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We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of at one point. This completes the classification of such solitons in two complex dimensions. [ABSTRACT FROM AUTHOR]

Let X be a compact orientable non-Haken 3-manifold modeled on the Thurston geometry Nil . We show that the diffeomorphism group Diff ⁡ (X) deformation retracts to the isometry group Isom ⁡ (X) . Combining this with earlier work by many authors, this completes the determination the homotopy type of Diff ⁡ (X) for any compact, orientable, prime 3-manifold X. [ABSTRACT FROM AUTHOR]

We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows, arXiv:2009.03243, 2020). Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric flow. We will study the geometric and analytic properties of this limiting flow, as well as the convergence in detail. We will also see that, under appropriate local curvature bounds, a limit of Ricci flows can be decomposed into a regular and singular part. The regular part can be endowed with a canonical structure of a Ricci flow spacetime and we have smooth convergence on a certain subset of the regular part. [ABSTRACT FROM AUTHOR]

We complete the proof of the Generalized Smale Conjecture, apart from the case of RP^3, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms, except S^3 and RP^3, as well as hyperbolic manifolds, to prove that the space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold X, the inclusion \operatorname {Isom}(X,g)\rightarrow \operatorname {Diff}(X) is a homotopy equivalence for any Riemannian metric g of constant sectional curvature. [ABSTRACT FROM AUTHOR]

In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional κ-solutions. In this paper, we present an alternative proof for this fact and show that compact κ-solutions are rotationally symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows. [ABSTRACT FROM AUTHOR]

This article addresses the general problem of single-look multi-master SAR tomography. For this purpose, we establish the single-look multi-master data model, analyze its implications for the single and double scatterers, and propose a generic inversion framework. The core of this framework is the nonconvex sparse recovery, for which we develop two algorithms: one extends the conventional nonlinear least squares (NLS) to the single-look multi-master data model and the other is based on bi-convex relaxation and alternating minimization (BiCRAM). We provide two theorems for the objective function of the NLS subproblem, which lead to its analytic solution up to a constant phase angle in the 1-D case. We also report our findings from the experiments on different acceleration techniques for BiCRAM. The proposed algorithms are applied to a real TerraSAR-X data set and validated with the height ground truth made available by an SAR imaging geodesy and simulation framework. This shows empirically that the single-master approach, if applied to a single-look multi-master stack, can be insufficient for layover separation, and the multi-master approach can indeed perform slightly better (despite being computationally more expensive) even in the case of single scatterers. In addition, this article also sheds light on the special case of single-look bistatic SAR tomography, which is relevant for the current and future SAR missions such as TanDEM-X and Tandem-L. [ABSTRACT FROM AUTHOR]

We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a topologically PSC 4-orbifold with vanishing first Betti number and second Betti number at most as large as the original one. [ABSTRACT FROM AUTHOR]

Multibaseline interferometric synthetic aperture radar (InSAR) techniques are effective approaches for retrieving the 3-D information of urban areas. In order to obtain a plausible reconstruction, it is necessary to use more than 20 interferograms. Hence, these methods are commonly not appropriate for large-scale 3-D urban mapping using TanDEM-X data, where only a few acquisitions are available in average for each city. This article proposes a new SAR tomographic processing framework to work with those extremely small stacks, which integrates the nonlocal filtering into SAR tomography inversion. The applicability of the algorithm is demonstrated using a TanDEM-X multibaseline stack with five bistatic interferograms over the whole city of Munich, Germany. A systematic comparison of our result with TanDEM-X raw digital elevation models (DEMs) and airborne LiDAR data shows that the relative height accuracy of two-third buildings is within 2 m, which outperforms the TanDEM-X raw DEM. The promising performance of the proposed algorithm paved the first step toward high-quality large-scale 3-D urban mapping. [ABSTRACT FROM AUTHOR]

We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics whose curvature operator has eigenvalues greater than - 1 can be evolved by the Ricci flow for some uniform time such that the eigenvalues of the curvature operator remain greater than - C . Here the time of existence and the constant C only depend on the dimension and the degree of non-collapsedness. We obtain similar generalizations for other invariant curvature conditions, including positive biholomorphic curvature in the Kähler case. We also get a local version of the main theorem. As an application of our almost preservation results we deduce a variety of gap and smoothing results of independent interest, including a classification for non-collapsed manifolds with almost non-negative curvature operator and a smoothing result for singular spaces coming from sequences of manifolds with lower curvature bounds. We also obtain a short-time existence result for the Ricci flow on open manifolds with almost non-negative curvature (without requiring upper curvature bounds). [ABSTRACT FROM AUTHOR]

In this paper we analyze Ricci flows on which the scalar curvature is globally or locally bounded from above by a uniform or time-dependent constant. On such Ricci flows we establish a new time-derivative bound for solutions to the heat equation. Based on this bound, we solve several open problems: 1. distance distortion estimates, 2. the existence of a cutoff function, 3. Gaussian bounds for heat kernels, and, 4. a backward pseudolocality theorem, which states that a curvature bound at a later time implies a curvature bound at a slightly earlier time. Using the backward pseudolocality theorem, we next establish a uniform L 2 curvature bound in dimension 4 and we show that the flow in dimension 4 converges to an orbifold at a singularity. We also obtain a stronger ε -regularity theorem for Ricci flows. This result is particularly useful in the study of Kähler Ricci flows on Fano manifolds, where it can be used to derive certain convergence results. [ABSTRACT FROM AUTHOR]

In this paper we analyze the long-time behavior of 3-dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric decomposition, there are only finitely many surgeries and the curvature is bounded by Ct-1 for large t . This proves a conjecture of Perelman for this class of initial topologies. The proof of this fact illustrates the fundamental ideas that are used in the subsequent papers of the author. [ABSTRACT FROM AUTHOR]

In this paper we develop a structure theory of Einstein manifolds or manifolds with lower Ricci curvature bounds for certain singular spaces that arise as geometric limits of sequences of Riemannian manifolds. This theory generalizes the results that were obtained by Cheeger, Colding and Naber in the smooth setting. In the course of the paper, we will carefully characterize the assumptions that we have to impose on this sequence of Riemannian manifolds in order to guarantee that the individual results hold. An important aspect of our approach is that we don't need impose any Ricci curvature bounds on the sequence of Riemannian manifolds leading to the singular limit. The Ricci curvature bounds will only be required to hold on the regular part of the limit and we will not impose any (synthetic) curvature condition on its singular part. The theory developed in this paper will have applications in the blowup analysis of certain geometric equations in which we study scales that are much larger than the local curvature scale. In particular, this theory will have applications in the study of Ricci flows of bounded scalar curvature, which we will describe in a subsequent paper. [ABSTRACT FROM AUTHOR]

In this paper we consider 4-dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singular solution of the Ricci flow on a closed 4-manifold. In particular, we study the geometry at infinity of such Ricci solitons under the assumption that their tangent flow at infinity is the product of R with a 3-dimensional spherical space form. We also classify the tangent flows at infinity of 4-dimensional steady soliton singularity models in general. [ABSTRACT FROM AUTHOR]

In this paper we establish stability results for symmetric spaces of noncompact type under Ricci flow, i.e. we show that any small perturbation of the symmetric metric is flown back to the original metric under an appropriately rescaled Ricci flow. It will be important for us which smallness assumptions we have to impose on the initial perturbation. We will find that as long as the symmetric space does not contain any hyperbolic or complex hyperbolic factor, we don't have to assume any decay on the perturbation. Furthermore, in the hyperbolic and complex hyperbolic case, we show stability under a very weak assumption on the initial perturbation. This will generalize a result obtained by Schulze et al. (Commun Anal Geom 19(5):1023-1047, ) in the hyperbolic case. The proofs of these results make use of an improved L-decay estimate for the heat kernel in vector bundles over symmetric spaces, which is of independent interest. [ABSTRACT FROM AUTHOR]

We show that every finite volume hyperbolic manifold of dimension greater than or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation. It will turn out that the main difficulty in the proof comes from a weak stability of the cusps which has to do with infinitesimal cusp deformations. We will overcome this weak stability by using a new analytical method developed by Koch and Lamm. [ABSTRACT FROM AUTHOR]

Data provided by most optical Earth observation satellites such as IKONOS, QuickBird, and GeoEye are composed of a panchromatic channel of high spatial resolution (HR) and several multispectral channels at a lower spatial resolution (LR). The fusion of an HR panchromatic and the corresponding LR spectral channels is called “pan-sharpening.” It aims at obtaining an HR multispectral image. In this paper, we propose a new pan-sharpening method named Sparse F usion of Images (SparseFI, pronounced as “sparsify”). SparseFI is based on the compressive sensing theory and explores the sparse representation of HR/LR multispectral image patches in the dictionary pairs cotrained from the panchromatic image and its downsampled LR version. Compared with conventional methods, it “learns” from, i.e., adapts itself to, the data and has generally better performance than existing methods. Due to the fact that the SparseFI method does not assume any spectral composition model of the panchromatic image and due to the super-resolution capability and robustness of sparse signal reconstruction algorithms, it gives higher spatial resolution and, in most cases, less spectral distortion compared with the conventional methods. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper the feasibility to monitor the shape and deformation of single buildings from space is investigated. The methodology is based on a fusion of persistent scatterer (PS) point clouds obtained from several stacks of meter-resolution synthetic aperture radar (SAR) data. This kind of high resolution imagery as well as accurate orbit information is available from, e.g., TerraSAR-X. The stacks are processed individually applying persistent scatterer interferometry (PSI), which provides deformation and height estimates for the PS. However, the geocoded PS point clouds cannot be simply merged in one common coordinate system, like UTM, by reason of residual offsets with respect to their final true positions. These deviations originate from the height uncertainty of the reference point, which has to be chosen during PSI processing of each stack. The presented methodology allows for a fusion of several PS point clouds, i.e., the correct reference point heights can be recovered. The algorithm is based on a point cloud matching procedure that consists of a determination of appropriate point correspondences and a minimization of the distances between all selected pairs of points in a least-squares sense. In addition, the reconstruction of the original motion vector from the deformation measurements in line of sight provided by PSI is desirable. The availability of separated motion components in vertical and horizontal directions greatly enhances the insights into deformation events at buildings and ground. To this end, the fused point clouds are used for a decomposition of motion components. By reason of the limited sensitivity of ascending and descending stacks of TerraSAR-X to deformation in north-southern directions the reconstruction of motion vector components is restricted to components in west-eastern and vertical directions. The latter are estimated in a least-squares adjustment including all PS within a spatially limited area. Deformation estimates of stacks from ascending and descending tracks must be included in order to separate motion components. The latter cannot be determined precisely from a combination of solely equal heading tracks, as the line of sight does not differ enough. Finally, deformation maps of the urban area are available that separately show seasonal and linear deformation in horizontal as well as vertical directions. These maps comprise important information on subsidence or uplift as well as structural stress at buildings due to thermal dilation. As a result of the presented methodology (and for the first time) sufficient and precise motion estimates are available for a detailed monitoring of single objects using meter-resolution SAR data in PSI. Several examples are discussed using the results of motion component estimation based on the fusion of four data stacks evaluated by PSI. [Copyright &y& Elsevier]

Tomographic synthetic aperture radar (SAR) inversion, including SAR tomography and differential SAR tomography, is essentially a spectral analysis problem. The resolution in the elevation direction depends on the elevation aperture size, i.e., on the spread of orbit tracks. Since the orbits of modern meter-resolution spaceborne SAR systems, such as TerraSAR-X, are tightly controlled, the tomographic elevation resolution is at least an order of magnitude lower than in range and azimuth. Hence, super-resolution (SR) reconstruction algorithms are desired. Considering the sparsity of the signal in elevation, a compressive sensing based super-resolving algorithm, named “Scale-down by L1 norm Minimization, Model selection, and Estimation Reconstruction” (SL1MMER, pronounced “slimmer”), was proposed by the authors in a previous paper. The ultimate bounds of the technique on localization accuracy and SR power were investigated. In this paper, the essential role of SR for layover separation in urban infrastructure monitoring is indicated by geometric and statistical analysis. It is shown that double scatterers with small elevation distances are more frequent than those with large elevation distances. Furthermore, the SR capability of SL1MMER is demonstrated using TerraSAR-X real data examples. For a high rise building complex, the percentage of detected double scatterers is almost doubled compared to classical linear estimators. Among them, half of the detected double scatterer pairs have elevation distances smaller than the Rayleigh elevation resolution. This confirms the importance of SR for this type of applications. [ABSTRACT FROM PUBLISHER]

In this paper, we present a new approach to the construction of Einstein metrics by a generalization of Thurston's Dehn filling. In particular in dimension 3, we will obtain an analytic proof of Thurston's result. [ABSTRACT FROM AUTHOR]

We address the problem of resolving two closely spaced complex-valued points from N irregular Fourier do- main samples. Although this is a generic super-resolution (SR) problem, our target application is SAR tomography (TomoSAR), where typically the number of acquisitions is N = 10 - 100 and SNR = 0-10 dB. As the TomoSAR algorithm, we introduce "Scale-down by LI norm Minimization, Model selection, and Estimation Reconstruction" (SL1MMER), which is a spectral estimation algorithm based on compressive sensing, model order selection, and final maximum likelihood parameter estimation. We investigate the limits of SLIMMER concerning the following questions. How accurately can the positions of two closely spaced scatterers be estimated? What is the closest distance of two scat- terers such that they can be separated with a detection rate of 50% by assuming a uniformly distributed phase difference? How many acquisitions N are required for a robust estimation (i.e., for separating two scatterers spaced by one Rayleigh resolution unit with a probability of 90%)? For all of these questions, we provide numerical results, simulations, and analytical approxima- tions. Although we take TomoSAR as the preferred application, the SLIMMER algorithm and our results on SR are generally applicable to sparse spectral estimation, including SR SAR focus- ing of point-like objects. Our results are approximately applicable to nonlinear least-squares estimation, and hence, although it is derived experimentally, they can be considered as a fundamental bound for SR of spectral estimators. We show that SR factors are in the range of 1.5-25 for the aforementioned parameter ranges of N and SNR. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar tomography (TomoSAR) extends the synthetic aperture principle into the elevation direction for 3-D imaging. It uses stacks of several acquisitions from slightly different viewing angles (the elevation aperture) to reconstruct the reflectivity function along the elevation direction by means of spectral analysis for every azimuth–range pixel. The new class of meter-resolution spaceborne SAR systems (TerraSAR-X and COSMO-Skymed) offers a tremendous improvement in tomographic reconstruction of urban areas and man-made infrastructure. The high resolution fits well to the inherent scale of buildings (floor height, distance of windows, etc.). This paper demonstrates the tomographic potential of these SARs and the achievable quality on the basis of TerraSAR-X spotlight data of urban environment. A new Wiener-type regularization to the singular-value decomposition method—equivalent to a maximum a posteriori estimator—for TomoSAR is introduced and is extended to the differential case (4-D, i.e., space–time). Different model selection schemes for the estimation of the number of scatterers in a resolution cell are compared and proven to be applicable in practice. Two parametric estimation algorithms of the scatterers' elevation and their velocities are evaluated. First 3-D and 4-D reconstructions of an entire building complex (including its radar reflectivity) with very high level of detail from spaceborne SAR data by pixelwise TomoSAR are presented. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar (SAR) tomography (TomoSAR) extends the synthetic aperture principle into the elevation direction for 3-D imaging. The resolution in the elevation direction depends on the size of the elevation aperture, i.e., on the spread of orbit tracks. Since the orbits of modern meter-resolution spaceborne SAR systems, like TerraSAR-X, are tightly controlled, the tomographic elevation resolution is at least an order of magnitude lower than in range and azimuth. Hence, super-resolution reconstruction algorithms are desired. The high anisotropy of the 3-D tomographic resolution element renders the signals sparse in the elevation direction; only a few pointlike reflections are expected per azimuth–range cell. This property suggests using compressive sensing (CS) methods for tomographic reconstruction. This paper presents the theory of 4-D (differential, i.e., space–time) CS TomoSAR and compares it with parametric (nonlinear least squares) and nonparametric (singular value decomposition) reconstruction methods. Super-resolution properties and point localization accuracies are demonstrated using simulations and real data. A CS reconstruction of a building complex from TerraSAR-X spotlight data is presented. [ABSTRACT FROM AUTHOR]

Standard synthetic aperture radar (SAR) processing algorithms use analytically derived transfer functions in the 2-D frequency and range/Doppler domains. These rely on the assumption of hyperbolic range histories of monostatic SARs with straight flight paths. For bistatic SARs, the range histories are no longer hyperbolic, and simple analytic transforms do not exist. This paper offers two solutions for bistatic SAR data processing under the restriction of quasi-stationarity, i.e., sufficiently equal velocity vectors of transmitter and receiver. 1) Moderately bistatic configurations can be handled satisfactorily by using hyperbolic range functions with a modified velocity parameter, which is a solution already well known for the accommodation of curved orbits in the monostatic case. This "equivalent velocity" approach is shown to be of surprising range of validity even for pronounced bistatic situations. It is not to be confused with the "equivalent monostatic flight path" approximation, which is shown to be inapplicable for any practical case. 2) With increasing separation of transmitter and receiver, the equivalent velocity approximation deteriorates. To cope with extreme bistatic configurations, a general approach named "NuSAR" is proposed, where the involved transfer functions are replaced by numerically computed ones. This paper describes how the transfer functions are computed from the given orbits and the shape of the Earth surface. In any of these two cases, the bistatic SAR data can be processed by standard SAR processors; only the conventional transfer functions need to be replaced. Neither are there time-domain prefocusing or postfocusing steps required nor complicated mathematical expansions involved. The presented algorithms are also applicable to very high resolution wide-swath (or squinted) SARs on curved orbits. [ABSTRACT FROM AUTHOR]

ScanSAR interferometry is an attractive option for efficient topographic mapping of large areas and for monitoring of large-scale motions. Only ScanSAR interferometry made it possible to map almost the entire landmass of the earth in the 11-day Shuttle Radar Topography Mission. Also the operational satellites RADARSAT and ENVISAT offer ScanSAR imaging modes and thus allow for repeat-pass ScanSAR interferometry. This paper gives a complete description of ScanSAR and burst-mode interferometric signal properties and compares different processing algorithms. The problems addressed are azimuth scanning pattern synchronization, spectral shift filtering in the presence of high squint, Doppler centroid estimation, different phase-preserving ScanSAR processing algorithms, ScanSAR interferogram formation, coregistration, and beam alignment. Interferograms and digital elevation models from RADARSAT ScanSAR Narrow modes are presented. The novel "pack-and-go" algorithm for efficient burst-mode range processing and a new time-variant fast interpolator for interferometrie eoregistration are introduced. [ABSTRACT FROM AUTHOR]

Presents information on a study that evaluated the interpolation kernels for interferometric synthetic aperture radar (SAR) processing for registration of complex signals. Theory of interpolation errors; Examples for interpolarators; Experimental results of the study.

Presents information on a study that investigated an approach to two-dimensional (2-D) phase unwrapping for synthetic radar (SAR) interferometry. Review of the problem of slope bias in least-squares phase unwrapping; Description on how adaptive multiresolution frequency estimation can overcome the problem; Simulation results.

Presents a study which focused on the underestimation of phase slope distortion of phase surfaces in two-dimensional phase unwrapping, by linear estimators. Information on synthetic aperture radar interferometry; Methodology used to conduct the study; Results of the study.

In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is 1 2 -Hölder continuous in a uniform sense. This implies that the distance function can be extended continuously up to the singular time. [ABSTRACT FROM AUTHOR]

Tomographic synthetic aperture radar (TomoSAR) inversion of urban areas is an inherently sparse reconstruction problem and, hence, can be solved using compressive sensing (CS) algorithms. This paper proposes solutions for two notorious problems in this field. First, TomoSAR requires a high number of data sets, which makes the technique expensive. However, it can be shown that the number of acquisitions and the signal-to-noise ratio (SNR) can be traded off against each other, because it is asymptotically only the product of the number of acquisitions and SNR that determines the reconstruction quality. We propose to increase SNR by integrating nonlocal (NL) estimation into the inversion and show that a reasonable reconstruction of buildings from only seven interferograms is feasible. Second, CS-based inversion is computationally expensive and therefore, barely suitable for large-scale applications. We introduce a new fast and accurate algorithm for solving the NL L1-L2-minimization problem, central to CS-based reconstruction algorithms. The applicability of the algorithm is demonstrated using simulated data and TerraSAR-X high-resolution spotlight images over an area in Munich, Germany. [ABSTRACT FROM AUTHOR]

Signal decorrelation poses a limitation to multipass SAR interferometry. In pursuit of overcoming this limitation to achieve high-precision deformation estimates, different techniques have been developed, with short baseline subset, SqueeSAR, and CAESAR as the overarching schemes. These different analysis approaches raise the question of their efficiency and limitation in phase and consequently deformation estimation. This contribution first addresses this question and then proposes a new estimator with improved performance, called Eigendecomposition-based Maximum-likelihood-estimator of Interferometric phase (EMI). The proposed estimator combines the advantages of the state-of-the-art techniques. Identical to CAESAR, EMI is solved using eigendecomposition; it is therefore computationally efficient and straightforward in implementation. Similar to SqueeSAR, EMI is a maximum-likelihood-estimator; hence, it retains estimation efficiency. The computational and estimation efficiency of EMI renders it as an optimum choice for phase estimation. A further marriage of EMI with the proposed Sequential Estimator by Ansari et al. provides an efficient processing scheme tailored to the analysis of Big InSAR Data. EMI is formulated and verified in relation to the state-of-the-art approaches via mathematical formulation, simulation analysis, and experiments with time series of Sentinel-1 data over the volcanic island of Vulcano, Italy. [ABSTRACT FROM AUTHOR]

A foreword to the February 2010 issue of the journal "IEEE Transactions on Geoscience Remote Sensing" is presented.

The TanDEM-X mission is the first free flying bistatic SAR mission. It has the primary objective to generate within a short time frame a global digital elevation model (DEM) of 10-m absolute vertical accuracy and 2-m relative height accuracy. For that, the whole land mass has been mapped at least twice with different baselines. The success of the mission depends on the accuracy of the final DEM and therefore on the reliability of the phase unwrapping (PU) algorithm. Hence, a robust and versatile PU method, which is in accordance with the acquisition concept, is necessary. This paper presents a new method that combines bistatic high-resolution interferometric data in order to perform an accurate PU on a huge amount of data. The dual-baseline PU correction (DB-PUC) framework addresses this challenge by correcting errors that occurred during the single-baseline PU procedure. It benefits from the additional information available through the differential interferogram and the stereo-radargrammetric phase, which are used to correct region-wise the ambiguity bands of the misestimated unwrapped phases to be less sensitive to noise and possible temporal changes. The multilevel of the DB-PUC approach makes it flexible, computationally efficient, and well adapted to deal with the various PU error scenarios. This framework is used operationally for the processing of the data of the TanDEM-X mission. [ABSTRACT FROM AUTHOR]

Wide-swath synthetic aperture radar (SAR) missions with short revisit times, such as Sentinel-1 and the planned NISAR and Tandem-L, provide an unprecedented wealth of interferometric SAR (InSAR) time series. However, the processing of the emerging Big Data is challenging for state-of-the-art InSAR analysis techniques. This contribution introduces a novel approach, named Sequential Estimator, for efficient estimation of the interferometric phase from long InSAR time series. The algorithm uses recursive estimation and analysis of the data covariance matrix via division of the data into small batches, followed by the compression of the data batches. From each compressed data batch artificial interferograms are formed, resulting in a strong data reduction. Such interferograms are used to link the “older” data batches with the most recent acquisitions and thus to reconstruct the phase time series. This scheme avoids the necessity of reprocessing the entire data stack at the face of each new acquisition. The proposed estimator introduces negligible degradation compared to the Cramér–Rao lower bound under realistic coherence scenarios. The estimator may therefore be adapted for high-precision near-real-time processing of InSAR and accommodate the conversion of InSAR from an offline to a monitoring geodetic tool. The performance of the Sequential Estimator is compared to state-of-the-art techniques via simulations and application to Sentinel-1 data. [ABSTRACT FROM PUBLISHER]

Recently, sparse signal representation of image patches has been explored to solve the pansharpening problem. Although these proposed sparse-reconstruction-based methods lead to promising results, three issues remained unsolved: 1) high computational cost; 2) no consideration given to the possibility of mutually correlated information in different multispectral channels; and 3) requirement that the spectral responses of the panchromatic (Pan) image and the multispectral image cover the same wavelength range, which is not necessarily valid for most sensors. In this paper, we propose a sophisticated sparse image fusion algorithm, which is named “jointly sparse fusion of images” (J-SparseFI). It is based on the earlier proposed sparse fusion of images (SparseFI) algorithm and overcomes the aforementioned three drawbacks of the existing sparse image fusion algorithms. The computational problem is handled by reducing the problem size and by proposing a fully parallelizable scheme. Moreover, J-SparseFI exploits the possible signal structure correlations between multispectral channels by introducing the joint sparsity model (JSM) and sharpening the highly correlated adjacent multispectral channels together. This is done by exploiting the distributed compressive sensing theory that restricts the solution of an underdetermined system by considering an ensemble of signals being jointly sparse. J-SparseFI also offers a practical solution to overcome spectral range mismatch between the Pan and multispectral images. By means of sensor spectral response and channel mutual correlation analysis, the multispectral channels are assigned to primary groups of joint channels, secondary groups of joint channels, and individual channels. Primary groups of joint channels, individual channels, and secondary groups of joint channels are then reconstructed sequentially, by the JSM or by modified SparseFI, using a dictionary trained from the Pan image or previously reconstructed high-resolution multispectral channels. A recipe of how to choose appropriate algorithm parameters, including the most crucial regularization parameter, is provided. The algorithm is evaluated and validated using WorldView-2-like images that are simulated using very high resolution airborne HySpex hyperspectral imagery and further practically demonstrated using real WorldView-2 images. The algorithm's performance is compared with other state-of-the-art methods. Visual and quantitative analyses demonstrate the high quality of the proposed method. In particular, the analysis of the difference images suggests that J-SparseFI is superior in image resolution recovery. [ABSTRACT FROM AUTHOR]

Abstract: In a recent contribution Ferretti and co-workers (Ferretti, A., Fumagalli, A., Novali, F., Prati, C., Rocca, F., Rucci, A., 2011. A new algorithm for processing interferometric data-stacks: SqueeSAR IEEE Transactions on Geoscience and Remote Sensing 49(9), pp. 3460–3470) have proposed the SqueeSAR method, a way to exploit temporally coherent distributed scatterers in coherent SAR data stacks. Elevation and deformation or subsidence estimates are obtained with accuracy similar as in the well known persistent scatterer interferometry (PSI). In this paper we propose an alternative approach and provide a first demonstration of the optimal estimation of distributed scatterers’ phase histories in urban areas. Different to SqueeSAR, we derive phase histories for each distributed scatterer pixel rather than for groups of pixels. We use the Anderson–Darling statistical test to identify neighboring samples of the same distribution. Prior to covariance matrix estimation required for maximum likelihood estimation we apply a multi-resolution defringe technique. By using TerraSAR-X high resolution spotlight data, it is demonstrated that we are able to retrieve reliable phase histories and motion parameter estimates from distributed scatterers with signal-to-noise-ratio far below the common range. [Copyright &y& Elsevier]

Fusion of optical and radar remote sensing data is becoming an actual topic of discussion recently in various application areas though the results are not always satisfactory. In this article, we analyse some disturbing aspects of fusing orthoimages from sensors having different acquisition geometries. These aspects arise due to errors in digital elevation models (DEM), used for image orthorectification, and the existence of 3-D objects in the scene which are not accounted in the DEM. We analyse how these effects influence the ground displacement in orthoimages produced from optical and radar data. Further, we propose sensor formations with acquisition geometry parameters which allow to minimise or compensate for ground displacements in different orthoimages due to the above-mentioned effects and to produce good prerequisites for the following fusion for specific application areas, e.g. matching, filling data gaps, classification, etc. To demonstrate the potential of the proposed approach, two pairs of optical-radar data were acquired over the urban area-Munich City, Germany. The first collection of WorldView-1 and TerraSAR-X (TS-X) data followed the proposed recommendations for acquisition geometry parameters, whereas the second collection of IKONOS and TS-X data was acquired with accidental parameters. The experiment confirmed our ideas fully. Moreover, it opens new possibilities for optical and radar image fusion. [ABSTRACT FROM AUTHOR]

In this paper, a simulation concept is presented for creating synthetic aperture radar (SAR) reflectivitymaps based on ray tracing. Three-dimensional models of man-made objects are illuminated by a virtual SAR sensor whose signal is approximated by rays sent through the model space. To this end, open-source software tools are adapted and extended to derive output data in SAR geometry followed by creating the reflectivity map. Rays can be followed for multiple reflections within the object scene. Signals having different multiple reflection levels are stored in separate image layers. For evaluating the potentials and limits of the simulation approach, simulated reflectivitymaps and distribution maps are compared with real TerraSAR-X images for various complex man-made objects like a skyscraper in Tokyo, the Wynn Hotel in Las Vegas, and the Eiffel Tower in Paris. The results show that the simulation can provide very valuable information to interpret complex SAR images or to predict the reflectivity of planned SAR image acquisitions. [ABSTRACT FROM AUTHOR]

In this paper, a simulation concept is presented for creating synthetic aperture radar (SAR) reflectivity maps based on ray tracing. Three-dimensional models of man-made objects are illuminated by a virtual SAR sensor whose signal is approximated by rays sent through the model space. To this end, open-source software tools are adapted and extended to derive output data in SAR geometry followed by creating the reflectivity map. Rays can be followed for multiple reflections within the object scene. Signals having different multiple reflection levels are stored in separate image layers. For evaluating the potentials and limits of the simulation approach, simulated reflectivitymaps and distribution maps are compared with real TerraSAR-X images for various complex man-made objects like a skyscraper in Tokyo, the Wynn Hotel in Las Vegas, and the Eiffel Tower in Paris. The results show that the simulation can provide very valuable information to interpret complex SAR images or to predict the reflectivity of planned SAR image acquisitions. [ABSTRACT FROM AUTHOR]

Recently, synthetic aperture radar (SAR) data with 1-m resolution acquired by satellites in spotlight mode became available to the public. In this paper, we elucidate the differences between interferometric processing of strip map and of spotlight SAR data, and we outline adequate algorithms for key processing steps such as azimuth Doppler filtering. We further present first TerraSAR-X spotlight interferograms, together with an evaluation of the paraeters that are critical for interferometry. Our results indicate a very good geometric accuracy, stability, and phase fidelity of the TerraSAR-X sensor and its products. From the interferograms, we are able to determine the heights of larger buildings and millimeter-scale structural deformation in several examples. The high detail level of imaged buildings and the good temporal phase coherence of urban areas in X-band make spotlight interferometry an exciting processing technique that enables new applications such as surveying individual buildings. [ABSTRACT FROM AUTHOR]

Abstract The primary objective of the German TanDEM-X mission is the generation of a globally available, highly accurate and detailed digital elevation model (DEM), with the final product having 12 m posting, 2 m relative and 10 m absolute vertical accuracy. The first version of this global DEM has been finalized by the German Aerospace Center (DLR), in September 2016. Our experience with the experimental application of non-local means filters to TanDEM-X data suggests that TanDEM-X has the potential of producing DEMs of even higher resolution and accuracy. The goal of this investigation is to explore the possibility of employing non-local InSAR filters to achieve an effective resolution of 6 m, with an equivalent posting, and a relative height error below 0.8 m, i.e. an increase of quality by a factor of 2 × 2 in resolution and a factor of 2 m/0.8 m = 2.5 in height accuracy — all in all one order of magnitude. Highlights • NL-InSAR can potentially improve the quality of TanDEM-X DEMs by a factor of ten. • NL-InSAR filter gives us significantly less biased coherence estimates. • An unwanted terrace-like artifact produced by NL-InSAR is observed and explained. • A special defringing pre-processing may be the key to eliminate these artifacts. [ABSTRACT FROM AUTHOR]

This paper presents a nonlocal interferometric synthetic aperture radar (InSAR) filter with the goal of generating digital elevation models (DEMs) of higher resolution and accuracy from bistatic TanDEM-X strip map interferograms than with the processing chain used in production. The currently employed boxcar multilooking filter naturally decreases the resolution and has inherent limitations on what level of noise reduction can be achieved. The proposed filter is specifically designed to account for the inherent diversity of natural terrain by setting several filtering parameters adaptively. In particular, it considers the local fringe frequency and scene heterogeneity, ensuring proper denoising of interferograms with considerable underlying topography as well as urban areas. A comparison using synthetic and TanDEM-X bistatic strip map data sets with existing InSAR filters shows the effectiveness of the proposed techniques, most of which could readily be integrated into existing nonlocal filters. The resulting DEMs outclass the ones produced with the existing global TanDEM-X DEM processing chain by effectively increasing the resolution from 12 to 6 m and lowering the noise level by roughly a factor of two. [ABSTRACT FROM AUTHOR]

$L_{1}$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many remote sensing problems, such as image fusion, target detection, image super-resolution, and others, and have led to promising results. However, solving such sparse reconstruction problems is computationally expensive and has limitations in its practical use. In this paper, we proposed a novel efficient algorithm for solving the complex-valued $L_{1}$ regularized least squares problem. Taking the high-dimensional tomographic synthetic aperture radar (TomoSAR) as a practical example, we carried out extensive experiments, both with the simulation data and the real data, to demonstrate that the proposed approach can retain the accuracy of the second-order methods while dramatically speeding up the processing by one or two orders. Although we have chosen TomoSAR as the example, the proposed method can be generally applied to any spectral estimation problems. [ABSTRACT FROM AUTHOR]

Differential synthetic aperture radar tomography (D-TomoSAR), similar to its conventional counterparts such as differential interferometric SAR and persistent scatterer interferometry, is only capable of capturing 1-D deformation along the satellite's line of sight. In this paper, we propose a method based on L1-norm minimization within local spatial cubes to reconstruct 3-D displacement vectors from TomoSAR point clouds available from at least three different viewing geometries. The methodology is applied on two pairs of cross-heading—combination of ascending and descending—TerraSAR-X (TS-X) spotlight image stacks over the city of Berlin. The linear deformation rate and the amplitude of seasonal deformation are decomposed, and the results from two test sites with remarkable deformation pattern are discussed in detail. The results, to our knowledge, demonstrate the first attempt for motion decomposition using TomoSAR data from multiple viewing geometries. [ABSTRACT FROM PUBLISHER]

On August 29, 2014, a lava eruption commenced in the Holuhraun plain, north-east of the Bárðarbunga caldera in Iceland. The eruption ended on February 27, 2015, thus lasting for a period of about 6 months. During these months the magma chamber below the caldera gradually deflated, feeding the eruption and causing the rare event of a slow caldera collapse. In this scenario, TanDEM-X remote sensing data are of particular interest. By producing medium-high resolution and accurate elevation models of the caldera, it is possible to evaluate volume losses and topographical changes to increase the knowledge about the ongoing activity. In particular, five TanDEM-X bistatic acquisitions have been commanded between August 01, 2014 and November 08, 2014, two of them before the volcanic eruption and three of them during the event. Additionally, to fully cover the volcanic activity, the lava field 48 km north-east of the caldera has also been monitored. In the first part of the paper, the expected elevation accuracy is studied on two levels. Absolute and relative height accuracies are analyzed by inspecting the X-band signal propagation into snow and by investigating the impact of the main geometrical system parameters and the local geomorphology. In the second part of the paper, the analysis is applied to the Bárðarbunga volcanic system, including a validation performed using complementary altimeter data. The main geophysical outcome is the accurate temporal height tracking of the entire caldera and the glacial volcanic system. The measured volume loss at the caldera location is about 1 billion cubic meters in two months with an average rate of subsidence of nearly 50 cm/day. These numbers confirm other independent sources and can be compared to lava volume measurements. Finally, the last segment of the dyke that propagated from the Bárðarbunga caldera to the Holuhraun lava field is mapped and a graben structure with a width of up to 1 km and a sinking of a few meters is reported. [ABSTRACT FROM AUTHOR]

Sentinel-1 (S-1) has an unparalleled mapping capacity. In interferometric wide swath (IW) mode, three subswaths imaged in the novel Terrain Observation by Progressive Scans (TOPS) SAR mode result in a total swath width of 250 km. S-1 has become the European workhorse for large area mapping and interferometric monitoring at medium resolution. The interferometric processing of TOPS data however requires special consideration of the signal properties, resulting from the ScanSAR-type burst imaging and the antenna beam steering in azimuth. The high Doppler rate in azimuth sets very stringent coregistration requirements, making the use of enhanced spectral diversity (ESD) necessary to obtain the required fine azimuth coregistration accuracy. Other unique aspects of processing IW data, such as azimuth spectral filtering, image resampling, and data deramping and reramping, are reviewed, giving a recipe-like description that enables the user community to use S-1 IW mode repeat-pass SAR data. Interferometric results from S-1A are provided, demonstrating the mapping capacity of the S-1 system and its interferometric suitability for geophysical applications. An interferometric evaluation of a coherent interferometric pair over Salar de Uyuni, Bolivia, is provided, where several aspects related to coregistration, deramping, and synchronization are analyzed. Additionally, a spatiotemporal evaluation of the along-track shifts, which are directly related to the orbital/instrument timing error, measured from the SAR data is shown, which justifies the necessity to refine the azimuth shifts with ESD. The spatial evaluation indicates high stability of the azimuth shifts for several slices of a datatake. [ABSTRACT FROM PUBLISHER]

The differential ionospheric path delay is a major error source in L-band interferograms. It is superimposed to topography and ground deformation signals, hindering the measurement of geophysical processes. In this paper, we proceed toward the realization of an operational processor to compensate the ionospheric effects in interferograms. The processor should be robust and accurate to meet the scientific requirements for the measurement of geophysical processes, and it should be applicable on a global scale. An implementation of the split-spectrum method, which will be one element of the processor, is presented in detail, and its performance is analyzed. The method is based on the dispersive nature of the ionosphere and separates the ionospheric component of the interferometric phase from the nondispersive component related to topography, ground motion, and tropospheric path delay. We tested the method using various Advanced Land Observing Satellite Phased-Array type L-band synthetic aperture radar interferometric pairs with different characteristics: high to low coherence, moving and nonmoving terrains, with and without topography, and different ionosphere states. Ionospheric errors of almost 1 m have been corrected to a centimeter or a millimeter level. The results show how the method is able to systematically compensate the ionospheric phase in interferograms, with the expected accuracy, and can therefore be a valid element of the operational processor. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a framework referred to as “geodetic synthetic aperture radar (SAR) tomography” that fuses the SAR imaging geodesy and tomographic SAR inversion (TomoSAR) approaches to obtain absolute 3-D positions of a large amount of natural scatterers. The methodology is applied on four very high resolution TerraSAR-X spotlight image stacks acquired over the city of Berlin. Since all the TomoSAR estimates are relative to the same reference point object whose absolute 3-D positions are retrieved by means of stereo SAR, the point clouds reconstructed using data acquired from different viewing angles can be geodetically fused. To assess the accuracy of the position estimates, the resulting absolute shadow-free 3-D TomoSAR point clouds are compared with a digital surface model obtained by airborne LiDAR. It is demonstrated that an absolute positioning accuracy of around 20 cm and a meter-order relative positioning accuracy can be achieved by the proposed framework using TerraSAR-X data. [ABSTRACT FROM AUTHOR]

Abstract: Orthorectification of satellite data is one of the most important pre-processing steps for application oriented evaluations and for image data input into Geographic Information Systems. Although high- and very high-resolution optical data can be rectified without ground control points (GCPs) using an underlying digital elevation model (DEM) to positional root mean square errors (RMSEs) between 3 m and several hundred meters (depending on the satellite), there is still need for ground control with higher precision to reach lower RMSE values for the orthoimages. The very high geometric accuracy of geocoded data of the TerraSAR-X satellite has been shown in several investigations. This is due to the fact that the SAR antenna measures distances which are mainly dependent on the terrain height and the position of the satellite. The latter can be measured with high precision, whereas the satellite attitude need not be known exactly. If the used DEM is of high accuracy, the resulting geocoded SAR data are very precise in their geolocation. This precision can be exploited to improve the orientation knowledge and thereby the geometric accuracy of the rectified optical satellite data. The challenge is to match two kinds of image data, which exhibit very different geometric and radiometric properties. Simple correlation techniques do not work and the goal is to develop a robust method which works even for urban areas, including radar shadows, layover and foreshortening effects. First the optical data have to be rectified with the available interior and exterior orientation data or using rational polynomial coefficients (RPCs). From this approximation, the technique used is the measurement of small identical areas in the optical and radar images by automatic image matching, using a newly developed adapted mutual information procedure followed by an estimation of correction terms for the exterior orientation or the RPC coefficients. The matching areas are selected randomly from a regular grid covering the whole imagery. By adjustment calculations, parameters from falsely matched areas can be eliminated and optimal improvement parameters are found. The original optical data are orthorectified again using the delivered metadata together with these corrections and the available DEM. As proof of method the orthorectified data from IKONOS and ALOS-PRISM sensors are compared with conventional ground control information from high-precision orthoimage maps of the German Cartographic Survey. The results show that this method is robust, even for urban areas. Although the resulting RMSE values are in the order of 2–6 m, the advantage is that this result can be reached even for optical sensors which do not exhibit low RMSE values without using manual GCP measurements. [Copyright &y& Elsevier]

Automated, image based methods for the retrieval of vegetation biophysical and biochemical variables are often hampered by the lack of a priori knowledge about land cover and phenology, which makes the retrieval a highly underdetermined problem. This study addresses this problem by presenting a novel approach, called CRASh, for the concurrent retrieval of leaf area index, leaf chlorophyll content, leaf water content and leaf dry matter content from high resolution solar reflective earth observation data. CRASh, which is based on the inversion of the combined PROSPECT+SAILh radiative transfer model (RTM), explores the benefits of combining semi-empirical and physically based approaches. The approach exploits novel ways to address the underdetermined problem in the context of an automated retrieval from mono-temporal high resolution data. To regularize the inverse problem in the variable domain, RTM inversion is coupled with an automated land cover classification. Model inversion is based on a two step lookup table (LUT) approach: First, a range of possible solutions is selected from a previously calculated LUT based on the analogy between measured and simulated reflectance. The final solution is determined from this subset by minimizing the difference between the variables used to simulate the spectra contained in the reduced LUT and a first guess of the solution. This first guess of the variables is derived from predictive semi-empirical relationships between classical vegetation indices and the single variables. Additional spectral regularization is obtained by the use of hyperspectral data. Results show that estimates obtained with CRASh are significantly more accurate than those obtained with a tested conventional RTM inversion and semi-empirical approach. Accuracies obtained in this study are comparable to the results obtained by various authors for better constrained inversions that assume more a priori information. The completely automated and image-based nature of the approach facilitates its use in operational chains for upcoming high resolution airborne and spaceborne imaging spectrometers. [ABSTRACT FROM AUTHOR]