Richard Bamler

The shuttle radar topography mission—a new class of digital elevation models acquired by spaceborne radar

For 11 days in February 2000, the Shuttle Radar Topography Mission (SRTM) successfully recorded by interferometric synthetic aperture radar (InSAR) data of the entire land mass of the earth between 60°N and 57°S. The data acquired in C- and X-bands are processed into the first global digital elevation models (DEMs) at 1 arc sec resolution, by NASA-JPL and German aerospace center (DLR), respectively. From the perspective of the SRTM-X system, we give in this paper an overview of the mission and the DEM production, as well as an evaluation of the DEM product quality. Special emphasis is on challenges and peculiarities of the processing that arose from the unique design of the SRTM system, which has been the first single-pass interferometer in space.

Synthetic aperture radar interferometry

Synthetic aperture radar (SAR) is a coherent active microwave imaging method. In remote sensing it is used for mapping the scattering properties of the Earths surface in the respective wavelength domain. Many physical and geometric parameters of the imaged scene contribute to the grey value of a SAR image pixel. Scene inversion suffers from this high ambiguity and requires SAR data taken at different wavelength, polarization, time, incidence angle, etc. Interferometric SAR (InSAR) exploits the phase differences of at least two complex-valued SAR images acquired from different orbit positions and/or at different times. The information derived from these interferometric data sets can be used to measure several geophysical quantities, such as topography, deformations (volcanoes, earthquakes, ice fields), glacier flows, ocean currents, vegetation properties, etc. This paper reviews the technology and the signal theoretical aspects of InSAR. Emphasis is given to mathematical imaging models and the statistical properties of the involved quantities. Coherence is shown to be a useful concept for system description and for interferogram quality assessment. As a key step in InSAR signal processing two-dimensional phase unwrapping is discussed in detail. Several interferometric configurations are described and illustrated by real-world examples. A compilation of past, current and future InSAR systems concludes the paper.

Precision SAR processing using chirp scaling

A space-variant interpolation is required to compensate for the migration of signal energy through range resolution cells when processing synthetic aperture radar (SAR) data, using either the classical range/Doppler (R/D) algorithm or related frequency domain techniques. In general, interpolation requires significant computation time, and leads to loss of image quality, especially in the complex image. The new chirp scaling algorithm avoids interpolation, yet performs range cell migration correction accurately. The algorithm requires only complex multiplies and Fourier transforms to implement, is inherently phase preserving, and is suitable for wide-swath, large-beamwidth, and large-squint applications. This paper describes the chirp scaling algorithm, summarizes simulation results, presents imagery processed with the algorithm, and reviews quantitative measures of its performance. Based on quantitative comparison, the chirp scaling algorithm provides image quality equal to or better than the precision range/Doppler processor. Over the range of parameters tested, image quality results approach the theoretical limit, as defined by the system bandwidth. >

A comparison of range-Doppler and wavenumber domain SAR focusing algorithms

Focusing of SAR data requires a space-variant two-dimensional correlation. Different algorithms are compared with each other in terms of their focusing quality and their ability to handle the space-variance of the correlation kernel: the range-Doppler approach with and without secondary range compression, modified range-Doppler algorithms, and four versions of the wavenumber domain processor. The phase aberrations of the different algorithms are given in analytic form. Numerical examples are presented for Seasat and ERS-1. A novel systems theoretical derivation of the wavenumber domain algorithm is presented. >

Phase statistics of interferograms with applications to synthetic aperture radar

Interferometric methods are well established in optics and radio astronomy. In recent years, interferometric concepts have been applied successfully to synthetic aperture radar (SAR) and have opened up new possibilities in the area of earth remote sensing. However interferometric SAR applications require thorough phase control through the imaging process. The phase accuracy of SAR images is affected by decorrelation effects between the individual surveys. We analyze quantitatively the influence of decorrelation on the phase statistics of SAR interferograms. In particular, phase aberrations as they occur in typical SAR processors are studied in detail. The dependence of the resulting phase bias and variance on processor parameters is presented in several diagrams.

Tomographic SAR Inversion by

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.

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Estimation of differential shift of image elements between two synthetic aperture radar (SAR) images is the basis for many applications, like digital elevation model generation or ground motion mapping. The shift measurement can be done nonambiguously on the macro scale at an accuracy depending on the range resolution of the system or on the micro scale by employing interferometric methods. The latter suffers from phase cycle ambiguities and requires phase unwrapping. Modern wideband high-resolution SAR systems boast resolutions as small as a few tens of a wavelength. If sufficiently many samples are used for macro-scale shift estimation, the accuracy can be increased to a small fraction of a resolution cell and even in the order of a wavelength. Then, accurate absolute ranging becomes precise enough to support phase unwrapping or even make it obsolete. This letter establishes a few fundamental equations on the accuracy bounds of shift estimation accuracy for several algorithms: coherent speckle correlation, incoherent speckle correlation, split-band interferometry, a multifrequency approach, and correlation of point scatterers in clutter. It is shown that the performance of split-band interferometry is close to the Crame/spl acute/r-Rao bound for a broad variety of bandwidth ratios. Based on these findings, Delta-k systems are proposed to best take advantage of the available radar bandwidth.

-Norm Regularization—The Compressive Sensing Approach

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.

Accuracy of differential shift estimation by correlation and split-bandwidth interferometry for wideband and delta-k SAR systems

Ionospheric propagation effects have a significant impact on the signal properties of low-frequency synthetic aperture radar (SAR) systems. Range delay, interferometric phase bias, range defocusing, and Faraday rotation are the most prominent ones. All the effects are a function of the so-called total electron content (TEC). Methods based on two-frequency global positioning system observations allow measuring TEC in the ionosphere with coarse spatial resolution only. In this letter, the potential of broadband L-band SAR systems for ionospheric TEC mapping is studied. As a basis, the dispersive nature of the ionosphere and its effects on broadband microwave radiation are theoretically derived and analyzed. It is shown that phase advance and group delay can be measured by interferometric and correlation techniques, respectively. The achievable accuracy suffices in mapping small-scale ionospheric TEC disturbances. A differential TEC estimator that separates ionospheric from tropospheric contributions is proposed

A Sparse Image Fusion Algorithm With Application to Pan-Sharpening

Addresses the problem of Doppler frequency estimation in the presence of speckle and receiver noise. An ultimate accuracy bound for Doppler frequency estimation is derived from the Cramer-Rao inequality. It is shown that estimates based on the correlation of the signal power spectra with an arbitrary weighting function are approximately Gaussian-distributed. Their variance is derived in terms of the weighting function. It is shown that a special case of a correlation-based estimator is a maximum-likelihood estimator that reaches the Cramer-Rao bound. These general results are applied to the problem of Doppler centroid estimation from SAR (synthetic aperture radar) data. >