• 14:20 Solving the integral of quadratic forms of covariance matrices for applications in polarimetric radar imagery

  Marino, Armando (1); Hajnsek, Irena (1,2) 1: ETH Zurich, Switzerland; 2: DLR HR, Germany

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  Polarimetric SAR has large potentials in improving the retrieval of bio-physical parameters from space. This paper is focused on the quadratic forms of the polarimetric covariance matrix [C], which are largely used in radar polarimetry. For instance, the intensity of any polarimetric target can be represented as the quadratic form of [C] considering the specific projection vector (or scattering mechanism) identifying the target [1]. If u is a projection vector the quadratic form can be written as: conjugate(transpose(u))[C]u. Another example of usage of quadratic forms is for calculating the Pol-InSAR coherence: gamma [2]. This is evaluated as the quadratic form of the Polarimetric and Interferometric covariance matrix [O12] divided by the root square of the quadratic forms of the polarimetric covariance matrices [C1] and [C2] for the two acquisitions. Changing the unitary vector, gamma changes and all the possible values of gamma form a coherence region (or loci) on a polar plot. The latter can be evaluated numerically with Monte Carlo simulations. Coherence loci are largely used to understand the nature of the observed targets and to extract parameters (for instance in the inversion of the RVoG model), but are often hard to interpret. In order to have a more synthetic information, the optimum coherences or extremes of the coherence loci can be plotted. However, they miss to provide any information regarding the distribution of the points inside the region (please note, the coherences are generally not uniformly distributed inside the region). In this context, it may be beneficial to know where the centre of mass of the region is. Such point can be calculated solving the integral of gamma over the complex unitary sphere of projection vectors. Up to now, such integral had not an analytical solution and the only way to evaluate it was by using numerical methodologies (e.g. Monte Carlo solution). This work is focused on finding the centre of mass of the coherence loci. Firstly, a mathematical proof is provided for showing that the integral of a quadratic form of any n x n matrix is equal to the trace of the matrix. Secondly, the integral of gamma is tackled and it is showed that it is possible to approximate it with an equivalent expression of gamma where the quadratic forms are substituted by the Traces of the matrices. Such operator is here defined as Trace Coherence (TC). Unfortunately, TC is only an approximation of the integral. In order to understand the quality of such approximation, extensive Monte Carlo simulations are performed showing that the magnitude of the differences rarely exceeds values of 0.01. The advantages of using TC compared to solving the integral numerically are several: 1) the computation is several order of magnitude faster allowing real time applications; 2) the analytical expression of the TC can be used in modelling for retrieval algorithms or threshold settings. Additionally, TC can be exploited in coherent change detection, since it is a “collective” value over all the possible coherences and therefore it is not influenced or biased by the choice of the polarimetric channel (i.e. a channel could show large change and another could show no change). The integrals solutions are validated exploiting real ESAR (DLR) data acquired during the AGRISAR campaign 2006 (L-band, quad-polarimetric). The analytical expressions are compared with the integrals solved by Monte Carlo Integration for a large number of points in the ESAR images. The error statistics are then estimated to assess the quality of the proposed solutions. Some examples of usage of the Trace Coherence for change detection is showed and compared with coherent change detection by a single polarimetric channel. References: [1] S. R. Cloude, Polarisation: Applications in Remote Sensing, Oxford University Press, 2009. [2] S. R. Cloude and K. P. Papathanassiou, “Polarimetric SAR interferometry,” IEEE Transactions on Geoscience and Remote Sensing., vol. 36(5), pp. 1551–1565, 1998.

  
   

• 15:40 Can higher-order statistics add information in model-based polarimetric decompositions?

  Eltoft, Torbjorn; Doulgeris, Anthony Paul UiT-the Arctic University of Norway, Norway

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  The backscatter of SAR signals from Arctic sea ice, and many other rough surfaces, is thought to be caused by a combination of several scattering mechanisms, in general categorized as surface scattering, volume scattering, and double bounce scattering. SAR polarimetry has the capability of decomposing the signals into components representing these specific mechanisms. One class of polarimetric decomposition theorems is denoted model-based decompositions, in which, a physical model is connected to the various scattering mechanisms. The Freeman-Durden three-component model is a well-known example of a model-based decomposition algorithm, where a specific parameterized model is associated with the covariance matrix of each of the above-mentioned components. There is experimental evidence that electromagnetic backscatter from sea ice in some cases has a high degree of depolarization. Depolarization is in some decomposition models mostly attributed to volume scattering. However, for sea ice backscattering it is anticipated that depolarization can also be caused by surface effects related to rough and highly deformed ice, as well as by volume type scattering from brine inclusions and inhomogeneities inside the ice column. Previous analysis of polarimetric decompositions of sea ice scenes using existing algorithms show that the power of the double bounce component often is an order of magnitude below the contribution from surface and volume scattering, and that high double bounce is restricted to isolated features. Hence, we will in this study explore model-based polarimetric decomposition using a model which consists of only two terms; a surface scattering component and a volume scattering component. The surface component is to be described by the extended Bragg (X-Bragg) model, which can also predict surface based depolarization. The volume component is modeled as an azimuth symmetric scattering mechanism, consisting of randomly oriented scatterers, geometrically categorized with a single shape parameter. In total, the model for the polarimetric coherence matrix has 6 unknowns, but only 5 independent equations to solve for the parameters. Hence, the system is underdetermined (like many decomposition models). We have explored how higher-order statistical moments can add information, and be used to obtain a determined set of equations. We will both discuss theoretical aspects of our methodology, and show results of performance studies based on simulated and real data.

  
   

• 15:20 The impact of system limitations on PolSAR data physical modeling: the TerraSAR-X case

  Makhoul, Eduardo; López-Martínez, Carlos; Broquetas, Antoni Universitat Politècnica de Catalunya, Spain

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  Spaceborne synthetic aperture radars (SAR) are potential sensors for globally monitoring the earth surface, since they can provide high resolution images independent from daylight and weather conditions. Exploiting polarimetry jointly with SAR confers the polarimetric SAR (PolSAR) instruments a unique and powerful capability to extract quantitative geophysical and biophysical information. For proper interpretation of the data from PolSAR sensors, physical models have to be precisely defined, such that adequate parametric inversion of the physical backscattering mechanism can be obtained. Most of the studies present in the literature propose well-defined physical models that can describe the different scattering mechanisms being imaged by the PolSAR sensors, but without taking into consideration the limitations induced by the imaging instrument itself. In this line, the work here presented discusses the need to properly include the impact of system-driven constrains when using polarimetry to model the backscattering mechanisms. This paper focuses specifically on the study of fully polarimetric TerraSAR-X (TSX) data, i.e., quad-polarized (quad-pol) data; which has been acquired with the experimental dual-receive antenna (DRA) mode. This acquisition is based on an along-track interferometric configuration, where the receive antenna is halved into two sub-apertures receiving simultaneously the H and V polarizations, while the transmitted polarization is toggled in a pulse-basis. Such a configuration has a tow-fold impact in the measured data: first, a receive gain reduction and so a loss of sensitivity, in terms of noise-equivalent sigma zero (NESZ) or equivalently in terms of signal-to-noise ratio (SNR); and second, a temporal lag between the different polarimetric channels, which could induce additional temporal decorrelation. The issue related to the SNR limitation when operating TSX in fully polarimetric mode has raised several times in the polarimetric community. The work here considered is in line with that topic, showing the need to properly consider the SNR in the polarimetric characterization when using quad-pol TSX data. Moreover, when imaging dynamic scenarios, such as the sea/ocean, the related backscattered field decorrelates during the time-lag (or coregistration time) between the different polarimetric channels for the DRA acquisition mode. Such an additional decorrelation source, which is both system and scenario dependent, should be included in the polarimetric modeling for proper interpretation of the data. In this sense, the work here presented tries to fill the gap between the physical approaches and the signal-based approximations, stressing the requirement to account for the technological limitations of current SAR missions when imaging challenging scenarios, such as the sea/ocean. To show the impact of such system-driven specificities when applying physical models to the received TSX signal, the validity of the well-known Bragg scattering model (X-Bragg) has been evaluated with real quad-pol TSX data over the sea/ocean, incorporating both the SNR and temporal decorrelations. It is also intended to extend such considerations to the general formulation of the volume scattering mechanism when imaged by current state-of-the-art missions such as TerraSAR-X.

  
   

• 14:00 PolSARproSim+: The enhanced coherent, polarimetric simulator for studying forest polarimetry and interferometry

  Ahmed, Razi; Hensley, Scott; Neumann, Maxim; Lavalle, Marco Jet Propulsion Lab, United States of America

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  PolSARproSim is a coherent forest SAR simulator, distributed as an open source software by the European Space Agency. Unlike other forest scattering softwares that model forests as multilayered homogenous structures with the canopies as clouds of randomly distributed scatterers, PolSARproSim simulates scattering from individual intricately constructed trees, with branches and leaves with somewhat realistic shapes, dimensions, locations and dielectric properties. This feature is attractive because it allows an assessment of the impact of physical movement or moisture changes on forest parameter estimation algorithms, such as polarimetric interferometry or tomography, in controlled yet somewhat realistic scenarios. Since, PolSARproSim was written as an educational tool with ease of use in mind it does have some limitations, namely that it can only simulate a homogenous stand, is limited to five species, generates tree parameters and locations based on some simple allometrics and does not introduce radar system artifacts such as thermal noise etc. In an effort to make the software more flexible and simulations more realistic, it has been modified to be able to simulate mixed stands, have external definition of species specific allometric parameters that essentially allow the user to simulate scattering from any number of tree species and to have the ability to specify tree by tree primitives such as location, height, dbh (diameter at breast height), crown radius and depth. In addition, PolSARproSim+ is now able to include motion or dielectric changes of leaves and branches between successive scenes to simulate temporal decorrelation due to wind or rain. The amount of spatial shift attributed to a branch or leaf (to simulate motion due to wind) is set to be a function of the object's height and size with configurable coefficients to allow flexibility. Moisture changes (effecting the dielectric properties) of both the ground and forest are also configurable in a similar manner. It is also capable of simulating a stack of interferograms with arbitrarily specified geometries for analyzing tomographic techniques, an external DEM can also be supplied to allow simulation from any topography. Simulation of system effects such as a flexible point spread function and thermal noise have also been implemented. The software utilizes multi-threaded architecture to significantly reduce computation time even with the added computational complexity.

  
   

• 14:40 Comparative Analysis of Temporal Decorrelation at P and L bands over Tropical forests : EM Simulations and Results from Tower based Experiments

  Villard, Ludovic; Le Toan, Thuy; Borderies, Pierre CESBIO, France

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  In the design of repeat-pass Polarimetric and Interferometric SAR (PolInSAR) acquisitions for forest biomass or height retrieval, temporal decorrelation is among one of the major constrains. Indeed, measurements of PolInSAR coherences do not only depend on forest parameters of interest (e.g related to canopy height, structure or underlying ground) but also on temporal changes of the medium between passes. Despite an abundant literature on the subject, corrections accounting for temporal decorrelation remain challenging, being even more complex than several independent causes may be involved, whether related to bio and geophysical changes (e.g due to forest growth, mortality or vegetation and soil water content variation) or displacements due to windy conditions. In the frame of the future P-band Biomass ESA mission, the TropiScat tower-based experiment took place in French Guyana, providing valuable time series to better characterize temporal decorrelation over tropical dense forests. To strengthen the data analysis, recent works have been also undertaken in Electro-Magnetic (EM) modeling, particularly interesting to reproduce and quantify the temporal decorrelation due to diurnal changes of vegetation water content (related to evapotranspiration) or due to windy conditions (mostly related to convection). In addition, these EM simulations have been performed to assess the impact of various descriptive parameters of the forest, whether related to its structure (e.g through the ratio between crown or trunk layers) or to the underlying terrain, particularly relevant to anticipate the up-coming results from the following tower based campaign "AfriScat" in Ghana. Likewise, EM simulations have been also performed to compare the results at P and L bands, from which significant differences have been found and used to show the great potential of a combine use to discriminate causes due to dielectric changes or displacements. These results find also important applications in the frame of TangoSat mission (SAOCOM companion satellite currently under feasibility study at ESA), bringing strong basis to simulate the impact of temporal effects on single-pass Tomographic SAR acquisitions. Furthermore, in terms of synergy between P and L band SAR, and given the possible faithful estimation of temporal decorrelation at L band from SAOCOM 0-baseline acquisitions, prospects to extrapolate the one at P-band would also bring important insights for Biomass mission.

  
   

• 15:00 Imaging a Wide Swath with Full Polarimetry

  Villano, Michelangelo; Papathanassiou, Konstantinos P.; Krieger, Gerhard; Moreira, Alberto German Aerospace Center (DLR), Germany

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  Several applications of synthetic aperture radar (SAR) require or at least benefit from full polarimetry. The availability of a restricted subspace of polarizations (e.g. dual- and compact polarimetry), in fact, only allows the retrieval of some of the key parameters for most of the polarimetric models. In the past, however, full polarimetry has been often discarded in the design of spaceborne SAR missions, as it implied a significant reduction of the swath width, already constrained by the requirement on azimuth resolution. Innovative SAR techniques, based on digital beamforming on receive, allow nowadays high-resolution wide-swath (HRWS) imaging through multiple elevation beams, which simultaneously map multiple sub-swaths. This concept can be implemented using either a planar antenna or a reflector, fed by a multichannel array. Furthermore, a continuous variation of the pulse repetition interval, i.e., staggered SAR, can be introduced to get rid of the “blind ranges” between the multiple sub-swaths, due to the fact that the radar cannot receive, while it is transmitting. This paper considers how the introduction of full polarimetry in HRWS imaging makes the design of the SAR system more challenging, due to the performance requirements on range ambiguities, azimuth ambiguities, and noise equivalent sigma zero, but represents a viable solution for frequent and seamless high-resolution fully-polarimetric imaging of the Earth’s landmass. Some system design examples are presented to highlight the potentialities and the limitations, also in relation to the requirements of the main applications of polarimetry. These innovative architectures and modes are currently being considered in a number of future SAR mission configurations as for example in DLR's-JAXA's Tandem-L , a polarimetric and interferometric L-band SAR mission aiming at monitoring dynamic processes on the Earth’s surface. They are also of great interest for future C-band SAR systems, where a lower antenna height is required for adequate ambiguity suppression.

  
   

Highlights

In May 2013, the Biomass mission concept was selected to become the next in the series of satellites developed to further our understanding of Earth.

Released: 21/06/2013

REPLAY EARTH EXPLORER 7 USER CONSULTATION MEETING (PART 1)

Released: 11/03/2013

POLinSAR 2013 Workshop

Released: 22/02/2013