De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition
Abstract
:1. Introduction
2. Methods
2.1. Multiscale Dispersion Entropy
- (1)
- Time series uj (j = 1, 2, …, N) are taken via a coarse graining preprocessing for non-overlapping segments xb and are obtained as follows:
- (2)
- xb is mapped to c classes from 1 to c. First, the normal cumulative distribution function (NCDF) is employed to map the segment to yb from 0 to 1:Finally, for each cm potential dispersion pattern, the relative frequency is defined as follows:
- (3)
- The MDE is obtained as follows:
2.2. Phase Space Reconstruction
2.2.1. Mutual Information Function
2.2.2. False Nearest Neighbors
2.3. Discrete Wavelet Transform
2.4. SVD Decomposition
- Overlap data to segments to ensure the continuity of the data;
- Calculate the MDE for each data segment, for which the value below the threshold is the noisy data segment;
- Apply phase space reconstruction to calculate the number of wavelet decomposition level in noisy data segments;
- Perform discrete wavelet transform and discrete wavelet inverse transform for multiple components;
- Decompose the components using iterative SVD to obtain the de-noised section;
- Reconstruct the MT de-noising signal with the useful data segments given in Step 1 and the de-noising data segments given in Step 5, where the average value of the two segments is adopted for the overlapping data.
3. Synthetic Cases
3.1. Entropy Analysis
3.2. Parameter Calculation
3.3. Performance Evaluation
4. Implementation for MT Field Data
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Different Signals | MAE | MSE | MFE | MDE |
---|---|---|---|---|
Noise-free signal | 0.2531 | 1.6493 | 0.1582 | 2.7568 |
With square wave | 0.4519 | 0.9279 | 0.1369 | 1.1521 |
With triangle wave | 0.3458 | 1.3142 | 0.1174 | 2.0091 |
With impulse noise | 0.3379 | 1.5034 | 0.1041 | 2.3361 |
With various noise | 0.4323 | 0.9013 | 0.1124 | 1.1055 |
Signals with Different Noise | Noisy Segment1 | Noisy Segment2 | Noisy Segment3 | Noisy Segment4 | Noisy Segment5 | Noisy Segment6 | Noisy Segment7 | Noisy Segment8 |
---|---|---|---|---|---|---|---|---|
Square wave | 4 | 5 | 4 | 5 | 4 | 5 | - | - |
Triangle wave | 5 | 5 | 4 | 5 | 4 | 4 | 4 | 4 |
Impulse noise | 4 | 5 | 4 | 4 | 4 | 5 | 4 | 4 |
Various noise | 4 | 5 | 4 | 4 | 4 | 4 | 4 | 4 |
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Zhou, R.; Han, J.; Guo, Z.; Li, T. De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition. Remote Sens. 2021, 13, 4932. https://doi.org/10.3390/rs13234932
Zhou R, Han J, Guo Z, Li T. De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition. Remote Sensing. 2021; 13(23):4932. https://doi.org/10.3390/rs13234932
Chicago/Turabian StyleZhou, Rui, Jiangtao Han, Zhenyu Guo, and Tonglin Li. 2021. "De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition" Remote Sensing 13, no. 23: 4932. https://doi.org/10.3390/rs13234932