SARTomography (SARTom) is an imaging technique that al- lows multiple phase centre separation in the vertical (height) direction, leading to a 3D reconstruction ofthe imaged scene. It is usually performed after standard 2D SAR processing and operates on a stack of coregistered SAR images. In  the first demonstration of airborne SARtomography, using Fourier beamforming techniques, has been carried out and the main constraints in terms of resolution and ambiguity rejec- tion have been analysed. If thenumberof scatterers to be solved inside a resolution cell is a priori known, it is possi- ble to reduce thenumberof acquisitions , anyhow, forthe 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
Onthe 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 ofthe shell-like roof in front ofthe test building. It is evident that M-SL1MMER significantly outperforms SL1MMER. In particular, when N = 6, i.e., using extremely small numberof scenes, the second layer estimated using SL1MMER is deteriorated by false alarms (cf. Fig. 2b) while M-SL1MMER still achieves reasonable results.
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 onthe 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 ofthe 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 ofthe residue ofthe fit is a means to characterize the quality ofthe 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 ofthe noise impact the probability of false alarm in the detection process.
– can be applied to estimate the APS of single point- like scatterers. This can be resampled and compensated forthe whole scene (see for example  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 . Fig. 3 shows the 6 pursuit monostatic interferograms of a high-rise building and its surroundings. Note that the fringes onthe 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 ofthe extremely small numberof pursuit monostatic pairs.
The objective of this first 3-D analysis is to get a first qualitative impression and understanding ofthe good- ness ofthe MB phase calibration, the characteristics ofthe 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 ofthe MB SAR data is mandatory prior to any tomographic processing  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 . 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  succeeds for a sufficient phase calibration of this dataset.
We start by considering the multilooking case, performing Boxcar filtering onthe 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 ofthe 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 , 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. theSAR 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
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 . Thus, we are able to compare the performance of CS to SVD-Wiener in the layover areas. Figure 5 shows the projections ofthe 4-D reconstruction forthe 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 onthe roof, the other onthe parking place onthe 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 forthe whole building. The center image of Figure 4 shows the surface model generated from the elevation estimates (converted to height). The full structure ofthe 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 ofthe 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.
The introduction of interferometry enables to overcome the saturation of entropy since the degree of interferometric decorrelation can be controlled by the size ofthe baseline and thus allows the separation of scattering mechanisms in height . “Polarimetric SAR Interferometry” (Pol- InSAR) exploits the variation ofthe interferometric coherence between two (or more) spatially separated tracksfor different polarizations . First established for forest applications, the Random-Volume-Over-Ground (RVoG) scattering model  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 onthe basis of a fixed function describing the backscattered power along height, e.g. exponential . 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 forthe volume layer. The OVoG approach allows the robust estimation ofthe 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 onthe 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 onthe shape ofthe vertical backscattered power function.
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 ofthe 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 thenumberoftracks, i.e., constellations C2–C3, enables us to reveal the robustness ofthe different methods. In contrast to WCS [Fig. 13(b) and (c)], these irregular baseline
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.
Several successful attempts have been made in order to re- duce thenumberof samples. For instance, the authors in  estimated theminimumnumberoftracks based on sub- space methods. In addition, in [2, 13] Compressed Sensing (CS) inversion techniques forSARtomography 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 ofSAR interferometry from a para- metric perspective was proposed in . 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.
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. Forthe last desiderate, an additional verification is included within the detection step.
Forthe first step, information about the forest stand is required. The forest is a composite environment, with different characteristics depending onthe 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 ofthe 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 ofthe 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.
SARtomography (SARTom) is an imaging technique that allows multiple phase centre separation in the vertical (height) direction, leading to a 3-dimensional (3D) reconstruction ofthe 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 ofthe layover problem are two ofthe 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 onthe test site of Dornstetten (Germany) involving the E-SAR system ofthe German Aerospace Center (DLR).
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 ofthe 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 ofthe proposed M- SL1MMER approach in terms of super-resolution power and robustness are evident.
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 tomographyofthe 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 ofthe Center for Remote Control of Ice Sheets during the 2008 campaign in Greenland.
Consequently, much interest has recently concerned theSAR 3-D tomography (Tomo-SAR) –. 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.
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 ofthe 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 onthe 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 ofSARtomography in alpine regions come across several challenges. Among them, a particularly complex issue is the phase cali- bration ofthe interferometric stack as a prerequisite for tomo- graphic inversion. The refractivity ofthe 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.
Since we have only limited numberof acquisitions for large- scale area, the SNR need to be dramatically increased in order to obtain the required accuracy. As shown in , 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
3100 with 100 kHz PRF and 1 km flight altitude and pro- viding 3-4 pts/m 2 point density onthe object. The strip ad- justment (matching adjacent slight strip data) was made us- ing TerraMatch. Ground hits were classified using TerraS- can . 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 ofthe first pulse echo and the DEM with the last pulse echo. The accuracy ofthe 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 .