Nach oben pdf On the minimum number of tracks for SAR tomography

On the minimum number of tracks for SAR tomography

On the minimum number of tracks for SAR tomography

SAR Tomography (SARTom) is an imaging technique that al- lows multiple phase centre separation in the vertical (height) direction, leading to a 3D reconstruction of the imaged scene. It is usually performed after standard 2D SAR processing and operates on a stack of coregistered SAR images. In [1] the first demonstration of airborne SAR tomography, using Fourier beamforming techniques, has been carried out and the main constraints in terms of resolution and ambiguity rejec- tion have been analysed. If the number of scatterers to be solved inside a resolution cell is a priori known, it is possi- ble to reduce the number of acquisitions [2], anyhow, for the general case this information is not known and a generic vol- umetric target has to be assumed. In this case, the ambiguity height V defines the baseline dN yq between the acquisitions
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Exploiting Group Sparsity in SAR Tomography

Exploiting Group Sparsity in SAR Tomography

On the top of our test building, reflections from building roof and façade are overlaid. In Fig. 4, dominating scattering from roof (red) can be seen in the first layer, whereas the corresponding parts of façade are visible in the second layer. Besides, parallelogram patterns in the second layer can be attributed to reflections within window frames. We do not expect many reflections from lower structures though, due to the large slope of the shell-like roof in front of the test building. It is evident that M-SL1MMER significantly outperforms SL1MMER. In particular, when N = 6, i.e., using extremely small number of scenes, the second layer estimated using SL1MMER is deteriorated by false alarms (cf. Fig. 2b) while M-SL1MMER still achieves reasonable results.
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SAR tomography as an add-On to PSI: Detection of coherent scatterers in the presence of phase instabilities

SAR tomography as an add-On to PSI: Detection of coherent scatterers in the presence of phase instabilities

The single dominant scatterers that exhibit long-term phase stability are generally termed as persistent scatterers (PS). PSI processing approaches often use a classifier to identify a priori a set of PS candidates, e.g., the permanent scatterers [ 1 ] approach uses the dispersion index as a proxy for phase stability. The PSI approaches based on the interferometric point target analysis (IPTA) framework, as in [ 3 , 8 ], employ low spectral diversity [ 3 , 9 – 11 ] as a proxy for phase stability in addition to the stability of the backscattering amplitude. Low dispersion index and low spectral diversity are indicative of good phase quality. The observed differential interferometric phases are fit to a phase model and the unknown parameters, such as the deformation velocity and the residual topography, are thereby estimated. The dispersion of the residue of the fit is a means to characterize the quality of the estimates. It is often used to compute the multi-interferogram complex coherence (MICC) [ 1 , 12 , 13 ] which can in turn be used as a test statistic to perform statistical detection i.e., to decide among the hypotheses whether a given PS candidate is a phase coherent single scatterer or if it comprises noise only. The statistics of the noise impact the probability of false alarm in the detection process.
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Bistatic-like Differential SAR Tomography

Bistatic-like Differential SAR Tomography

[37]–[39] can be applied to estimate the APS of single point- like scatterers. This can be resampled and compensated for the whole scene (see for example [40] and the references therein). Alternatively, topographic updates of single point- like scatterers can be first estimated using only bistatic-like interferograms and then compensated in conventional repeat- pass interferograms for APS estimation [32]. Fig. 3 shows the 6 pursuit monostatic interferograms of a high-rise building and its surroundings. Note that the fringes on the building facade appear to be highly coherent. For Tandem-L, we would expect even higher coherence, especially for distributed scatterers. This is due to minimized temporal decorrelation in the bistatic mode, as well as the outstanding penetration depth in L-band. In the next subsection, the sparse reconstruction is enhanced by exploiting joint sparsity among different resolution cells, in order to circumvent the issue of the extremely small number of pursuit monostatic pairs.
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First Multi-Frequency Investigation of SAR Tomography for Vertical Structure of Agricultural Crops

First Multi-Frequency Investigation of SAR Tomography for Vertical Structure of Agricultural Crops

The objective of this first 3-D analysis is to get a first qualitative impression and understanding of the good- ness of the MB phase calibration, the characteristics of the occurring scattering and the main differences in spe- cies, polarisation and frequency. For this purpose, the Capon beamformer has been chosen to reconstruct the power distribution along height. A careful phase calibra- tion of the MB SAR data is mandatory prior to any tomographic processing [4] to compensate for a residual phase screen resulting from platform motion. For im- proving the radiometric fidelity, a minimum entropy criterion is applied in addition [7]. It is worth remarking that at higher frequencies an accurate phase calibration becomes challenging since the phase distortion is pro- portional to the baseline error normalized to the wave- length. Nevertheless, the method in [7] succeeds for a sufficient phase calibration of this dataset.
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Single-Look SAR Tomography of Urban Areas

Single-Look SAR Tomography of Urban Areas

We start by considering the multilooking case, performing Boxcar filtering on the set of data covariance matrices using a 15 × 3 (range/azimuth) pixel window. More pixels in range are employed for multilooking, in order to make more evident the spatial mixture of sources when comparing to the single-look case, presented later on. One of the main challenges in SAR remote sensing for urban areas is related to the presence of several scattering mechanisms concurring in the backscattered signal. In this context, a study carried in [24], exploiting coherent scatterers, has shown that a data- driven approach can partially help in reconstructing the orientation/radiation pattern of scatterers. Generally, complex scatterers like buildings are randomly oriented w.r.t. the SAR coordinates and one cannot assume their orientation being favorable to the flight direction. Therefore, due to the required multilooking, scattering contribution (source) mixtures will be recorded in the covariance matrix impacting the final reconstruction. For this reason, although the considered building is by chance parallel to the azimuth/flight direction, range multilooking has also been included. This is also
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Compressive sensing for high resolution differential SAR tomography - the SL1MMER algorithm

Compressive sensing for high resolution differential SAR tomography - the SL1MMER algorithm

Figure 4 shows the TS-X intensity map. The presence of two scatterers within an azimuth-range pixel is expected in layover areas and has been validated in [5]. Thus, we are able to compare the performance of CS to SVD-Wiener in the layover areas. Figure 5 shows the projections of the 4-D reconstruction for the pixel P (red dot) to elevation direction, i.e. the reflectivity profile. Two scatterers with slightly different velocities have been detected by SVD- Wiener (red line), one on the roof, the other on the parking place on the ground. The blue line in Figure 4 shows the result using CS. Two very close scatterers have been detected, i.e. D-TomoSAR via CS provides super resolution up to 2m in height (i.e. about 4m in elevation) in this case. With the approximately one year time spread of our data set, nonlinear (e.g. thermally induced) movements of different building parts must be expected. Hence, by using our time warp method, the surface model and amplitude map of seasonal motion is obtained for the whole building. The center image of Figure 4 shows the surface model generated from the elevation estimates (converted to height). The full structure of the convention center has been captured at a very detailed level. Besides the building, more detail such as the roads surrounding the convention center, as well as two bridges above the roads which have weak but correlated returns are clearly resolved. The height estimates are very precise compared to the 33m elevation resolution due to the high SNR of TS-X data. The right image of Figure 4 represents the amplitude map of the seasonal motion. The amplitude variance is smooth for individual structural blocks with sudden amplitude changes between adjacent blocks. The amplitude difference is up to 8mm.
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Multi-Frequency Polarimetric SAR Tomography for the 3-D Characterization and Monitoring of Agricultural Crops

Multi-Frequency Polarimetric SAR Tomography for the 3-D Characterization and Monitoring of Agricultural Crops

The introduction of interferometry enables to overcome the saturation of entropy since the degree of interferometric decorrelation can be controlled by the size of the baseline and thus allows the separation of scattering mechanisms in height [30]. “Polarimetric SAR Interferometry” (Pol- InSAR) exploits the variation of the interferometric coherence between two (or more) spatially separated tracks for different polarizations [31]. First established for forest applications, the Random-Volume-Over-Ground (RVoG) scattering model [31] assumes a volume layer, modeled as a cloud of particles with no preferred orientation, on top of a ground layer with polarization- dependent scattering properties. The interferometric volume coherence can be obtained by minimizing the ground-to-volume power ratio in the polarimetric space and can be expressed as a function of plant height and the extinction coefficient on the basis of a fixed function describing the backscattered power along height, e.g. exponential [32]. When applying Pol-InSAR techniques to agricultural crops, the Oriented-Volume-over-Ground (OVoG) model was introduced [6,33] in order to account for possible anisotropic propagation effects inside the vegetation volume, i.e. considering polarization dependency also for the volume layer. The OVoG approach allows the robust estimation of the agricultural crop height by using single- or multi-baseline fully polarimetric acquisitions across different frequencies [33-35]. Besides this, Pol-InSAR model inversions yield the ground-to-volume ratio and the extinction at the different polarizations which can give insight on the scattering scenario and are related to biophysical parameters [34,36]. Nevertheless, the observation space with one baseline is still limited and therefore requires an a priori assumption on the shape of the vertical backscattered power function.
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Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas

Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas

For validation purposes, we selected 400 contiguous az- imuth positions at two different range locations (indicated by the yellow rectangles and the red lines in Fig. 3). As a result, we obtained tomographic slices as a function of az- imuth and height of dimensions 176 m by 40 m (n = 128), respectively. In both cases, we took a nine-by-nine window. In Fig. 11, we used Fourier beamforming for a range distance of 4816.30 m. Fig. 11(a)–(c) displays the normalized sum of the power distributions throughout polarimetric channels using the constellations C1–C3, respectively. Likewise, as presented in Fig. 12, we carried out the reconstruction with Capon’s beamformer. Alternatively, Fig. 13 shows the results obtained via WCS using λ 1 = λ 2 = 0.5 [see (16)], (3), and a Daubechies Symmlet wavelet with four vanishing moments and three levels of decomposition. Evidently, all methods bear comparison with each other for C1 [see Figs. 11(a), 12(a), and 13(a)]. However, a reduction in the number of tracks, i.e., constellations C2–C3, enables us to reveal the robustness of the different methods. In contrast to WCS [Fig. 13(b) and (c)], these irregular baseline
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Demonstration of Single-Pass Millimeterwave SAR Tomography for Forest Volumes

Demonstration of Single-Pass Millimeterwave SAR Tomography for Forest Volumes

In general, rough surfaces cause diffuse scattering, whereas smooth surfaces result in specular reflections. At millimeter- wave frequencies, most surfaces appear rough, and diffuse scattering dominates the images, leading to coherent averaging within the resolution cells. Since this is an effect similar to mul- tilook processing, the inherent speckle effect appears less severe than in common radar bands. In addition, the high sensitivity with respect to surface roughness certainly provides a benefit, when analysis techniques based on distributed scatterers rather than point scatterers are used.
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Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas

Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas

Several successful attempts have been made in order to re- duce the number of samples. For instance, the authors in [9] estimated the minimum number of tracks based on sub- space methods. In addition, in [2, 13] Compressed Sensing (CS) inversion techniques for SAR tomography were suc- cessfully developed and applied. Nevertheless, the signals of interest were sparse in the space domain; a situation that is rarely true when it comes to volumetric scatterers. Alter- natively, an extension of SAR interferometry from a para- metric perspective was proposed in [12]. In a nutshell, this work employs covariance matching estimation techniques in order to estimate the effective scattering center of differ- ent scattering mechanisms, along with their backscattered power.
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Statistical Analysis for Improvement of Double Persistent Scatterers Detection in SAR Tomography

Statistical Analysis for Improvement of Double Persistent Scatterers Detection in SAR Tomography

Synthetic Aperture Radar (SAR) tomography presents the advantage of multiple stable targets detection within same pixel. Fast-sup-GLRT (generalized likelihood ratio test based on support estimation) algorithm proved to be an ideal compromise between detection capabilities and computational complexity. In this work, a multi-look version of this detector which exploits the advantages of Capon estimation is examined. Statistical analysis of estimation and detection processes are conducted to compare the performances of sequential non-linear least-squares (NLLS) search and Capon filtering of projected data for double PS identification. Main objective is to exploit the super-resolution advantages of NLLS method without the risk of multiple stable targets classification from the same scattering contribution. For the last desiderate, an additional verification is included within the detection step.
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The SARTOM Project; Tomography for enhanced target detection for foliage penetrating airborne SAR

The SARTOM Project; Tomography for enhanced target detection for foliage penetrating airborne SAR

For the first step, information about the forest stand is required. The forest is a composite environment, with different characteristics depending on the type of forest; hence a ground truth campaign must be conducted to ensure that the modelled forest has similar characteristics to the forest under consideration. In general we are not interested in the simulation of exact specific scenarios. Instead we are interested in the overall statistical description of the forest characteristics, so we can study the electromagnetic behaviour with a sensitivity analysis. In this case knowledge about individual trees is superfluous, and a mean description of the forest is sufficient. PRIS is able to input both exact and approximate information about the forest scenarios. However in this paper the simulation will be carried out by the use of averaged information.
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Imaging of targets beneath foliage with SAR tomography

Imaging of targets beneath foliage with SAR tomography

SAR tomography (SARTom) is an imaging technique that allows multiple phase centre separation in the vertical (height) direction, leading to a 3-dimensional (3D) reconstruction of the imaged scene. It is usually performed after standard 2D SAR repeat-pass processing and operates on a stack of coregistered SAR images. Retrieval of volume structure informa- tion (e.g. for forest classification) and the solution of the layover problem are two of the most promising applications. In this paper the application of SARTom to image targets hidden beneath foliage is presented. This method is applied to L-band airborne data acquired during a tomographic campaign that took place in September 2006 on the test site of Dornstetten (Germany) involving the E-SAR system of the German Aerospace Center (DLR).
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Group Sparsity in SAR Tomography – Experiments on TanDEM-X Data Stacks

Group Sparsity in SAR Tomography – Experiments on TanDEM-X Data Stacks

For this purpose, we propose a novel workflow marrying the globally available 2D building footprint GIS data and the group sparsity concept for TomoSAR inversion. In the first stage, online freely assessable 2D building footprints are used for extracting detailed high rise building features including building masks, orientations, and the iso-height lines in SAR image stacks. Then, the group sparsity model, named as M-SL1MMER, is employed for joint TomoSAR inversion of the identified iso- height pixels. The proposed approach is validated using TanDEM-X data stacks. Compared to the single-snapshot sparsity model, as used in SL1MMER, the superior performance of the proposed M- SL1MMER approach in terms of super-resolution power and robustness are evident.
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Sparse SAR Tomography of Ice Sheet and Bed

Sparse SAR Tomography of Ice Sheet and Bed

Modern radars for radio-echo sounding of ice sheets carry multiple receive channels in cross-track, allowing for clutter suppression, as well as for synthetic aperture radar tomography of the ice sheet and bed. Tomographic processing pro- vides 3-D information about the sub-surface topography, bed conditions and internal layers’ orientation. We explore synthetic aperture radar tomography based on sparse signal reconstruction, offer a particular algorithm implementa- tion and demonstrate its performance using data acquired by the Multichannel Coherent Radar Depth Sounder of the Center for Remote Control of Ice Sheets during the 2008 campaign in Greenland.
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Superresolution Differential Tomography: Experiments on Identification of Multiple Scatterers in Spaceborne SAR Data

Superresolution Differential Tomography: Experiments on Identification of Multiple Scatterers in Spaceborne SAR Data

Consequently, much interest has recently concerned the SAR 3-D tomography (Tomo-SAR) [7]–[18]. Tomo-SAR combines multibaseline (MB) acquisitions constituting a cross-track spa- tial array to achieve focused fully 3-D images through elevation beamforming (BF), i.e., spatial (baseline) spectral estimation, thus overcoming the limitation of standard InSAR techniques. Basically, Tomo-SAR can be regarded as a coherent (i.e., amplitude and phase) data combination technique in which the amplitude information is useful for exploiting the mod- ulation induced by the beating phenomena to separate the multiple signals and to enhance the statistical accuracy even for single scatterers. In doing so, Tomo-SAR can add more features for solving InSAR height and reflectivity misinterpre- tation caused by layover geometries in natural or urban areas and for applications involving estimation of forest biomass and height, subcanopy topography, soil humidity, and ice thickness.
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SAR tomography for spatio-temporal inversion of coherent scatterers in villages of alpine regions

SAR tomography for spatio-temporal inversion of coherent scatterers in villages of alpine regions

processing, which represent a missed opportunity to get more information about the underlying anthropogenic or natural de- formation process. Compared to metropolitan regions with several man-made structures, the prevalence of coherent scat- terers in alpine regions is already low, while at the same time layovers are generally more widespread due to the rugged- ness of the topography. Settlements and other infrastructure in the valleys are often partly and sometimes completely in layover cast by the adjoining mountain(s). Moreover, mass movements of interest such as landslides and rockfalls often take place in mountainous regions. Timely deformation mea- surements on slopes close to the villages can potentially assist in preventing untoward incidents. These concerns motivate this investigation on the potential of differential SAR tomog- raphy [3, 4, 5] as a means to resolve the layovers and allow spatio-temporal inversion of individually coherent scatterers interfering in the same resolution cell. The prospects of SAR tomography in alpine regions come across several challenges. Among them, a particularly complex issue is the phase cali- bration of the interferometric stack as a prerequisite for tomo- graphic inversion. The refractivity of the troposphere changes spatially over the scene as well as from one pass to the next, incurring variable phase delays which in general do not cancel out in interferogram formation, leaving behind a phase foot- print, i.e the atmospheric phase. It acts as a disturbance in fo- cusing the scatterers in 3-D [6, 7] and needs to be corrected. In mountainous regions, the local atmospheric conditions and the propagation paths through the troposphere may strongly vary spatially due to the extremely rugged topography which may change by as much as a few kilometers between the val- ley floor and the mountain top. Therefore, the atmospheric correction in such areas is more involved.
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Non-local SAR tomography for large-scale urban mapping

Non-local SAR tomography for large-scale urban mapping

Since we have only limited number of acquisitions for large- scale area, the SNR need to be dramatically increased in order to obtain the required accuracy. As shown in [13], non-local procedure is efficient way to increase the SNR of interfero- grams without notable resolution distortion. The NL-means concept redefines the neighborhood of a pixel c in a very gen- eral sense as any set of pixels s in the image (local or non- local) such that a small patch around s is similar to the patch around c. It can combine similar patches into a weighted max- imum likelihood estimator
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SAR Coherence Tomography For Boreal Forest With Aid of Laser Measurements

SAR Coherence Tomography For Boreal Forest With Aid of Laser Measurements

3100 with 100 kHz PRF and 1 km flight altitude and pro- viding 3-4 pts/m 2 point density on the object. The strip ad- justment (matching adjacent slight strip data) was made us- ing TerraMatch. Ground hits were classified using TerraS- can [6]. Digital Surface Model (DSM) relevant to treetops was obtained by taking the highest point within a 1-m grid and missing points were interpolated by Delaunay triangula- tion. The canopy height model (CHM) was then obtained by subtracting the Digital Elevetion Model DEM from the cor- responding DSM. The crown DSM was calculated by means of the first pulse echo and the DEM with the last pulse echo. The accuracy of the obtained DEM is better than 20 cm for forested terrain. The CHM includes a -70 cm bias in obtained tree heights and about 0.5 m std error. Information at indi- vidual tree level can be derived from CHM using methods depicted in [7].
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