Discrete Green’s methods and their application to two-dimensional phase unwrapping

Maranò, Stefano; Palmieri, F.; Franceschetti, Giorgio

doi:10.1364/josaa.19.001319

Cited by 7 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Attempts have additionally been made to ensure optimal phase estimation by integer least square (LS) [23], goodness-of-fit [15], adaptive phase optimization [24], and by using corner reflectors to validate phase observations [25,26]. However, the spatio-temporal PhU [27,28] remains yet a challenging and ill-posed problem that possibly leads to the incorrect estimation of deformation TS. Among many others, the phase inversion algorithm based on L 1 -norm minimization [29] and phase closure technique [30] have been implemented to correct such errors.…”

Section: Introductionmentioning

confidence: 99%

Spatio-Temporal Quality Indicators for Differential Interferometric Synthetic Aperture Radar Data

et al. 2022

View full text Add to dashboard Cite

Satellite-based interferometric synthetic aperture radar (InSAR) is an invaluable technique in the detection and monitoring of changes on the surface of the earth. Its high spatial coverage, weather friendly and remote nature are among the advantages of the tool. The multi-temporal differential InSAR (DInSAR) methods in particular estimate the spatio-temporal evolution of deformation by incorporating information from multiple SAR images. Moreover, opportunities from the DInSAR techniques are accompanied by challenges that affect the final outputs. Resolving the inherent ambiguities of interferometric phases, especially in areas with a high spatio-temporal deformation gradient, represents the main challenge. This brings the necessity of quality indices as important DInSAR data processing tools in achieving ultimate processing outcomes. Often such indices are not provided with the deformation products. In this work, we propose four scores associated with (i) measurement points, (ii) dates of time series, (iii) interferograms and (iv) images involved in the processing. These scores are derived from a redundant set of interferograms and are calculated based on the consistency of the unwrapped interferometric phases in the frame of a least-squares adjustment. The scores reflect the occurrence of phase unwrapping errors and represent valuable input for the analysis and exploitation of the DInSAR results. The proposed tools were tested on 432,311 points, 1795 interferograms and 263 Sentinel-1 single look complex images by employing the small baseline technique in the PSI processing chain, PSIG of the geomatics division of the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC). The results illustrate the importance of the scores—mainly in the interpretation of the DInSAR outputs.

show abstract

Section: Introductionmentioning

confidence: 99%

Spatio-Temporal Quality Indicators for Differential Interferometric Synthetic Aperture Radar Data

et al. 2022

View full text Add to dashboard Cite

show abstract

“…However, Green functions are not properly functions in the usual sense, since they are formally defined as distributions. Distributional theory, Green functions, and the use of Green identities have been successfully implemented in many theoretical and applied works, e.g., SAR theory [5][6][7], scattering and wave propagation [8][9][10][11][12], wave diffraction and electrodynamics [13][14][15][16], phase unwrapping [17][18][19][20], etc.…”

Section: Introductionmentioning

confidence: 99%

The retarded potential of a non-homogeneous wave equation: introductory analysis through the Green Functions

et al. 2018

View full text Add to dashboard Cite

The retarded potential, a solution of the non-homogeneous wave equation, is a subject of particular interest in many physics and engineering applications. Examples of such applications may be the problem of solving the wave equation involved in the emission and reception of a signal in a synthetic aperture radar (SAR), scattering and backscattering, and general electrodynamics for media free of magnetic charges.However, the construction of this potential solution is based on the theory of distributions, a topic that requires special care and time to be understood with mathematical rigor. Thus, the goal of this study is to provide an introductory analysis, with a medium level of formalism, on the construction of this potential solution and the handling of Green functions represented by sequences of well-behaved approximatingfunctions.

show abstract

“…The spatio-temporal consistency index [36] is, as well, spatially variable and its contribution is hindered for sparsely distributed measure-ment points. Nonetheless, the spatio-temporal PhU [37], [38] is yet a challenging problem that leads to the incorrect estimation of deformation time-series (TS). The inevitable nature of the errors, as well as the issue being barely addressed so far, and due to the in-sensitiveness of already available quality estimates to PhU errors calls for more quality metrics [35].…”

Section: Contentsmentioning

confidence: 99%

Spatio-temporal quality metrics for satellite SAR interferometric data

Wassie

View full text Add to dashboard Cite

(English) The availability of RADAR images for monitoring Earth’s surface and its changes over time prompt the development of several interferometric SAR (InSAR) algorithms and methodologies. The Multi-temporal InSAR (MT-InSAR) techniques- being the one, generally, aim at extracting the temporal evolution of displacements of targets with coherent scattering behavior from a stack of SAR acquisitions that are taken from the same area and processed relative to temporal and spatial references. On the other hand, due to the complex nature of SAR measurements, addressing all possible model parameters in a comprehensive manner is still challenging and is a source of error and misinterpretation. As a well-established spaceborne geodetic technique with various applications, the accuracy of MT-InSAR products does matter, and hence potential error sources must be mitigated. The accuracy of displacement time-series (TS) estimates, in many cases, is governed by the quality and number of exploited images, associated interferograms, and selected measurement points. Such data and derived results are heavily influenced by factors, including environmental conditions at times of measurement acquisition and the processing algorithms used. Incomplete representations of factors in modeling MT-InSAR measurements may, as well, lead to omission errors and hence an incorrect estimation and interpretation of the displacement TS. Any uncertainty in the accuracy of the MT-InSAR products compromises their reliability in sensitive applications. In line with this, tools to detect, identify, and classify interferometric measurements that are particularly impacted by phase unwrapping (PhU) errors had been developed with the aim to identify and mitigate potential errors in the data— ultimately improving the quality and valuing the worth of MT-InSAR measurements. These tools make use of estimated phase residuals derived from a redundant network of unwrapped interferograms to formulate threshold-based quality scores as indicators of the reliability of the measurement points, images in a TS, images, and interferograms. Multiple pairs of baseline-constrained Sentinel-1 SAR images were considered to assess the potential of the tools to automatically detect, identify, and mitigate errors in the framework of the PSIG processing chain. The techniques were applied pixel by pixel in space and time to associate reliability scores highlighting the influence of global and local PhU errors in the course of the phase estimation. Experiments had generally justified that error mitigation strategies which include the exclusion of less reliable measurements from the network had relieved the impacts of errors and improved the TS estimation. Another important aspect of the thesis is the use of the point score tool as a post-PhU pixel filtering technique. The methodology contributes by providing quantitative information on the percentage of reliable pixels immediately after the PhU step. The experiments in this regard justified that the tool adds extra dimensions to common pixel selection techniques and is responsible for mitigating limitations on PhU error correction methodologies. Using it in conjunction with existing point selection techniques further guaranteed the inclusion of reliable points in the process. The results demonstrated that the proposed techniques significantly improved the quality of InSAR data. Besides, implications for various applications that rely on MT-InSAR datasets— such as those used in monitoring mining areas and infrastructures and those ground deformations induced either by natural or anthropogenic phenomena, have been justified. Potential avenues for future research to further improve the qualities of interferometric products including the quantification of interferometric measurement point location uncertainties are also envisioned. (Español) La creciente disponibilidad de imágenes RADAR para monitorear la superficie de la Tierra y sus cambios a lo largo del tiempo ha impulsado el desarrollo de varios algoritmos y metodologías de SAR (Synthetic Aperture Radar) interferométrico (InSAR). Las conocidas técnicas Multi-temporales InSAR (MT-InSAR) tienen como objetivo extraer la evolución temporal de los desplazamientos de puntos medidos. Esto se realiza sobre blancos con un comportamiento coherente en una pila de adquisiciones SAR sobre la misma área. Debido a la naturaleza compleja de las mediciones SAR, abordar todos los parámetros posibles del modelo de manera integral sigue siendo un desafío y es una fuente de error. Como una técnica geodésica bien establecida, la precisión de los productos MT-InSAR es importante y, por lo tanto, se deben mitigar las posibles fuentes de error. Cualquier incertidumbre en la precisión de los productos MT-InSAR compromete su fiabilidad en aplicaciones sensibles. En línea con esto, en esta tesis se han desarrollado herramientas para detectar, identificar y clasificar las mediciones interferométricas que se ven particularmente afectadas por los errores de desarrollo de fase, con el objetivo de identificar y mitigar posibles errores en los datos, mejorando entonces la calidad de las mediciones de MT-InSAR. Estas herramientas utilizan residuos de fase estimados derivados de una red redundante de interferogramas enrollados para formular índices de calidad basados en umbrales como indicadores de la fiabilidad de los puntos de medición, de las imágenes en una serie temporal, en imágenes y en interferogramas. Las técnicas se aplicaron píxel por píxel en el espacio y en el tiempo para asociar índices de fiabilidad que resaltaran la influencia de los errores de desarrollado de fase globales y locales. Los experimentos corroboran la estrategia propuesta. Otro aspecto importante de la tesis es el uso de la herramienta de índice de fiabilidad como técnica de selección de píxeles. La metodología proporciona información cuantitativa sobre el porcentaje de píxeles fiables inmediatamente después del desarrollo de fase. En general, los resultados demostraron que las técnicas propuestas mejoraron significativamente la calidad de los datos InSAR, por ejemplo, al excluir puntos erróneos automáticamente a partir de millones de puntos de medición. Además, se han justificado las implicaciones para varias aplicaciones que se basan en conjuntos de datos MT-InSAR, como los que se utilizan para monitorizar áreas e infraestructuras mineras y aquellas deformaciones delsuelo inducidas por fenómenos naturales o antropogénicos. Se prevén posibles vías de investigación futura para mejorar aún más las cualidades de los productos interferométricos.

show abstract

Discrete Green’s methods and their application to two-dimensional phase unwrapping

Cited by 7 publications

References 12 publications

Spatio-Temporal Quality Indicators for Differential Interferometric Synthetic Aperture Radar Data

Spatio-Temporal Quality Indicators for Differential Interferometric Synthetic Aperture Radar Data

The retarded potential of a non-homogeneous wave equation: introductory analysis through the Green Functions

Spatio-temporal quality metrics for satellite SAR interferometric data

Contact Info

Product

Resources

About