SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics
Abstract
:1. Introduction
2. Phase Filtering of Shearlet Domain Based on Interferometric Phase Statistics
2.1. Interferometric Phase Statistics
2.2. Phase Model
2.3. Interferometric Phase Shearlet Transform
- are well localized;
- have parabolic scaling;
- are highly directionally sensitive;
- are spatially localized;
- and are optimally sparse.
2.4. The Proposed Filter
- (1)
- The real and imaginary parts of InSAR interferogram are processed by the shearlet transform, which are then decomposed into multiscale and multidirectional frequency bands , where is scale index, is direction index.
- (2)
- The threshold is then determined by the following procedure.
- Create a phase standard deviation look-up table between different coherence and multi-look number, as shown in Table 1.
- For a given interferogram, the standard deviation map can be generated pixel by pixel using the look-up table of the coherence and multi-look.
- Median robust estimator
- Calculate the threshold , for . denotes the average energy distribution of white noise in the shearlet coefficient on scale in direction . is the standard deviation defined by the proposed method.
- (3)
- After the new shrinkage threshold of every shearlet coefficient is obtained, we use the soft-thresholding formulation to shrink the shearlet coefficients.
- (4)
- Then the real and imaginary parts of the shearlet coefficients are processed by the inverse shearlet transform and the filtered real and imaginary parts are combined to get the filtered interferogram.
3. Validation with Simulation Data
4. Validation with Real Data
4.1. Validation with the Interferogram over the Etna Volcano
4.2. Validation with the Interferogram over Hong Kong
5. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Coherence | Multi-Look Number | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ... | |
0.001 | 1.813 | 1.813 | 1.813 | 1.812 | 1.812 | 1.812 | 1.812 | 1.811 | 1.811 | 1.811 | ... |
0.002 | 1.812 | 1.812 | 1.811 | 1.810 | 1.810 | 1.809 | 1.809 | 1.809 | 1.808 | 1.808 | ... |
0.003 | 1.812 | 1.810 | 1.809 | 1.808 | 1.808 | 1.807 | 1.807 | 1.806 | 1.805 | 1.805 | ... |
0.004 | 1.811 | 1.809 | 1.808 | 1.807 | 1.806 | 1.805 | 1.804 | 1.803 | 1.803 | 1.802 | ... |
0.005 | 1.810 | 1.808 | 1.806 | 1.805 | 1.803 | 1.802 | 1.801 | 1.801 | 1.800 | 1.799 | ... |
0.006 | 1.809 | 1.806 | 1.804 | 1.803 | 1.801 | 1.800 | 1.799 | 1.798 | 1.797 | 1.796 | ... |
0.007 | 1.808 | 1.805 | 1.803 | 1.801 | 1.799 | 1.798 | 1.796 | 1.795 | 1.794 | 1.793 | ... |
0.008 | 1.807 | 1.804 | 1.801 | 1.799 | 1.797 | 1.795 | 1.794 | 1.792 | 1.797 | 1.790 | ... |
0.009 | 1.806 | 1.802 | 1.800 | 1.797 | 1.795 | 1.793 | 1.791 | 1.790 | 1.788 | 1.787 | ... |
0.010 | 1.805 | 1.801 | 1.798 | 1.795 | 1.793 | 1.791 | 1.789 | 1.787 | 1.785 | 1.784 | ... |
... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
Filter | Positive Residues | Negative Residues | Residue Reduction (%) | PSD (×105) | SPD (×105) | RMSE |
---|---|---|---|---|---|---|
Unfiltered | 10,005 | 10,008 | - | 3.4254 | 2.5439 | - |
Goldstein | 5430 | 5431 | 45.73 | 2.5304 | 1.9945 | 0.2820 |
Wavelet | 2817 | 2824 | 71.81 | 1.9773 | 1.7258 | 0.1824 |
Lee | 2339 | 2342 | 76.61 | 1.8647 | 1.6119 | 0.1705 |
Proposed | 790 | 792 | 92.09 | 1.3952 | 1.3223 | 0.1693 |
Filter | Positive Residues | Negative Residues | Residue Reduction (%) | PSD (×105) | SPD (×105) | RMSE |
---|---|---|---|---|---|---|
Unfiltered | 9901 | 9905 | - | 6.1753 | 4.5503 | - |
Goldstein | 3556 | 3559 | 64.08 | 3.4275 | 2.6937 | 0.1711 |
Wavelet | 2248 | 2241 | 77.34 | 2.8216 | 2.3629 | 0.1499 |
Lee | 2667 | 2671 | 73.04 | 3.3403 | 2.7315 | 0.1117 |
Proposed | 1825 | 1826 | 81.56 | 2.5054 | 2.2158 | 0.0979 |
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He, Y.; Zhu, J.; Fu, H.; Xie, Q.; Xu, B.; Zhang, B. SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics. Appl. Sci. 2017, 7, 141. https://doi.org/10.3390/app7020141
He Y, Zhu J, Fu H, Xie Q, Xu B, Zhang B. SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics. Applied Sciences. 2017; 7(2):141. https://doi.org/10.3390/app7020141
Chicago/Turabian StyleHe, Yonghong, Jianjun Zhu, Haiqiang Fu, Qinghua Xie, Bing Xu, and Bing Zhang. 2017. "SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics" Applied Sciences 7, no. 2: 141. https://doi.org/10.3390/app7020141
APA StyleHe, Y., Zhu, J., Fu, H., Xie, Q., Xu, B., & Zhang, B. (2017). SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics. Applied Sciences, 7(2), 141. https://doi.org/10.3390/app7020141