375
[39] Wu YS, Li XK (2016) Elimination of cross-terms in the Wigner-Ville distribution of multi-component LFM signals. Iet Signal Processing 11(6): 657-662. https://doi.org/10.1049/iet-spr.2016.0358
[40] Wu YS, Li XK, Wang Y (2018) Extraction and classification of acoustic scattering from underwater target based on Wigner-Ville distribution. Applied Acoustics 138: 52-59. https://doi.org/10.1016/j.apacoust.2018.03.026
[41] Yang XM, Zhou YT, and Liu SQ, Yin JP (2022) Research on complexity change of stock market based on approximate entropy. 2022 Asia Conference on Algorithms, Computing and Machine Learning (CACML), Hangzhou, China, 649-652. https://doi.org/10.1109/CACML55074.2022.00113
[42] Yang Y, Li YK (2016) Blind source separation based on time-frequency morphological characteristics for rigid acoustic scattering by underwater objects. Journal of Marine Science and Application 15(2): 201-207. https://doi.org/10.1007/s11804-016-1352-z
[43] Zou HX, Lu XG, Dai QH, Li YD (2002) Nonexistence of cross-term free time-frequency distribution with concentration of Wigner-Ville distribution. Science in China (Series) 3: 174-180. https://doi.org/10.1360/02yf9015

Memo

Memo:
Received date:2024-6-17;Accepted date:2024-8-13。<br>Foundation item:Supported by the National Natural Science Foundation of China (62201171).<br>Corresponding author:Ge Yu,E-mail:yuge221@hrbeu.edu.cn
Last Update: 2025-08-27