Differential SAR interferometry (DInSAR) measures the displacement of the ground occurring between the acquisition intervals of SAR image pairs using the phase difference of the SAR signal in the line-of-sight direction (Fig. 4) [26]. Firstly, SAR image pairs are coregistrated using the amplitude correlation approach, resulting in a subpixel coregistration accuracy (i.e., better than 1/10 of a pixel) to avoid the decorrelation of interferograms. Subsequently, the differential phase calculation of the corregistered SAR images is performed as follows [27]:
$$\Delta \varphi_{Int} = angle(SLC_{1} {*}SLC_{2} ) = \varphi_{m} { - }\varphi_{s}$$
(1)
$$\Delta \varphi_{D - Int} = \Delta \varphi_{Int} { - }\varphi_{Topo\_simu}$$
(2)
where \(SLC_{m}\) and \(SLC_{s}\) denote the signals of the master and slave images, respectively; \(\varphi_{m}\) and \(\varphi_{s}\) denote the phases of the master and slave images, respectively; \(\varphi_{{T{\text{opo}}\_simu}}\) denotes the simulated height-related phase. \(angle( \cdot )\) is the angle of the complex data; \(( * )\) is the conjugate multiplication of the complex data. Since the displacement-related phase changes linearly with the ground motion, the displacement can be calculated from the differential phase and the known SAR observation geometry.
Since the wavelength of the X-band radar signal is only a few centimeters (3.1 cm for TerraSAR-X), the DInSAR measurement approach should be sensitive to changes in the ground object, and millimeter accuracy can be reached theoretically. Due to the effect of spatiotemporal decorrelation and the atmospheric phase disturbance [28], the precision of DInSAR measurements can decline to centimeters in practice.
PSInSAR
A novel InSAR technique referred to as PSInSAR was proposed [29] to overcome the limitations of temporal and geometrical decorrelation and separate the displacement phase from other phase components of the differential interferogram (e.g., atmospheric phase). PSInSAR has the potential for millimeter-level ground motion mapping [15].
The first step of the PSInSAR procedure is the PS candidate selection. Points coherent over long time intervals are selected by indicators, such as the amplitude dispersion [30]. For the ith point, the phase components can be simplified as follows:
$$(\Delta \varphi_{D\_Int} )_{i} = (\varphi_{ele} )_{i} + (\varphi_{def} )_{i} + (\varphi_{APS} )_{i} + (\varphi_{dec} )_{i}$$
(3)
where \(\varphi_{m}\) denotes the elevation phase, \(\varphi_{def}\) is the deformation phase, \(\varphi_{APS}\) denotes the atmospheric phase, and \(\varphi_{dec}\) is the noise phase. Subsequently, a triangulated irregular network is constructed to connect adjacent points. The phase of the adjacent points is subtracted to mitigate atmospheric and other noise. Subsequently, a periodogram or solution space search method is used to estimate the unknown parameters of the motion and residual height between adjacent points, followed by a network adjustment to reconstruct the absolute parameters of each PS point. Finally, a spatiotemporal filter is used to remove the atmospheric phase signals since they are highly correlated in space and weakly in time [29].
The PSInSAR approach utilizes a strict candidate point selection threshold; only ground features such as buildings, bridges, and other structures that remain coherent over time can be retrieved. With an appropriate SAR dataset and careful data processing, the PSInSAR approach can reach submillimeter accuracy [15, 16]. However, a fixed PSInSAR threshold may cause a low density of candidate points in the research region, especially in vegetated areas where the landscape changes quickly over time. The low density of the PS points can affect the robustness of the PSInSAR algorithm by changing the structure and density of the network during PSInSARnSAR processing.
SBAS
The SBAS approach [31] is a creative MTInSAR technique. Unlike PSInSAR, SBAS utilizes a combination of image pairs with a small temporal and spatial baseline to maintain the temporal and spatial correlation. This combination increases the temporal sampling rate and improves the coherence of the interferograms, resulting in more reliable points in the final deformation maps.
In the SBAS technique, SAR image pairs with a small temporal and spatial baseline between the orbits were selected to generate the interferograms, preserving the temporal and spatial coherence characteristics of the interferograms [32]. Subsequently, multilooking [33] and filtering were used to decrease the noise and increase the image coherence. Then, phase unwrapping was performed using the minimum-cost flow algorithm [34] to obtain the relative phase from the original modulo-2π differential phase. The relationship between the motion-related phase and ground displacement is linear after phase unwrapping. Due to the potential disconnection between different subsets, singular value decomposition (SVD) was used to reconstruct the time-series deformation of the coherent points. The final step of SBAS is spatiotemporal filtering, which utilizes the temporal and spatial statistics of the data to identify undesired atmospheric artifacts [32]:
where B is the matrix after SVD; \(\Delta \phi\) denotes the phase of the differential interferograms; v denotes the deformation velocity to be solved. The SBAS method provides a higher spatial density of the deformation measurement points than the PSInSAR approach and has better adaptability in non-urban areas. However, the averaging processes (multilooking and filtering) may decrease the accuracy of the SBAS method. In addition, the accuracy of the SBAS method is highly sensitive to the accuracy of the phase unwrapping algorithm, whose robustness may not be high in vegetated areas that exhibit temporal decorrelation or in mountain areas with digital elevation model (DEM) errors.