Phase unwrapping through fringe-line detection in synthetic aperture radar interferometry (original) (raw)
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On the importance of path for phase unwrapping in synthetic aperture radar interferometry
Applied Optics, 2011
Phase unwrapping is a key procedure in interferometric synthetic aperture radar studies, translating ambiguous phase observations to topography, and surface deformation estimates. Some unwrapping algorithms are conducted along specific paths based on different selection criteria. In this study, we analyze six unwrapping paths: line scan, maximum coherence, phase derivative variance, phase derivative variance with branch-cut, second-derivative reliability, and the Fisher distance. The latter is a new path algorithm based on Fisher information theory, which combines the phase derivative with the expected variance to get a more robust path, potentially performing better than others in the case of low image quality. In order to compare only the performance of the paths, the same unwrapping function (phase derivative integral) is used. Results indicate that the Fisher distance algorithm gives better results in most cases.
Multiresolution phase unwrapping for SAR interferometry
IEEE Transactions on Geoscience and Remote Sensing, 1999
An approach to two-dimensional (2-D) phase unwrapping for synthetic aperture radar (SAR) interferometry is presented, based on separate steps of coarse phase and fine phase estimation. A technique called adaptive multiresolution is introduced for local fringe frequency estimation, in which difference frequencies between resolution levels are estimated and summed such that a sufficiently conservative phase gradient field is maintained. A coarse unwrapped phase of the full terrain height is then constructed using weighted least-squares based on coherence weighting. This coarse phase is used in a novel approach to slope-adaptive spectral shift filtering and to reduce the phase variation of the interferogram. The resulting interferogram can be more accurately multilooked and unwrapped with any algorithm. In this paper, fine phase construction is done with weighted least-squares and with weights determined by simple morphological operations on residues. The approach is verified on a simulated complex interferogram and real SAR data.
1998
The advent of interferometric synthetic aperature radar for geophysical studies has resulted in the need for accurate, efficient methods of two-dimensional phase unwrapping. Inference of the lost integral number of cycles in phase measurements is critical for three-pass surface deformation studies as well as topographic mapping and can result in an order of magnitude increase in sensitivity for two-pass deformation analysis. While phase unwrapping algorithms have proliferated over the past ten years, two main approaches are currently in use. Each is most useful only for certain restricted applications. All these algorithms begin with the measured gradient of the phase field, which is subsequently integrated to recover the unwrapped phases. The earliest approaches in interferometric applications incorporated residue identification and cuts to limit the possible integration paths, while a second class using least-squares techniques was developed in the early 1990's. We compare the approaches and find that the residue-cut algorithms are quite accurate but do not produce estimates in regions of moderate phase noise. The least-squares methods yield complete coverage but at the cost of distortion in the recovered phase field. A new synthesis approach, combining the cuts from the first class with a least-squares solution, offers greater spatial coverage with less distortion in many instances.
Three-Dimensional Phase Unwrapping for Satellite Radar Interferometry, I: DEM Generation
IEEE Transactions on Geoscience and Remote Sensing, 2014
Determining the Earth's surface topography and deformation with interferometric synthetic aperture radar involves measurement of phase, which, for a typical coherent radar signal, can only be done modulo 2π. The cycle of ambiguity inherent in the phase measurement has to be unwrapped over all observation dimensions (e.g., azimuth, range, and time) to remove the 2π ambiguity of the phase measurements. For a time series of SAR images, useful for reducing noise in topographic applications or measuring time-varying surface deformation, the necessary steps to connect ambiguous radar phase measurements are more challenging, and the operation may be termed 3-D phase unwrapping. We describe a 3-D unwrapping approach using an extended Kalman filter. Our approach readily exploits existing information, and is robust in the presence of noise. For all tested data sets, it provides improved accuracy compared to existing approaches.
Topographic mapping from interferometric synthetic aperture radar observations
Journal of Geophysical Research, 1986
Interferometric synthetic aperture radar observations provide a means for obtaining high-resolution topographic terrain maps from data acquired simultaneously at two slightly displaced antennas. Calculation of the three-dimensional coordinates of all the points in a radar image can be made from the combination of along-track, slant range, and interferometer fringe measurements. Thus the result compensates for the layover exhibited by conventional radar maps and removes the false targets generated by multiple signal paths to a given object in the scene. We have derived a topographic map of a portion of the San Francisco Bay Area utilizing data that were recorded by a radar system mounted on a NASA CV990 aircraft and processed by a general purpose digital computer. This map displays the height above sea level of a region approximately 11 km by 10 km in size, sampled on an 11-m pixel grid. Uncertainties in the estimated height result from imprecise knowledge of the observational geometry, radar bandwidth limitations, and finite signal-to-noise ratios. For our system, each factor contributed approximately 3-4 m to a relative rms error of about 6 m. Additional global errors of the order of 10 m can result from inaccurate monitoring of aircraft attitude. The statistical variation of the height measurements from the ocean portion of the map, which we can presume to be quite flat, is 2-10 m rms, which is consistent with the theoretical estimate. Comparison of our results with U.S. Geological Survey contour maps indicates a high degree of correlation between the two sets of altitude data. Radar interferometry was first used in earth-based observations of Venus [Rogers and Ingalls, 1969] to separate ambiguous echos from the northern and southern hemispheres. Subsequently, elevation data were obtained by interferometric observation of the Moon I-Zisk, 1972a, b], where antenna directivity was sufficient to eliminate the north-south ambiguity. Radar interferometry with a changing baseline due to the earth's rotation enabled both resolution of the ambiguity and measurement of elevations for Venus I-Rumsey et al., 1974]. Observations of interference fringes modulated by Earth topography have also been obtained in aircraft measurements [Graham, 1974]. We report here our high-resolution topographic map of the earth resulting from an extension of interferometric synthetic aperture radar techniques. Topographic maps are typically determined from stereo pair optical photographs [Slama et al., 1980], in which vertical relief causes the same terrain to appear in slightly different positions for different look angles: this shift in location is interpreted in terms of the height of the terrain. More recently, stereo pair radar imagery has also been used to produce topographic maps (M. Kobrick and F. Leberl, unpublished manuscript, 1984). However, the methods used are extensions of the or•tical stereo technique rather than the interferometric approach described here. In the interferometer case the observable terrain shift is of the order of the radar wavelength rather than the resolution cell size. Thus a major problem in both the optical and radar stereo techniques, that of recognizing the resolution elements in the two stereo images, is circumvented. Such indentification is particularly difficult in coherent radar images because of the "speckle" phenomenon; different views of the same element are only statistically related. We present data that were recorded using a side-looking synthetic aperture radar system mounted on a NASA CV990 aircraft and subsequently processed at the Jet Propulsion Lab
3-D synthetic aperture radar interferometry phase unwrapping using extended Kalman filters
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2013
Synthetic Aperture Radar Interferometry (InSAR) observations allow researchers to map elevations, analyze surface deformation, and even detect ground water level changes from satellites orbiting the Earth. The InSAR phase measurements are inherently wrapped between 0 and 2π. For most physical interpretation methods the phase measurements have to be unwrapped to reveal the full scale of the observations. The unwrapping of multi-dimensional phase data is still a field of active research and here we present an algorithm using an Extended Kalman Filter (EKF). The current implementation of our EKF algorithm utilizes a piecewise linear approximation in space and a simple model in the third dimension (e.g. time). The algorithm starts from wrapped, unfiltered interferograms and filters and unwraps the results at the same time solving for a common topography or deformation rate, starting from the highest quality point in the coherent area and proceeding to unwrap highest quality neighbors. The highest quality neighbors are determined according to the Fisher's Distance, which is a phase quality measure similar to the more commonly used phase derivative variance, but also includes the interferogram coherence. In this presentation we demonstrate the effectiveness of our algorithm for the applications of DEM generation and deformation rate analysis using real data.
3D Phase Unwrapping Based on Quality Indicators of Differential SAR Interferograms
2016
The Generalization and the temporal continuity of DInSAR 3D phase unwrapping involve methods of contextual voxels unwrapping. 2D Methods can be applied to each interferogram in the 3D phase volume independently of the entire volume unwrapping. However, these methods cannot detect the phase shift necessary to ensure temporal continuity of the reconstructed phase. In contrast, the 3D methods which operate in the volume of the phase can avoid this problem. In this papier, 3D phase unwrapping process that we propose is based on the phase unwrapping guided by the edges reliability, estimated by quality indices in three planes. We have used, for this purpose, quality maps generated by the first and second 3D derived and 3D pseudo-correlation. We tested the process on simulated interferograms, then applied to real interferograms obtained from ERS1/ERS2 SAR images acquired on a southern Algeria region.
Improving phase unwrapping techniques by the use of local frequency estimates
IEEE Transactions on Geoscience and Remote Sensing, 1998
In multi-pass space-borne SAR interferometry, the two acquisitions often present low correlation levels and very noisy phase measurements which are incompatible with automatic phase unwrapping. Instead of dealing with many residues due to erroneous wrapped phase di erences, we propose to use the local frequency as measured by a spectral analysis algorithm presented in a previous paper 1]. For this purpose we present two conventional unwrapping algorithms, one local, the other global, that we revisit to bene t from the robust local frequency estimates. For a local approach based on path following techniques, we use the frequency estimates in a slope compensated lter which extend the complex averaging up to a su cient number of look to eliminate residues due to the noise. Then we connect residues due to non-interferometric features along mask components resulting from the detection of lay-overs and uncorrelated areas. For a global approach such as weighted least squares methods, we demonstrate that the use of noisy discrete phase gradient leads to a biased solution. To avoid this drawback, we propose to use the local frequency estimate and associated measure of con dence as phase gradient and weight. Results are presented on both topographic and di erential interferograms obtained from ERS-1 European radar satellite over various landscapes and over the displacement eld of the Landers 1992 earthquake.
IEEE Transactions on Geoscience and Remote Sensing, 1998
This paper explains the underestimation of phase slope and the consequent distortion of the phase surface, observed in two-dimensional (2-D) phase unwrapping by linear estimators. like least squares methods applied to synthetic aperture radar (SAR) interferometry. These methods minimize the difference between the gradient of the unwrapped phase and the wrapped differences of the measured wrapped phase. Using the probability distributions of phase noise and phase differences for a given coherence, the probability of a phase gradient error giving rise to a nonconservative vector field is derived. It is shown that this phase gradient error has nonzero mean in the presence of phase slopes. Linear phase estimators cannot distinguish the mean phase gradient error from a true phase slope; hence, the unwrapped phase shows a slope bias. This bias is quantified as a function of coherence and the number of independent samples that are averaged. The theoretical results are confirmed by simulations.