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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.


Unwrapped maps (left) and rewrapped maps (right) based on MC and PDV: (a) unwrapped map of MC; (b) unwrapped map of PDV; (c) rewrapped map of MC; (d) rewrapped map of PDV.
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sensors-15-16336-f005: Unwrapped maps (left) and rewrapped maps (right) based on MC and PDV: (a) unwrapped map of MC; (b) unwrapped map of PDV; (c) rewrapped map of MC; (d) rewrapped map of PDV.

Mentions: Figure 5 shows the corresponding unwrapped and rewrapped results guided by MC and PDV. This can be compared with Figure 3b,e, which show the unwrapped and rewrapped results where path tracking is guided by FD. If we focus on the unwrapped maps, it can be seen that the FD method (shown in Figure 3) obtains a more continuous unwrapped phase and a greater maximum subsidence. This fits the subsidence map and interferogram better—the area with dense fringes has large subsidence. This is because the FD index combines the phase derivative with the expected phase variance (based on coherence), which is more robust and suitable for mountainous areas with less persistent scatters. From the rewrapped maps, the MC method retains most of the details, due to the fact that MC only accounts for the correlation without considering the spatial similarity of the differential interferogram. The highly correlated pixels are usually permanent scatters with little noise, so working along this index may lead to a clearer rewrapped map. However, it is not reliable in areas with fast subsidence that are covered in vegetation. For example, the Corner Reflector pixel located in a fast subsidence area is usually treated as high quality pixel by the MC method, due to the high coherence value. This is clearly not reasonable, since fast subsidence can lead to signal aliasing, preventing the real situation of the subsidence from being reflected. If it is used as a reference in earlier steps, there will be more error propagation. The PDV method takes the spatial difference into account without considering the coherence, which may weaken the overall reliability. Therefore, a continuous but low maximum unwrapped phase result is obtained by PDV. In summary, the FD method is more suitable for guiding the path of CKFPU algorithm where there is high noise and large phase gradients.


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)

Unwrapped maps (left) and rewrapped maps (right) based on MC and PDV: (a) unwrapped map of MC; (b) unwrapped map of PDV; (c) rewrapped map of MC; (d) rewrapped map of PDV.
© Copyright Policy
Related In: Results  -  Collection

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

sensors-15-16336-f005: Unwrapped maps (left) and rewrapped maps (right) based on MC and PDV: (a) unwrapped map of MC; (b) unwrapped map of PDV; (c) rewrapped map of MC; (d) rewrapped map of PDV.
Mentions: Figure 5 shows the corresponding unwrapped and rewrapped results guided by MC and PDV. This can be compared with Figure 3b,e, which show the unwrapped and rewrapped results where path tracking is guided by FD. If we focus on the unwrapped maps, it can be seen that the FD method (shown in Figure 3) obtains a more continuous unwrapped phase and a greater maximum subsidence. This fits the subsidence map and interferogram better—the area with dense fringes has large subsidence. This is because the FD index combines the phase derivative with the expected phase variance (based on coherence), which is more robust and suitable for mountainous areas with less persistent scatters. From the rewrapped maps, the MC method retains most of the details, due to the fact that MC only accounts for the correlation without considering the spatial similarity of the differential interferogram. The highly correlated pixels are usually permanent scatters with little noise, so working along this index may lead to a clearer rewrapped map. However, it is not reliable in areas with fast subsidence that are covered in vegetation. For example, the Corner Reflector pixel located in a fast subsidence area is usually treated as high quality pixel by the MC method, due to the high coherence value. This is clearly not reasonable, since fast subsidence can lead to signal aliasing, preventing the real situation of the subsidence from being reflected. If it is used as a reference in earlier steps, there will be more error propagation. The PDV method takes the spatial difference into account without considering the coherence, which may weaken the overall reliability. Therefore, a continuous but low maximum unwrapped phase result is obtained by PDV. In summary, the FD method is more suitable for guiding the path of CKFPU algorithm where there is high noise and large phase gradients.

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.