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Evaluation of a Cubature Kalman Filtering-Based Phase Unwrapping Method for Differential Interferograms with High Noise in Coal Mining Areas.

Liu W, Bian Z, Liu Z, Zhang Q - Sensors (Basel) (2015)

Bottom Line: Phase unwrapping can have a dramatic influence on the monitoring result.The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study.The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

View Article: PubMed Central - PubMed

Affiliation: School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China. liuliucumt@126.com.

ABSTRACT
Differential interferometric synthetic aperture radar has been shown to be effective for monitoring subsidence in coal mining areas. Phase unwrapping can have a dramatic influence on the monitoring result. In this paper, a filtering-based phase unwrapping algorithm in combination with path-following is introduced to unwrap differential interferograms with high noise in mining areas. It can perform simultaneous noise filtering and phase unwrapping so that the pre-filtering steps can be omitted, thus usually retaining more details and improving the detectable deformation. For the method, the nonlinear measurement model of phase unwrapping is processed using a simplified Cubature Kalman filtering, which is an effective and efficient tool used in many nonlinear fields. Three case studies are designed to evaluate the performance of the method. In Case 1, two tests are designed to evaluate the performance of the method under different factors including the number of multi-looks and path-guiding indexes. The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study. Two case studies are then designed to evaluate the feasibility of the proposed phase unwrapping method based on Cubature Kalman filtering. The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

No MeSH data available.


Three phase quality maps with FD, MC and PDV: (a) FD quality map; (b) MC quality map; (c) PDV quality map.
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sensors-15-16336-f004: Three phase quality maps with FD, MC and PDV: (a) FD quality map; (b) MC quality map; (c) PDV quality map.

Mentions: Figure 4 shows the three phase quality maps with each of the different quality indexes. Figure 4a–c are the quality maps calculated by FD, MC and PDV, respectively. A darker color in these graphs represents worse quality, and vice versa. At first glance, there are more similarities overall between Figure 4a,b, but there are also obvious differences. On the whole, Figure 4a is brighter than Figure 4b. This is because the values calculated by FD are mainly distributed in the lower range while the values of MC have a better dispersion. In addition, some pixels show low quality in Figure 4a but high quality in Figure 4b. Taking a typical pixel as an example, pixel A is an artificial Corner Reflector and is homologous in the subgraphs. However, pixel A exhibits quite different qualities in each of the three graphs. In Figure 4a, pixel A is very dark which means that the pixel is low quality. This is because FD reflects similarities between each pixel and its surroundings. In this example, the surrounding area of the Corner Reflector is covered by ground objects which are seriously uncorrelated, so the similarity is very low and the FD value is much higher. However, in Figure 4b, the opposite effect is shown. Since MC is used to indicate the correlation between each pixel in the two SLC images, more stable ground objects always lead to a greater coherence. Additionally, there is a slower change from a poor quality area to high quality area in Figure 4c. In other words, it is insensitive to different objects. Equation (29) can be interpreted as meaning that PDV only reflects the statistical characteristics of pixels in a given window without emphasizing the information of the current pixel, so some details are smoothed out. In summary, FD and MC are more sensitive than PDV. Compared with MC, the FD method considers both spatial diversity and coherence randomness, and is more robust and comprehensive for guiding the path of phase unwrapping.


Evaluation of a Cubature Kalman Filtering-Based Phase Unwrapping Method for Differential Interferograms with High Noise in Coal Mining Areas.

Liu W, Bian Z, Liu Z, Zhang Q - Sensors (Basel) (2015)

Three phase quality maps with FD, MC and PDV: (a) FD quality map; (b) MC quality map; (c) PDV quality map.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4541881&req=5

sensors-15-16336-f004: Three phase quality maps with FD, MC and PDV: (a) FD quality map; (b) MC quality map; (c) PDV quality map.
Mentions: Figure 4 shows the three phase quality maps with each of the different quality indexes. Figure 4a–c are the quality maps calculated by FD, MC and PDV, respectively. A darker color in these graphs represents worse quality, and vice versa. At first glance, there are more similarities overall between Figure 4a,b, but there are also obvious differences. On the whole, Figure 4a is brighter than Figure 4b. This is because the values calculated by FD are mainly distributed in the lower range while the values of MC have a better dispersion. In addition, some pixels show low quality in Figure 4a but high quality in Figure 4b. Taking a typical pixel as an example, pixel A is an artificial Corner Reflector and is homologous in the subgraphs. However, pixel A exhibits quite different qualities in each of the three graphs. In Figure 4a, pixel A is very dark which means that the pixel is low quality. This is because FD reflects similarities between each pixel and its surroundings. In this example, the surrounding area of the Corner Reflector is covered by ground objects which are seriously uncorrelated, so the similarity is very low and the FD value is much higher. However, in Figure 4b, the opposite effect is shown. Since MC is used to indicate the correlation between each pixel in the two SLC images, more stable ground objects always lead to a greater coherence. Additionally, there is a slower change from a poor quality area to high quality area in Figure 4c. In other words, it is insensitive to different objects. Equation (29) can be interpreted as meaning that PDV only reflects the statistical characteristics of pixels in a given window without emphasizing the information of the current pixel, so some details are smoothed out. In summary, FD and MC are more sensitive than PDV. Compared with MC, the FD method considers both spatial diversity and coherence randomness, and is more robust and comprehensive for guiding the path of phase unwrapping.

Bottom Line: Phase unwrapping can have a dramatic influence on the monitoring result.The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study.The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

View Article: PubMed Central - PubMed

Affiliation: School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China. liuliucumt@126.com.

ABSTRACT
Differential interferometric synthetic aperture radar has been shown to be effective for monitoring subsidence in coal mining areas. Phase unwrapping can have a dramatic influence on the monitoring result. In this paper, a filtering-based phase unwrapping algorithm in combination with path-following is introduced to unwrap differential interferograms with high noise in mining areas. It can perform simultaneous noise filtering and phase unwrapping so that the pre-filtering steps can be omitted, thus usually retaining more details and improving the detectable deformation. For the method, the nonlinear measurement model of phase unwrapping is processed using a simplified Cubature Kalman filtering, which is an effective and efficient tool used in many nonlinear fields. Three case studies are designed to evaluate the performance of the method. In Case 1, two tests are designed to evaluate the performance of the method under different factors including the number of multi-looks and path-guiding indexes. The result demonstrates that the unwrapped results are sensitive to the number of multi-looks and that the Fisher Distance is the most suitable path-guiding index for our study. Two case studies are then designed to evaluate the feasibility of the proposed phase unwrapping method based on Cubature Kalman filtering. The results indicate that, compared with the popular Minimum Cost Flow method, the Cubature Kalman filtering-based phase unwrapping can achieve promising results without pre-filtering and is an appropriate method for coal mining areas with high noise.

No MeSH data available.