Conference Agenda

InSAR time-series analysis is an extremely useful tool for monitoring long-term ground deformation over large areas of the planet. Accurate monitoring of ground deformation is important for understanding the processes that lead to natural disasters, and the health and safety of society. The discovery of a phase bias, or fading signal, has put the accuracy of methods that utilise spatial filtering and short-temporal interferograms, into question. The magnitude of the bias is dependent on the landcover type of the resolution cell and researchers have found it can correlate with the water content of the vegetation and soil. The phase loop closure is the summed phase of a series of interferograms that creates a closed loop in time. Due to the phase bias (and phase noise), multilooked interferograms may exhibit a non-zero phase loop closure. When time series InSAR methods require short-temporal baseline interferograms, the non-zero phase closure accumulates to strongly bias the deformation measurements. The longer the interferograms in the time series are, the smaller this bias is. For this reason, methods that utilise short-term interferograms, such as small baseline InSAR, are at risk of having inaccurate deformation measurement results. Various methodologies exist to correct and mitigate the phase loop misclosure by restoring consistency to the interferograms. Other methods that involve phase linking are less affected by the phase bias since they are able to use both long and short temporal baseline interferograms to restore consistency to the data. While these methods can successfully correct InSAR time series, they do not explain the mechanics causing the bias in the first place. In this study, we compare the phase bias in C-band and L-band data for an area centered on Milan, Italy. The reason for using multiple types of SAR data comes down to the way that microwaves interact with the surface. Vegetation, because of its variation in scattering characteristics, is dependent on the wavelength of the microwaves. By comparing the phase bias present in the two datasets and correlating it with landcover data, we explore the differences in how the phase bias manifests for the different wavelengths. The chosen area contains a mixture of landcover types and has a level of rainfall that means we can see the bias clearly. This work is particularly important for the upcoming L-band NISAR mission where the phase bias will be stronger than for C- and X-band missions.

The short revisit time offered by the Sentinel-1 satellite allows for interferograms spanning a short interval to maintain better coherence, resulting in a more accurate estimate of rapid deformation. Additionally, a greater number of acquisitions helps reduce noise contribution in InSAR time series analyses. However, the use of shorter-interval, multilooked interferograms can introduce a bias, also known as a “fading signal”, in the interferometric phase, which results in unreliable velocity estimates. To address this, we have previously developed an empirical mitigation strategy that corrects the phase bias based on the assumption that the change in strength of the bias in interferograms of different length has a constant ratio (Maghsoudi et al. 2022). We employ two constant values and to linearly relate the bias in the longer interferograms to the sum of the corresponding biases in the short interferograms. While the algorithm is successful in correcting the phase bias in the study region, the universality of the method remains untested.

In this presentation we will explore the applicability of the proposed method across various scenarios. Specifically, we will test the following:

• The validity of our assumption in different land covers and rainfall regimes: our current assumption of constant values for and was valid in the frames that we tested in Turkey. We test the validity of this assumption for other regions with different landcover and different scattering behaviors.
• The impact of gaps in the time-series: despite the frequent acquisition of Sentinel-1 data with short temporal baselines in most regions, there may still be gaps in the time-series caused by a lack of acquisition or decorrelation factors such as vegetation, cultivation, or snow cover. To address this, we test the use of a temporal smoothing constraint in our least squares inversion.
• Whether the approach can be expanded to a densified network of interferograms: in our original implementation, we used and to estimate phase bias corrections for the three nearest interferograms, limiting us to three connections per epoch. However, in this study, we extend this idea by introducing new constant values in the observation equations for each temporal baseline interferogram, allowing us to correct longer interferograms and have more than three connections per epoch.
• The impact of the Sentinel-1B failure: The failure resulted in certain frames exhibiting a mixture of various acquisition patterns in the time-series, including some intervals of 6 days and some of 12 days. To resolve this issue, we have adjusted our observation equations to enable the joint estimation of constant values for both acquisition patterns in our simultaneous inversion.

Correcting for the phase bias is particularly important for InSAR processing systems, such as the COMET LiCSAR system (Lazecký et al. 2020), which aims to study geohazards over large areas. We will show the impact of phase bias correction on one or more tectonic areas within the Alpine-Himalayan tectonic belt.

References

Lazecký, M., Spaans, K., González, P.J., Maghsoudi, Y., Morishita, Y., Albino, F., Elliott, J., Greenall, N., Hatton, E., Hooper, A., Juncu, D., McDougall, A., Walters, R.J., Watson, C.S., Weiss, J.R., & Wright, T.J. (2020). LiCSAR: An Automatic InSAR Tool for Measuring and Monitoring Tectonic and Volcanic Activity. Remote Sensing, 12

Maghsoudi, Y., Hooper, A.J., Wright, T.J., Lazecky, M., & Ansari, H. (2022). Characterizing and correcting phase biases in short-term, multilooked interferograms. Remote Sensing of Environment, 275, 113022

Soil moisture levels vary spatially at scales related to agricultural field extent, which is a much finer scale than is possible to resolve with spaceborne or even airborne radiometric instrumentation. Active radar provides a finer resolution than most radiometer systems and may be used to detect changing soil moisture through the InSAR closure phase parameter. Closure phase refers to the net phase when linking three interferograms formed from three acquisitions so that the net phase in single-look interferograms is zero. The closure phase can become nonzero when regions of pixels are averaged spatially (in multilooked images) before the net phase is computed. Further, the closure phase reflects changes in the medium dielectric constant if there are scatterers of varying depths within the medium.

We have developed a model showing that systematic non-zero closure phase results from scattering from objects at different depths in a medium of time-varying dielectric, such as from changes in soil moisture. We have found that, under certain circumstances, we can predict soil moisture from closure phase using a data reduction approach that includes a cumulative sum of closure phase over time and subtraction of a bias term.

Here, we show that for a Sentinel-1 InSAR swath over Oklahoma, an empirical approach can be used to predict soil moisture time series from closure phase time series through a single model realization. Our model is based on the statistical averaging of the closure phase over a number of pixels; for our InSAR validation, therefore, we assume multilooking across a large enough number of pixels to generate a stable statistical average. Both model and data show that, after computing a cumulative sum of the closure phase, a “runaway” bias is detected; we do a simple fit to the bias signal and subtract it to force the cumulative closure phase into a fixed range. (While the “bias” that we subtract may contain information, our approach is to correlate soil moisture with a parameter that doesn’t continually increase – since soil moisture varies within a fixed range). We find that this parameter, which we call bias-corrected cumulative closure phase, is correlated with soil moisture.

We validate our results with in situ soil moisture data and find that soil moisture and closure phase can be highly correlated. Our in situ data comes from 39 sites across Oklahoma’s Mesonet system, each equipped with a sensor measuring soil moisture daily at 5 cm depth; we average soil moisture over the period of the closure phase triplet for our calculations. We use a time series of closure phase triplets from adjacent scenes in Sentinel-1; the small temporal baseline corresponds to a large closure phase. We find that the correspondence between soil moisture and our phase-closure-derived parameter varies by geography and landcover type, suggesting that differently detailed physical processes are at play. While some areas have stronger correlations than others, the areas that are correlated tend to behave similarly, and we can use the same fit between soil moisture and closure phase to generate predictions.

SAR Interferometry (InSAR) is a popular tool for monitoring the Earth's surface deformation due to its ability to detect small changes over time. However, one of the critical challenges in InSAR is extracting meaningful information from the interferometric phase, which is influenced by atmospheric conditions, topography, and decorrelations. Several techniques have been proposed to address these issues and improve the quality of the interferometric phase [1].

One technique is based on Permanent/Persistent Scatterers (PS) InSAR, which tracks deformation through time using individual scatterers dominating the signal from a resolution cell [2]. While this technique provides high-quality deformation information at point target locations, more is needed to obtain accurate results in natural scenes due to the low density of persistent scatterers. An alternative approach is based on distributed scatterers (DS), which are commonly found in natural environments and offer the potential to leverage information more effectively. The Small Baseline Subsets (SBAS) approach accounts for signal decorrelation, which selects interferogram subsets for a temporal analysis using short spatial and temporal baselines [3]. This approach has demonstrated promising results in various applications such as ground deformation monitoring and surface elevation mapping. However, deformation measurements on distributed targets often require spatial multi-looked filtering.

Another approach is the Phase Linking (PL) method, which integrates all interferometric combinations into equivalent single-reference (ESR) phases based on their statistical characteristics [4]. The PL algorithm is the maximum likelihood estimation (MLE) of ESR phases from all single-look complex (SLC) image combinations. The PL method exploits all wrapped interferometric phases to optimize the phase quality and can be used in conventional PSI processing. The SqueeSAR technology is one example of the PL method, which uses a phase triangulation algorithm [5].

This paper highlights the importance of the PL technique in developing SAR techniques from PSDS to ComSAR. Finally, the potential of Deep Learning as a valuable tool to improve the accuracy and efficiency of the Phase Linking process is discussed.

The closure phase problem refers to the fact that, for multilooked interferometric pixels, the closure phase can be non-zero, unlike the single-pixel case, where it is always zero. This is because volumetric targets such as forests and glaciers have non-symmetric scattering properties; hence, the zero-closure model is inadequate for such scenarios. The multilooked interferograms assume a mathematical model representing the volumetric target as an "equivalent point target" with a "phase center" position. The selection and weighting of interferograms can affect the accuracy of the reconstructed phase history. To address this statistical misclosure, the phase linking technique is used to estimate the linked phases accurately, which is critical for mitigating decorrelation effects on SAR data. Several studies have enhanced the precision and computational efficiency of PL estimation since the work of Guarnieri and Tebaldini (2009) [4]. These include the Broyden-Fletcher-Goldfarb-Shanno algorithm, equal-weighted and coherence-weighted factors, the Eigen decomposition-based algorithm, compression techniques, and regulation methods. The PL algorithms differ in the weight criteria adopted in each algorithm, which can be coherence-based, sparsity-based, or other forms of regularization. Coherence-based weight criteria consider the coherence of the interferograms in estimating the linked phases. Sparsity-based weight criteria consider the sparsity of the solution, where the solution should have as few non-zero components as possible. Regularization-based weight criteria consider other forms of regularization, such as smoothness or low rank, to improve the accuracy of the estimation.

The PSDS technique is a two-step approach used in InSAR applications to detect and monitor changes in the Earth's surface. In the first step, the PL technique is applied to all the interferograms available from N images, jointly exploiting them to estimate the N-1 linked phases [1,5]. In the second step, the PSDS technique removes signal decorrelations and estimates the parameters of interest, such as the elevation error and constant velocity. The ComSAR technique is a data compression approach that reduces the size of the time series stack in multipass SAR, allowing for efficient interferometric processing [6]. The ComSAR scheme in signal processing has benefits beyond just reducing the computational burden; it also prevents the need for updating and re-estimating the entire phase history in the face of every single acquisition. The TomoSAR (https://github.com/DinhHoTongMinh/TomoSAR) package is an open-source implementation of the PSDSInSAR and ComSAR algorithms optimized for analyzing Big InSAR Data. The code is heavy on memory use but can be processed on a cluster with sufficient RAM. The good news is that the TomoSAR service is free under a scientific collaboration.

Deep Learning (DL) has the potential to revolutionize the Phase Linking process in SAR imaging by providing an end-to-end solution that can learn the complex relationships between the interferometric phases and the ESR phase from data. Using specialized neural network architectures, such as the UNet and Complex CNN, can effectively handle the complex-valued nature of SAR data. DL training can be performed by providing a large dataset of SAR images and their corresponding ESR phases, enabling the network to automatically learn the most relevant features and relationships from the data. The advantages of exploiting DL for Phase Linking include handling non-stationary phase noise and outliers more effectively and reducing the computational cost of the process, making it more suitable for near-real-time processing of Big SAR data.

[1] Ho Tong Minh, D.; Hanssen, R.; Rocca, F. Radar Interferometry: 20 Years of Development in Time Series Techniques and Future Perspectives. Remote Sensing 2020, 12.

[2] Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Transactions on geoscience and remote sensing 2001, 39, 8–20

[3] Berardino, P.; Fornaro, G.; Lanari, R.; Sansosti, E. A New Algorithm for Surface Deformation Monitoring Based on Small Baseline Differential SAR Interferograms. Geoscience and Remote Sensing, IEEE Transactions on 2002, 40, 2375–2383.

[4] Guarnieri, A.M.; Tebaldini, S. On the Exploitation of Target Statistics for SAR Interferometry Applications. Geoscience and Remote Sensing, IEEE Transactions on 2008, 46, 3436–3443.

[5] Ferretti, A.; Fumagalli, A.; Novali, F.; Prati, C.; Rocca, F.; Rucci, A. A New Algorithm for Processing Interferometric Data-Stacks: SqueeSAR. Geoscience and Remote Sensing, IEEE Transactions on 2011,49, 3460–3470.

[6] Ho Tong Minh, D.; Ngo, Y.N. Compressed SAR Interferometry in the Big Data Era. Remote Sensing 2022, 14, 1–13.

Mature, reliable, and high-resolution soil moisture products globally are critical for improving climate models, monitoring and mitigating landslide hazards, and enhancing geotechnical engineering and reservoir management. In this presentation, we discuss the recent advances and a new algorithm that uses Interferometric Synthetic Aperture Radar (InSAR) time-series analysis to measure soil moisture.

The InSAR time-series analysis techniques have been widely used to measure ground surface displacement. There is growing evidence that temporal and spatial variation of soil moisture contributes to non-zero closure phase and a bias to the estimated displacement time-series. We demonstrate that the bias in the displacement time-series can be potentially used to estimate soil moisture.

Building on our existing model (Zheng et al., 2022), which explains closure phases in multi-looked InSAR measurements, we derive a physical multi-layer model that relates moisture to the phase of SAR Single Look Complex (SLC) measurements. Using the empirical relation between the dielectric constant and moisture change, our model links moisture changes directly to SAR measurements instead of interferometric phases (De Zan et al., 2015), and therefore preserving zero closure phase in single-look interferometric phases. Using a stack of Sentinel-1 data over Barstow-Bristol trough, California, we demonstrate that our model successfully explains a time-series of InSAR displacement bias and observed cumulative closure phase in which the bias time-series correlates with multiple recorded rain events. Our model predicts an observed range decrease for several acquisitions after each rain event. The accumulated range change settles until the next rain event when another episode of range decrease repeats and accumulates to the range change history. We demonstrate that this unique observation and model can potentially be used to map soil moisture time-series with high spatial resolution globally.