Study On Multi-baseline Phase Unwrapping Algorithm

Nowadays, Synthetic Aperture Radar with Interferometric techniques (InSAR) are one of the most important approach in3-dimensional mapping of the terrain already, and two-dimensional Phase Unwrapping (PU) algorithms is the essential key procedure of InSAR system. Unfortunately, the traditional single baseline phase unwrapping methods are based on phase continuity hypothesis, that is to say, less than π of the phase difference between adjacent pixels is required. However, the hypothesis is not always satisfied in the world especially when mapping the rugged terrain. In order to overcome the drawbacks of the single baseline techniques, the multi-baseline (or multi-frequency) InSAR system is proposed. As the importantly promising technique of 3-dimension remote sensing in the future, the multi-baseline (or multi-frequency) system not only overcomes drawbacks of single baseline but also facilitates phase unwrapping with the baseline diversity (or frequency diversity). At the beginning, the multi-baseline (or multi-frequency) system is designed without phase unwrapping, but due to the bad noise robustness of the Chinese Reminder Theorem (CRT), it also needs to phase unwrapping. Taking the multi-baseline case for example, compared with the single baseline phase unwrapping problem, a more complicated situation is faced in multi-baseline phase unwrapping problem, to begin with, the L1-norm solution of multi-baseline phase unwrapping problem is never equivalent to the corresponding integer program, and no efficient algorithms of the multi-baseline phase unwrapping integer programming exist by now. On the other side, multi-baseline phase unwrapping has to process a huge dataset. More information is of benefit to phase unwrapping, but it brings a challenge for the computer hardware. Under such condition, an advanced computer hardware is required.In this dissertation, multi-baseline phase unwrapping techniques are regarding as the purpose, and many methods are proposed with the drawbacks of exist alogrithms, the limitation of computer hardware and the character of the realistic multi-baseline dataset being considered. The dissertation is organized as follow:1, The L1+L∞-Norm Multi-baseline Phase-Unwrapping AlgorithmIn this section, the difference between the single-baseline and the multi-baseline phase unwrapping problem is first discussed, and the reason of why the solution of the L1-norm multi-baseline phase unwrpping problem is never equivalent to that of the corresponding integer programming is given. In order to overcome the huge memory requirement of the traditional L1-norm method, a mixed-norm multi-baseline phase unwrapping method is proposed, which is named the L1+L∞-norm multi-baseline phase-unwrapping algorithm, where an L∞-norm cost function is employed to substitute for that of the L’-norm corresponding to the constraints between different interferograms to decrease the dimension of the optimization varable. The proposed improvement not only does good to decrese the memory requirement but also to the efficiency of the algorithm. With regards to the nonequivalence between the proposed method and the integer programming, an approximate estimation method is also proposed. Experiment with simulated and realistic dataset demonstrates that the proposed estimation method is effecive to estimate ambiguity numbers, besides, another experiment taking simultated dataset with different coefficient is also performed and the performance and elipsed time are also brought into comparison. By the experiment, the benefit of te proposed method is confirmed.2, The L∞+L1-Norm Multi-baseline Phase-Unwrapping AlgorithmIn order to decrease the memory required and improve the phase unwrapping performance of the traditional L’-norm method and the improved L1+L∞-norm multi-baseline phase unwrapping method when serious noise present, another mixed-norm multi-baseline phase unwrapping method is proposed in this section, which is named the L∞+L1-norm multi-baseline phase-unwrapping algorithm. Being different from the L1+L∞-norm multi-baseline phase-unwrapping algorithm, an L∞-norm cost function is employed to substitute for that of the L’-norm corresponding to the constraints between neighbor pixel within the same interferogram. Compared with that of the traditional L1-norm method, the length of the optimization varable in the newly proposed method is reduced by about 57%. On the other hand, the proposed method releases the strictness of the constraints corresponding to the neignbor pixels within the same interferogram and sustains that between different interferograms, which makes the solution not always satisfy the phase continuity hypothesis. Experiment demonstrates that the proposed method is able to unwrap interferometric phase but with filtering phenomenon. Realistic dataset experiment shows that the proposed method performes better that the traditional L’-norm method.3, A Cluster-Anslysis-Based Noise-Robust Phase-Unwrapping Algorithm for Multibaseline InterferogramsThe worse noise robustness of the Chinese Reminder Therorem (CRT) limits ita application in multi-baseline phase unwrapping, and the basic approaches to improve the noise robustness of the CRT-based multi-baseline phase unwrapping method contains, on the one hand, improving the noise robustness of the CRT method itself, on the other hand, decreasing the noise level of dataset in hand using cluster-analysis method. In this section, the bad performance of the traditional CA (Cluster Analysis) method is introduced first, and the reason is stated in the following. On the one hand, the histogram method in the CA method is unable to seperate different cluster when their intercept value is close. On the other hand, the cluster analysis performance of the traditional CA method is severely suffering from the variation in intercept within the cluster. With regards to the first drawback, more information of the intercept (the relative range and azimuth position in the image) is suggested to be added, therefore, the cluster analysis is performed in a higher-dimension than that of the traditional CA method. Under such condition, different cluster with close intercept value can be seperated in higher-dimension, since they are far apart in the space. With regards to the variation in intercept across the image, the density information of the intercept image is employed to distinguish the boundary of different cluster, and then a density connectivity analysis is performed to implement clustering. The density-based clustering method presented in this section is a specialized DBSCAN (Density-Based Spatial Clustering of Application with Noise) algorithm. The main difference between the original and the proposed density-based clustering method is that, to begin with, the data framework of the improved density-based clustering algorithm is designed according to the multi-baseline phase unwrapping dataset, which make the time complexity of the proposed clustering method be an linear algorithm, while the time complexity of the original method is O(NlogN). On the other hand, an adaptive parameter determination strategy of the density-based clustering algorithm is proposed to avoid using time consuming method. Furthermore, based on the density-based clustering alorithm, a cluster-analysis based noise robust multi-baseline phase unwrapping method is introduced in this section. The performance of the proposed density-based clustering algorithm is tested via an experiment with a 10000×10000 realistic dataset, from which we can see that the proposed method performs well than that of the traditional CA method and is able to overcome the bad influence of variation in intercept, besides, the proposed noise robust multi-baseline phase unwrapping method is with a low time complexity and memory complexity, therefore, it is suitable to handle large scale dataset. As regards to the noise robustness of the proposed method, experiment shows that severe noise only leads to noise points but does no effect on cluster analysis of area with good quality.4, An Improved Cluster Analysis AlgorithmDue to the lower efficiency of original procedure in the density-based clustering algorithm, a novel procedure is presented in this section where whether the point to be processed is a core point or not is first determined and what follows is the density-based connectivity analysis. According to the preceeding improvement, it is able to avoid calculating whether some points are core points or not again and again. With regards to the huge amount of noise points generated in the process of clustering, an L∞-norm defined distance between two different points is proposed. The benefit of the modification is that, on the one hand, it is good for decreasing the calculation when determining the distance of two different points, on the other hand, it leads to less noise points since the further distance is, the huge the variation in intercept is allowed compared with the original L2-norm, that is to say, more points are included in the ε-neighborhoodthe. Experiment on realistic and simulated dataset demonstrate that the improved clustering algorithm is able to generate less noise point, reduce clusters small in size and decrease the consuming time.