## 2 Methodology
### DS-InSAR Phase Optimization  
PS-InSAR technology often suffers from a low density of PS pixels due to environmental complexity and the presence of poor-quality interferograms. In contrast, DS-InSAR technology improves interferogram quality through filtering and phase optimization. It identifies statistically homogeneous pixels (SHPs) via hypothesis testing on time-series amplitude images and subsequently fuses PS candidates (PSCs) and distributed scatterer candidates (DSCs), significantly increasing the density of monitoring points [23; 24]. In this study, DS-InSAR processing was applied to the Sentinel-1A dataset to assess the advantages of high temporal revisit frequency and high spatial resolution in improving point density, as well as to verify the consistency of deformation results derived from multiple datasets. Subsequently, these inversion results were compared against those obtained using traditional PS-InSAR techniques on the \"Fucheng-1\" and \"Shenqi\" datasets. To enhance the processing efficiency and achieve a higher density of monitoring points, in this study, we first screened image pixels using the amplitude deviation (DA) threshold method: pixels with DA \(\leq\) 0.49 were retained, with those with DA \(<\) 0.25 directly recognized as PSC targets, while pixels with DA values within the range of 0.25 \(-\) 0.49 underwent a two-sample Kolmogorov-Smirnov (KS) test [7]. Pixels outside of this range were excluded from further testing. The inspection window was set to \(31\times 11\) in the range and azimuth directions, respectively, within which all neighboring pixels were compared with the central pixel to assess whether their temporal amplitude distributions were statistically consistent [9]. Phase values of homogeneous pixels were used to calculate the central pixel's phase value through weighted averaging, with the weights determined based on the correlation coefficients between the central pixel and each homogeneous pixel [25]. A coherence coefficient covariance matrix was constructed for the entire set of interferograms, and phase optimization was conducted on all-combination differential interferograms via the eigenvalue decomposition of the coherence matrix. That is to say, for any distributed target, the coherence matrix \(T\) can be expressed as follows [26]:  
\[T=E\left[yy^{H}\right]\approx\frac{1}{N_{p}}{\sum_{\alpha\in\Omega}}\ yy^{H} \tag{1}\]  
where \(y=[y_{1},y_{2},\ldots,y_{N}]\) is the complex vector after normalization; \(y^{H}\) is the conjugate transpose of \(y\); \(\Omega\) is the set of homogeneous points of the distributed target; and \(N_{p}\) is the number of these homogeneous points. In addition, \(E\left[\left|y_{i}\right|^{2}\right]=1\); the coherence matrix \(T\) captures the coherence and related information of the distributed target's homogeneous points. Additionally, as the coherence matrix is positive-definite, it can undergo eigenvalue decomposition, represented as follows [27]:  
\[T=U\Lambda U^{H}=\sum_{i=1}^{N}\lambda_{i}u_{i}u_{i}^{H} \tag{2}\]  
where \(\Lambda\) is a diagonal matrix and \(\Lambda=diag(\lambda_{1},\lambda_{2},\ldots,\lambda_{N})\); \(\lambda_{i}\) represents the \(N\) eigenvalues of the coherence matrix and \(u_{i}\) is the eigenvector corresponding to each eigenvalue \(\lambda_{i}\). In the comparison of eigenvalues, larger ones indicate that their corresponding eigenvectors are optimal estimates, while others are treated as noise. Normally, the maximum eigenvalue surpasses the rest. Thus, the coherence matrix \(T\) can be expressed as the sum of two parts:  
\[T=T_{signal}+T_{noise}=\sum_{i=1}^{m}\lambda_{i}u_{i}u_{i}^{H}+\sum_{m+1}^{N }\lambda_{i}u_{i}u_{i}^{H}\approx T_{signal} \tag{3}\]  
where \(T_{signal}\) and \(T_{noise}\) are the coherence matrices for signals and noise, respectively; when the eigenvalues of noise are small enough to be ignored, the maximum eigenvalue's corresponding eigenvector gives the optimized phase for the distributed target.