## 5 Discussion  
This paper presents a new method, namely CPPCA, for the phase reconstruction problem in MT-InSAR applications. This method models SAR observation sample vectors from the perspective of probability. By resolving the optimization problem defined with respect to this model, the reconstructed interferometric signals can be derived. Theoretically, this method has an equivalent accuracy compared to the EVD method. The most distinct feature of the proposed method is that no coherence matrix is required to be generated during the entire phase reconstruction process. Moreover, this method has an excellent computational efficiency, which makes it especially suitable for high-dimensional SAR stacks. As can be observed from the previous section, the proposed CPPCA method seems to perform \"worse\" on the real data than on the simulated data. Let us take \(N=101\) as an example. The proposed CPPCA method requires 1.44 s to deal with the simulated data, which is approximately \(1/12\) of the traditional EVD method's time expenditure. On the other hand, the execution time required by the CPPCA method for the real data is \(1/10\) of that of the EVD method. As mentioned previously, a constant \(M=50\) is used to generate simulated data. In the case of real data, \(M\) is larger than 300 on average (although the number of SHPs on each pixel decreases as the dimension of the SAR stack rises), as a relatively large window size \(15\times 45\) is used for SHP identification. As mentioned previously, the computational complexity of probabilistic principle component analysis can be denoted as \(O(MN)\). That is to say, the computational complexity of the proposed CPPCA method highly depends on the number of samples. This is the main reason causing the inconsistent performances of the CPPCA method on the simulated and the real data. Therefore, in real applications, the computational performance of the CPPCA phase reconstruction can be effectively improved by decreasing the window size for sample selection. However, if the window size is unreasonably small, a solid statistical analysis cannot be assured, and hence inaccurate phase reconstruction results will be obtained. It has been repeatedly suggested that phase reconstruction can be considered to be a filter process with respect to SAR observation vectors [31; 41]. From the perspective of signal processing, the quality of filter results is highly dependent to the signal-to-noise ratio of the original data. In other words, in the area with low coherence, no phase reconstruction methods are capable of providing reliable interferometric phase estimates. Therefore, to ensure the accuracy of MT-InSAR measurements, such unreliable results have to be deleted before subsequent interferometric analyses. In the last experiment, in order to retrieve the corresponding annual deformation rate and DEM error maps, a commonly used MT-InSAR processing strategy is applied to the phase reconstruction results from the both EVD method and CPPCA method. The proposed PGoF factor is used to mask unreliable phase reconstruction estimates. For the purpose of comprehensive validation, a relatively  
Figure 7: The annual deformation rate/DEM error maps obtained based on the EVD results (**a**,**d**) and the CPPCA results (**b**,**e**). The corresponding difference maps are presented in (**c**,**f**). low PGoF is used. Therefore, a small portion of phase reconstruction results, either from the proposed CPPCA method or the conventional EVD method, might be severely biased from the \"true\" interferometric phase values. Where this is the case, biased double-differenced deformation rate and DEM error estimates will be contained in the reference networks. Hence the final maps integrated from such networks will be contaminated in local areas. This is the main reason why the deformation rate/DEM error maps from the two methods are different from each other within a tiny portion of areas.