After about two decades of research activities and experiments, 3-D SAR Tomography [1], stemming from multibaseline SAR Interferometry [2] to get resolution capabilities in the height dimension for remote sensing of complex scenarios, has matured tending to the operational level [3-8]. Beyond applications to layover solution in height mapping of urban areas [8], the other most investigated remote sensing application is 3-D imaging of forest layers [1,3,5,7,9], especially for biomass monitoring, and dedicated spaceborne missions have been studied or are under development to this goal [3]. However, the main investigated, experimented, and adopted 3-D Tomography focusing algorithms, that are based on array processing of the multibaseline complex data obtained by multiple passes of a standard SAR system for height beam forming and steering [1,7,9], are often affected by temporal coherence loss of the (natural) scatterers [2,10]; this is well known to produce defocusing and blurring effects in the height imaging [1,9,10]. Beyond the possibility to consider resorting to special decorrelation-robust focusing 4D (3D+Time) algorithms [9] applicable for some baseline-time acquisition patterns, or to consider dedicated advanced SAR system configurations, the issue of temporal decorrelation still constitutes a particular criticality in the development of operational spaceborne missions for forest Tomography, such as the ESA Biomass mission [3]. Oddily enough, during the maturation of SAR Tomography, beyond some practice and indications got from experimental observations and simulated analyses, practically no effort has been dedicated to the development of an analytical theory to study and understand effects of temporal decorrelation on 3-D imaging, while a couple of papers have been dedicated to analyze effects of phase miscalibration [4,6], and recently seasonal and weather effects have been tackled. In this context, in this work an analytical theory is presented of the statistical behaviour of the height Point Spread Function (PSF) of 3-D SAR Tomography, with reference to the Fourier beamforming focusing algorithm [1,6,10], in presence of temporal decorrelation; the theory is based on first closed form derivations [10] obtained at the beginning of the 3-D SAR Tomography area, and is expanded also presenting general yet representative case studies, and more specific examples. It is expected that this analytical statistical characterization of the PSF of Fourier beamforming Tomography for a general partially temporal coherent scatterer can be useful, being the PSF the first main indicator of imaging quality for any image formation technique, and Fourier beamforming being one of the most diffused algorithms for array processing-based SAR Tomography. The presented analytical derivations in particular, given a typical expected or representative temporal decorrelation model [2,10], allow to easily quantify the average behaviour of the defocused and blurred PSF shape, and to get corresponding insights on different trends of PSF behaviour for different temporal decorrelation scales and baseline acquisition patterns versus time; in an operational context, this paves the way to a handy imaging quality prediction for 3-D Tomography oriented system feasibility studies, mission planning, and optimization, accounting in a detailed quantitative manner for temporal decorrelation and complementing the phase miscalibration oriented developments [4,6]. Specifically, the analytical statistical PSF characterization is particularized for both typical short- and long-term decorrelation models [2,10], and normalized general-purpose yet well representative case studies are reported for both regular baseline acquisitions in time and scattered baseline-time acquisition patterns, showing the corresponding average 3-D Tomography PSF shape for varying decorrelation degrees, that is different in terms of mainlobe and sidelobes behaviours, respectively; related insights are given. Analysis of the statistical dispersion of the PSF profile under decorrelation effects is also attacked. Comparison of the analytical derivations with simulations are reported confirming the predictions and illustrating the derived insights. Comparison with examples from real (airborne P-band) data will be possibly included at the conference. Moreover, case studies are shown with parameters mimicking the incoming P-band Biomass system [3], and the future planned NASA-ISRO NISAR system [11] with reference to its L-band channel (more critical for forest spaceborne Tomography that in fact is not currently, at the best of the Authors’ knowledge, a targeted application for this mission); effect of (hypothesized) mission parameter changes are possibly illustrated as well. Hints on the application of this analytical theory of statistical PSF behaviour to an operational oriented imaging quality prediction of 3-D Tomography are finally given.
Analysis of Temporal Decorrelation Effects on Point Spread Function of 3-D Tomo Beamforming
F. Lombardini
;
2019-01-01
Abstract
After about two decades of research activities and experiments, 3-D SAR Tomography [1], stemming from multibaseline SAR Interferometry [2] to get resolution capabilities in the height dimension for remote sensing of complex scenarios, has matured tending to the operational level [3-8]. Beyond applications to layover solution in height mapping of urban areas [8], the other most investigated remote sensing application is 3-D imaging of forest layers [1,3,5,7,9], especially for biomass monitoring, and dedicated spaceborne missions have been studied or are under development to this goal [3]. However, the main investigated, experimented, and adopted 3-D Tomography focusing algorithms, that are based on array processing of the multibaseline complex data obtained by multiple passes of a standard SAR system for height beam forming and steering [1,7,9], are often affected by temporal coherence loss of the (natural) scatterers [2,10]; this is well known to produce defocusing and blurring effects in the height imaging [1,9,10]. Beyond the possibility to consider resorting to special decorrelation-robust focusing 4D (3D+Time) algorithms [9] applicable for some baseline-time acquisition patterns, or to consider dedicated advanced SAR system configurations, the issue of temporal decorrelation still constitutes a particular criticality in the development of operational spaceborne missions for forest Tomography, such as the ESA Biomass mission [3]. Oddily enough, during the maturation of SAR Tomography, beyond some practice and indications got from experimental observations and simulated analyses, practically no effort has been dedicated to the development of an analytical theory to study and understand effects of temporal decorrelation on 3-D imaging, while a couple of papers have been dedicated to analyze effects of phase miscalibration [4,6], and recently seasonal and weather effects have been tackled. In this context, in this work an analytical theory is presented of the statistical behaviour of the height Point Spread Function (PSF) of 3-D SAR Tomography, with reference to the Fourier beamforming focusing algorithm [1,6,10], in presence of temporal decorrelation; the theory is based on first closed form derivations [10] obtained at the beginning of the 3-D SAR Tomography area, and is expanded also presenting general yet representative case studies, and more specific examples. It is expected that this analytical statistical characterization of the PSF of Fourier beamforming Tomography for a general partially temporal coherent scatterer can be useful, being the PSF the first main indicator of imaging quality for any image formation technique, and Fourier beamforming being one of the most diffused algorithms for array processing-based SAR Tomography. The presented analytical derivations in particular, given a typical expected or representative temporal decorrelation model [2,10], allow to easily quantify the average behaviour of the defocused and blurred PSF shape, and to get corresponding insights on different trends of PSF behaviour for different temporal decorrelation scales and baseline acquisition patterns versus time; in an operational context, this paves the way to a handy imaging quality prediction for 3-D Tomography oriented system feasibility studies, mission planning, and optimization, accounting in a detailed quantitative manner for temporal decorrelation and complementing the phase miscalibration oriented developments [4,6]. Specifically, the analytical statistical PSF characterization is particularized for both typical short- and long-term decorrelation models [2,10], and normalized general-purpose yet well representative case studies are reported for both regular baseline acquisitions in time and scattered baseline-time acquisition patterns, showing the corresponding average 3-D Tomography PSF shape for varying decorrelation degrees, that is different in terms of mainlobe and sidelobes behaviours, respectively; related insights are given. Analysis of the statistical dispersion of the PSF profile under decorrelation effects is also attacked. Comparison of the analytical derivations with simulations are reported confirming the predictions and illustrating the derived insights. Comparison with examples from real (airborne P-band) data will be possibly included at the conference. Moreover, case studies are shown with parameters mimicking the incoming P-band Biomass system [3], and the future planned NASA-ISRO NISAR system [11] with reference to its L-band channel (more critical for forest spaceborne Tomography that in fact is not currently, at the best of the Authors’ knowledge, a targeted application for this mission); effect of (hypothesized) mission parameter changes are possibly illustrated as well. Hints on the application of this analytical theory of statistical PSF behaviour to an operational oriented imaging quality prediction of 3-D Tomography are finally given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
