On the Use of Weighted Least-Squares Approaches for Differential Interferometric SAR Analyses: The Weighted Adaptive Variable-lEngth (WAVE) Technique

Abstract

This paper concentrates on the study of the Weighted Least-squares (WLS) approaches for the generation of ground displacement time-series through Differential Interferometric SAR (DInSAR) methods. Usually, within the DInSAR framework, the Weighted Least-squares (WLS) techniques have principally been applied for improving the performance of the phase unwrapping operations as well as for better conveying the inversion of sequences of unwrapped interferograms to generate ground displacement maps. In both cases, the identification of low-coherent areas, where the standard deviation of the phase is high, is requested. In this paper, a WLS method that extends the usability of the Multi-Temporal InSAR (MT-InSAR) Small Baseline Subset (SBAS) algorithm in regions with medium-to-low coherence is presented. In particular, the proposed method relies on the adaptive selection and exploitation, pixel-by-pixel, of the medium-to-high coherent interferograms, only, so as to discard the noisy phase measurements. The selected interferometric phase values are then inverted by solving a WLS optimization problem. Noteworthy, the adopted, pixel-dependent selection of the “good” interferograms to be inverted may lead the available SAR data to be grouped into several disjointed subsets, which are then connected, exploiting the Weighted Singular Value Decomposition (WSVD) method. However, in some critical noisy regions, it may also happen that discarding of the incoherent interferograms may lead to rejecting some SAR acquisitions from the generated ground displacement time-series, at the cost of the reduced temporal sampling of the data measurements. Thus, variable-length ground displacement time-series are generated. The mathematical framework of the developed technique, which is named Weighted Adaptive Variable-lEngth (WAVE), is detailed in the manuscript. The presented experiments have been carried out by applying the WAVE technique to a SAR dataset acquired by the COSMO-SkyMed (CSK) sensors over the Basilicata region, Southern Italy. A cross-comparison analysis between the conventional and the WAVE method has also been provided.

On the Phase Nonclosure of Multilook SAR Interferogram Triplets

“…We would like to remark that, in our work, we do not want to discriminate one another the different inherent, local signals that contribute to the phase biased signal nor the time-series of the inherent phase contributions. Conversely, we want to estimate and mitigate the effect of the "composite" global systematic phase biased components on the ground deformation products, as obtained using Mt-InSAR algorithms (e.g., [18], [19], [39], [47], [54]).…”

“…It is worth remarking that the additional long-baseline ML interferograms are exclusively used to compute the phase bias. However, they are not exploited to generate the ground deformation time-series using an SB-oriented algorithm [18], [19], [39], [47], [54].…”

Multi-Temporal Small Baseline Interferometric SAR Algorithms: Error Budget and Theoretical Performance

“…, N be the perpendicular and temporal baselines of the (i, j)-th interferometric SAR data pairs. Among the vast amount of interferometric SAR techniques developed in almost the last thirty years to study the Earth's surface displacements, the class of small baseline (SB) methods, see for instance [25,27,31,33,37,38], is widely used. The SB methods were principally developed to investigate the ground displacement signals of distributed targets (DS's), which correspond to spatially-distributed objects on the ground with no dominant point-wise scatterers that are affected by the spatial and temporal decorrelation phenomena [40].…”

“…In particular, over the last twenty years, the DInSAR technology gradually evolved towards new advanced multi-temporal interferometric SAR (MT-InSAR) techniques [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], for the generation of ground displacement time-series. In this context, the two main classes of the Persistent Scatterers (PS) [21,36] and the Small Baseline (SB) [16,[25][26][27][37][38][39] methods emerged, and were principally used for the detection of the displacements affecting point-wise persistent scatterers (PS) and distributed scatterers (DS) on the terrain, respectively. On the one hand, the PS methods analyzed the displacement of SAR scenes' radar pixels, at the single-look resolution scale, characterized by a dominant scatterer that maintained its phase stability over the entire SAR data time-series.…”

On the Use of Interferometric Synthetic Aperture Radar Data for Monitoring and Forecasting Natural Hazards

“…In this regard, Ferretti et al (2011) propose the SqueeSAR algorithm, which jointly processes point scatterers and distributed scatterers, thus improving the density and quality of measurement points over non-urban areas, and Fornaro et al (2014) extend SqueeSAR, enabling the identification of multiple scattering mechanisms from the analysis of the covariance matrix. Extensions of the SBAS algorithm have been proposed by Lauknes et al (2010), where better robustness is achieved using an L 1 -norm cost function, Shirzaei (2012), where the accuracy is enhanced by using new methods for identification of stable pixels and wavelet-based filters for reducing artifacts, and Falabella et al (2020), where the usability is extended to low-coherence regions using a weighted least-squares approach. Moreover, Hetland et al (2012) propose an approach, called multiscale InSAR time series, that extracts spatially and temporally continuous ground deformation fields using a wavelet decomposition in space and a general parametrization in time.…”