Numerous imaging techniques measure data that are mathematically wrapped to the finite interval. The measured phase by sar or sas is in the interval of. The algorithm can bring about accurate phase unwrapping and good noise suppression simultaneously by incorporating the true phase and its derivative in the state vector estimation through the ukf process. Results show that the proposed algorithm works faster than the joses proposed phase unwrapping via graph cut puma. Twodimensional 2d phase unwrapping is a key step in the existing advanced metrology technologies such as optical interferometry, optical threedimensional 3d measurement, and satellite radar interferometry sar. We develop here a theoretical framework for 3d phase unwrapping and also describe two algorithms for implementation, both of which can be applied to synthetic aperture radar interferometry. Synthetic aperture radar interferometry, proc ieee, vol. Inference of the lost integral number of cycles in phase measurements is critical for threepass surface deformation studies as well as topographic mapping and can result in an order of magnitude increase in. The paper addresses the problem of the development of robust algorithms for unwrapping the interferometric phase if produced in the sar interferometry. A phase unwrapping algorithm for interferometric fringes based on the unscented kalman filter ukf technique is proposed. Ici algorithm and the next to unwrap phase by using global phase unwrapping algorithm. The problem of phase unwrapping in two dimensions has been studied extensively in the past two decades, but the threedimensional 3d problem has so far received relatively little attention. This paper presents a new phase unwrapping algorithm for wrapped phase fringes through combining a cubature information particle filter with an efficient local phase gradient estimator and an efficient qualityguided strategy based on heapsort.
We present here a new integer programming formulation for phase unwrapping of multidimensional data. Inference of the lost integral number of cycles in phase measurements is critical for threepass surface deformation studies as well as. Phase unwrapping algorithms puas are commonly employed to remove this ambiguity and, hence, obtain the absolute phase. The phase information of a complex field is routinely obtained using coherent measurement techniques as, e.
Sentinel1 insar phase unwrapping using s1tbx and snaphu. Simultaneous unwrapping and low pass filtering of continuous. For instance, in remote sensing applications 2 like synthetic aperture radar sar or sonar sas, phase difference between the terrain and the radar is captured by two or more antennas. In this recipe, we will use snaphu, which is a twodimensional phase unwrapping algorithm developed by chen and zebker see section h. To enable use of the fast fourier transform the com. A twodimensional region growing least squares phase unwrapping algorithm for interferometric sar processing. The algorithm could unwrap some high phase variation map which the fft algorithm could not solve. Sar, interferometry, phase unwrapping, least squares, synthetic algorithm 1.
A fast, automated, ndimensional phase unwrapping algorithm. In this paper various algorithms are defined for phase unwrapping out of these the phase fringe counting approach and minimum spanning tree methods algorithms provide fast phase detection. In this paper, a pathindependent unwrapping method is proposed. Osa phase unwrapping algorithms for radar interferometry. Schofield, volkov and zhu phase unwrapping the general problem of phase unwrapping boils down to the correct extraction of the true phase. In the field of synthetic aperture radar sar interferometry, where the data usually consists of a stack of timeconsecutive interferograms, it was previously suggested to utilize.
Phase unwrapping, least square optimisation, digital elevation model introduction. Fast and robust threedimensional best path phase unwrapping algorithm hussein s. This paper, taking the multibaseline insar interferometric synthetic aperture radar system as an example, proposes a fast method for multiplebaseline and multifrequency band phase unwrapping in the frequency domain. Fast phase unwrappng algorithm for interferometric applications. Efficient phase unwrapping architecture for digital. The phase distribution of two holograms are subtracted and then a fast phase unwrapping algorithm is carried out to have a continuous, net phase profile of object 32. Phase unwrapping for sar interferometry a data fusion. Index termsnetwork optimization, statistical estimation, synthetic aperture radar interferometry, twodimensional phase unwrapping. Ieee transactions on geoscience and remote sensing 37, 2215 2226. The phase unwrapping is a significant and difficult procedure for profilometry based on fringe. The cubature information particle filter that not only is independent from noise statistics but also is not constrained by the nonlinearity of the. A method for packingunpacking indices of points in a photograph that is based on bitwise operations is developed.
After discussing schofields fast fourier transform fft algorithm, a weighted discretecosinetransformbased dctbased phase unwrapping pu algorithm is described. The algorithm, implemented and tested on 2d and 3d mr images, is currently being used for epi unwarping and rapid, automated shimming applications in fmri. Robust algorithms for phase unwrapping in sar interferometry. The phase unwrapping problem consists in recovering a real function u defined on a discrete set i. Fast phase unwrappng algorithm for interferometric. The performance of the proposed method is evaluated against three representative pu algorithms. The cubature information particle filter that not only is independent from noise statistics but also is not constrained by the. Twodimensional phase unwrapping theory, algorithms and. Phase unwrapping by synthetic weighted multigrid algorithm. Osa fast and accurate phaseunwrapping algorithm based. The majority of existing phase unwrapping techniques are pathfollowing methods, which explicitly or implicitly define an intelligent path and integrate phase difference along the path to mitigate the effect of erroneous pixels. We developed an algorithm called corphu, using phase closure of triplets of interferograms to correct unwrapping errors left after phase unwrapping. A fast algorithm for generating a growth ring of target pixels and an algorithm for merging regions are created. Phase unwrapping the wrapped phase comes in the range of 0, 2x1 and the goal of phase unwrapping is to get a continuous phase out of it.
Osa fast phase unwrapping algorithm for interferometric. Multibaseline and multifrequency band can improve the performance of phase unwrapping. Pdf fast twodimensional phaseunwrapping algorithm based. In this paper, the performance of three spatial phase unwrapping algorithms, branchcut phase unwrapping algorithm bc, minimum discontinuity algorithm md, and fast phase. Insar is one of many applications that use the technique. Applying the algorithm to a large topographic interferogram acquired over central alaska, we find that the technique is less prone to unwrapping artifacts than more simple tiling approaches. Phase unwrapping consists in the reconstruction of the phase difference of the radiation received by two sar systems as a function of the azimuth and slant range coordinates. Phaseunwrapping algorithm for the measurement of 3d. N, where norm algorithm is proposed for a twodimensional mri phase unwrapping. Twodimensional phase unwrapping pu is a crucial processing step of synthetic aperture radar interferometry insar. A fast phase unwrapping algorithm for sar interferometry abstract.
A wide range of interferometric techniques recover phase information that is mathematically wrapped on the interval. In this paper, we give a brief description of the mathematical base of phase unwrapping, and a detailed description of the unweighted and weighted least square phase unwrapping algorithm. Esa publications estec postbus 299 2200 ag noordwijk the netherlands tel. It depends on a quality map to unwrap the most reliable voxels first and the least reliable voxels last. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Denoising phase unwrapping algorithm for precise phase shifting interferometry j. Comparison and combination of three spatial phase unwrapping. Interferometric synthetic aperture radar phase unwrapping based on. Forest mapping and monitoring with interferometric synthetic. Phase unwrapping is a key problem in many coherent imaging systems, including time series synthetic aperture radar interferometry insar, with two spatial and one temporal data dimensions. Discussion about the dctfft phaseunwrapping algorithm.
Obtaining the true unwrapped phase is a longstanding problem. Abstractphase unwrapping is the key problem in building the elevation map of a scene from interferometric synthetic aperture radar sar system data. The advent of interferometric synthetic aperature radar for geophysical studies has resulted in the need for accurate, efficient methods of twodimensional phase unwrapping. A set of experimental results illustrates the effectiveness of the proposed algorithm, and its competitiveness with stateoftheart algorithms. With the rapid advance of insar technology, the scale of interferograms is. The paper presents an improved version of the regiongrowing algorithm for the interferometric phase unwrapping of the radar images. Fast fourierbased phase unwrapping on the graphics. We present an algorithm that solves the phase unwrapping problem, using a combination of fourier techniques.
Four dimensional phase unwrapping of dynamic objects in. The phase unwrapping problem is the key problem in interferometry, for simplicity we restrict our attention to the sar synthetic aperture radar interferometry problem. Phase field synthetic aperture radar phase unwrap interferometric synthetic aperture radar radar interferometry these keywords were added by machine and not by the authors. A wide range of reconstruction algorithms has been developed to obtain the true, unwrapped phase by adding an integral multiple of 2. The performance of this technique was tested on both. Extended kalman filter phase unwrapping smooth algorithm in. In this work a fast, fully automated, robust phase. The generation of highresolution dem from interferometric sar has resulted in the need for accurate and efficient methods of 2dimensional phase unwrapping. A fast multibaseline and multifrequency band phase. Osa practical phase unwrapping of interferometric fringes. Phase unwrapping is the reconstruction of a function on a grid given the value modulo of the function on the grid. A new algorithm based on coded phase is proposed in this paper. The phase unwrapping problem is not well defined in fact it has infinitely many solutions, so that it must be regularized to be satisfactorily solvable.
However, traditional singlebaseline sb pu algorithms except the l 0 norm pu strategy 49, 50 build dipole cuts between each pair of residues. The coherence coefficient map and residue guided least square. Osa efficient phase unwrapping algorithm based on cubature. The existence of large lowcoherence regions and rapidtopography variations poses challenges. We base our work on a region growing phase unwrapping algorithm originally developed for sar interferometry xu and cumming, 1999. We develop here a theoretical framework for 3d phase unwrapping and also describe two algorithms for implementation, both of which can be applied to synthetic aperture radar interferometry insar time. Here, we propose a fast phase unwrapping algorithm to realize highspeed quantitative interferometric microscopy, by shifting mod 2.
The most evident disadvantage of the recent advances in phase unwrapping is a lack of generality, i. There are different approaches to the problem, some of them described in 1,2. Two practicable methods are proposed based on the greens first identify with properly chosen greens functions satisfying the imposed newmanns boundary conditions. Solving the phase unwrapping problem by a parametrized. Phase unwrapping consists in the reconstruction of the phase difference of the radiation received by two sar. We assess its efficiency on two data sets in lebanon and turkey, respectively with envisat and sentinel1 satellites. Fast twodimensional phase unwrapping algorithm based on sorting by reliability following a noncontinuous path 2dsrncp 25 is used to process the unwrapping phase.
The phase unwrapping process may be performed offline in some of these applications, whose primary concern is the quality of the unwrapped phases. Phase unwrapping is the key problem in building the elevation map of a scene from interferometric synthetic aperture radar sar system data. This process is experimental and the keywords may be updated as the learning algorithm improves. Discussion about the dctfft phaseunwrapping algorithm for. The execution time for our algorithm is equivalent to the computation time. Then in terms of the interferometric phase, it means we can write the first term represents the phase difference measured for the flat earth, i. In this paper, the performance of three spatial phase unwrapping algorithms, branchcut phase unwrapping algorithm bc, minimum. Eege 157 b, week 3 3 10 radar interferometry trigonometry continued now let represent the look angle to a point on a flat earth as shown in the figure.
The advent of interferometric sar for geophysical studies has resulted in the need for accurate, efficient methods of twodimensional phase unwrapping. Improvements are presented in order to use this method in areas with intensely fluctuated fringe lines. Intrinsically these methods are not developed for discontinuous functions. A fast phase unwrapping algorithm for sar interferometry. In the 1990s, insar was then used for the study of. In all cases the problem is that the measuredphase signal can only take on values in a range, whilst the original phase signal can take on. Fast and robust threedimensional best path phase unwrapping. Phase unwrapping algorithms for radar interferometry. What we believe to be a novel threedimensional 3d phase unwrapping algorithm is proposed to unwrap 3d wrappedphase volumes. Measurement techniques such as optical interferometry, interferometric synthetic aperture radar, tomographic imaging, fringe projection profilometry and magnetic resonance imaging involve measurement of phase which is essentially proportional to the particular physical parameter of interest. A fast phase unwrapping algorithm for sar interferometry core. The phase distribution of two holograms are subtracted and then a fast phase unwrapping algorithm is carried out to have a continuous, net phase profile of. Conclusions in this paper, the results achieved so far using persistent scatterer interferometry and sentinel1 images have been shown. First, the algorithm converts the weightednormminimizationbased phase unwrapping problem into a linear system problem whose system coefficient matrix is a large, symmetric one.
Interferometric synthetic aperture radar insar is a geodetic technique developped in the 1970s for geophysical applications and, originally, to construct topographic maps of the earth graham 1974. Phase unwrapping rocca 5 the technique shown is successful provided that the true gradient is bounded to. Fast twodimensional phaseunwrapping algorithm based on sorting by reliability following a noncontinuous path 2dsrncp 25 is used to process. The execution time for our algorithm is equivalent to the computation time required for performing. It identifies the order of the fringe by projecting fringes with coded phase onto the object and performs fast phase unwrapping.
Pdf multiresolution phase unwrapping for sar interferometry. New methods of phase unwrapping in sar interferometry. Unwrapping the phase corresponds to finding the correct m i,j, which can be difficult in the presence of noise. Osa fast and robust threedimensional best path phase. Guidelines for sar interferometry processing and interpretation tm19, february 2007 editor. Phase unwrapping is a key problem in all quantitative applications of sar synthetic aperture radar interferometry zebker and godstein, 1986, and in several other fields oppenheim and lim, 1981. The minimum cost flow mcf 1 phase unwrapping algorithm describes a global cost minimization. A fast phase unwrapping algorithm for sar interferometry ieee. A comparison of phase unwrapping techniques in synthetic. Digital elevation models can be computed from ers interferometric products. Interferometric synthetic aperture radar insar is a powerful tool to measure the digital elevation.
Osa phase unwrapping in three dimensions with application. Phase unwrapping in three dimensions with application to insar. Please refer to for detailed discussion of the algorithm. Next, we give a brief overview of the phase unwrapping problem. Simulations indicate that the proposed algorithm has better accuracy. Phase unwrapping is a challenging task for interferometry based techniques in the presence of noise.
Typically, the measurement is obtained in the form of. Keyword phase unwrapping, puma, interferometry sar, magnetic resonance imaging, graph cuts i. Processing strategies for phase unwrapping for insar applications charles l. Extended kalman filter phase unwrapping smooth algorithm. Jun 10, 2019 twodimensional 2d phase unwrapping is a key step in the existing advanced metrology technologies such as optical interferometry, optical threedimensional 3d measurement, and satellite radar interferometry sar. We present a robusttonoise phaseunwrapping algorithm based on a global analysis of the interferogram. An approach to twodimensional 2d phase unwrapping for synthetic aperture radar sar interferometry is presented, based on separate steps of coarse phase and fine phase estimation. Validation of a novel phase unwrap algorithm using true. Such a phase unwrapping procedure is also important in other applications, including synthetic aperture radar interferometry insar and magnetic resonance imaging mri. Sparse markov random field method for phase unwrapping. However research carried out within geri may be taking the first steps to understanding the process of phase unwrapping algorithm failure 6. The technique follows a discrete unwrapping path to perform the unwrapping process.
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