Synthetic Aperture Radar Phase Research Articles

InDeandCoE: A framework based on multi-scale feature fusion and residual learning for interferometric SAR remote sensing image denoising and coherence estimation

Synthetic aperture radar (SAR) interferometry is a high-resolution microwave remote sensing imaging method. Over the past two decades, many researchers working on remote sensing have applied this technology in various disciplines, including environmental monitoring, disaster monitoring, and elevation mapping. However, due to the existence of many influencing factors in the acquisition stage, such as atmospheric humidity and temperature, the reflected wave signals from the ground will be disturbed when received by remote sensing satellites. The presence of noise in interferograms is inevitable. Therefore, the accuracy of interferometric SAR phase denoising and coherence estimation has a decisive impact on the validity of subsequent processing results. In this paper, we pioneer the use of a nested U-net as a feature extractor for interferometric SAR phase and coherence. In addition, we build a phase filter and a coherence estimator by using the residual learning module. With the aim of determining the unique non-local similarity of InSAR images, we use non-local convolution and channel attention mechanisms to extract features in different dimensions of the interferogram. Through quantitative and qualitative experiments, the proposed method performs better in phase denoising and coherence estimation than state-of-the-art methods.

Sub-aperture SAR imaging with uncertainty quantification

In the problem of spotlight mode airborne synthetic aperture radar (SAR) image formation, it is well-known that data collected over a wide azimuthal angle violate the isotropic scattering property typically assumed. Many techniques have been proposed to account for this issue, including both full-aperture and sub-aperture methods based on filtering, regularized least squares, and Bayesian methods. A full-aperture method that uses a hierarchical Bayesian prior to incorporate appropriate speckle modeling and reduction was recently introduced to produce samples of the posterior density rather than a single image estimate. This uncertainty quantification information is more robust as it can generate a variety of statistics for the scene. As proposed, the method was not well-suited for large problems, however, as the sampling was inefficient. Moreover, the method was not explicitly designed to mitigate the effects of the faulty isotropic scattering assumption. In this work we therefore propose a new sub-aperture SAR imaging method that uses a sparse Bayesian learning-type algorithm to more efficiently produce approximate posterior densities for each sub-aperture window. These estimates may be useful in and of themselves, or when of interest, the statistics from these distributions can be combined to form a composite image. Furthermore, unlike the often-employed -regularized least squares methods, no user-defined parameters are required. Application-specific adjustments are made to reduce the typically burdensome runtime and storage requirements so that appropriately large images can be generated. Finally, this paper focuses on incorporating these techniques into SAR image formation process, that is, for the problem starting with SAR phase history data, so that no additional processing errors are incurred. The advantage over existing SAR image formation methods are clearly presented with numerical experiments using real-world data.

UAV-Based P-Band SAR Tomography With Long Baseline: A Multimaster Approach

Due to the advantage of flexible and rapid deployment, unmanned aerial vehicle (UAV)-based synthetic aperture radar (SAR) tomography (TomoSAR) is a promising technology in 3-D urban mapping. The long baseline is indispensable for P-band SAR systems to achieve high elevation resolution. It will introduce two problems. On the one hand, the unavoidable spatial decorrelation brings serious phase noise and sidelobes in 3-D imaging. On the other hand, the noticeable image distortion fails the image registration and the TomoSAR data stack (TDS) construction. Aiming at the above problems, this article proposes a multimaster (MM) TomoSAR approach via three main contributions. First, the traditional TomoSAR signal model is extended to the MM case to improve the number of baselines and the average image coherence of the TDS and suppress the sidelobes. Second, a short-baseline-recursion image registration method is proposed to achieve high-precision image registration. Third, a TDS optimization processing consisting of interferometric SAR (InSAR) phase screening and baseline sign reassignment is introduced. Moreover, a clustering-based outliers’ elimination method is also adopted to ensure the 3-D imaging quality. Computer simulation and long-baseline P-band UAV-SAR experiment validate the proposed approach.

Efficient SAR Imaging Integrated With Autofocus via Compressive Sensing

In synthetic aperture radar (SAR) imaging, perturbations in the motion of the moving platform induce an undesired phase error due to imprecise knowledge of the motion, which results in the significant degradations in the quality of SAR images. In this paper, we present an efficient compressive sensing (CS)-based SAR imaging integrated with autofocus technique. The novel approach is based on an estimation-theoretic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm-based approach coupled with Tikhonov-type regularization which combines an observation model of the SAR image formation process with the CS reconstruction problem of the SAR image regarding the sparsity. The optimization problem derived by considering spatially variant phase errors along azimuth domain and the dataset sampled at low rates can be effectively addressed by an efficient iterative method, wherein each iteration both SAR image formation and phase error correction are simultaneously carried out. The simulations and experimental results are presented to validate the effectiveness of the proposed method in terms of reliable image recovery and efficient computational complexity.

Integrated Denoised Synthetic Aperture Radar Images for Enhanced Digital Elevation Model Generation

Synthetic aperture radar (SAR) enables imaging of topographic surfaces day and night in different atmospheric conditions. SAR imaging systems record both intensity and phase information of the backscattered signals. Acquired intensity information is often exposed to speckle noise, and gathered phase information is usually corrupted by thermal and other types of noise. Thus, these types of noises have negative effects on interpretation of SAR images. Digital elevation model (DEM) can be generated by interferometric SAR using two SAR images, of the same area, with slightly different look angles. The generated DEM is affected by the corruption of both intensity and phase information. In this paper, a proposed framework of convolutional neural network (CNN) and modified Wiener filter (MWF) is suggested in DEM generation process. The main purpose of the proposed framework is minimizing not only speckle noise of input SAR images but also phase noise of the interferogram. Thus, an enhanced DEM can be generated. Extensive experiments are carried out and different DEMs are generated from original SAR and from both despeckled SAR images and filtered interferogram. Results and comparative analyses show significant improvements in both quality and vertical accuracy of the DEM generated by the proposed hybrid (CNN-MWF) framework.

Statistical Exploration of SENTINEL-1 Data, Terrain Parameters, and in-situ Data for Estimating the Near-Surface Soil Moisture in a Mediterranean Agroecosystem

Reliable near-surface soil moisture (θ) information is crucial for supporting risk assessment of future water usage, particularly considering the vulnerability of agroforestry systems of Mediterranean environments to climate change. We propose a simple empirical model by integrating dual-polarimetric Sentinel-1 (S1) Synthetic Aperture Radar (SAR) C-band single-look complex data and topographic information together with in-situ measurements of θ into a random forest (RF) regression approach (10-fold cross-validation). Firstly, we compare two RF models' estimation performances using either 43 SAR parameters (θNovSAR) or the combination of 43 SAR and 10 terrain parameters (θNovSAR+Terrain). Secondly, we analyze the essential parameters in estimating and mapping θ for S1 overpasses twice a day (at 5 a.m. and 5 p.m.) in a high spatiotemporal (17 × 17 m; 6 days) resolution. The developed site-specific calibration-dependent model was tested for a short period in November 2018 in a field-scale agroforestry environment belonging to the “Alento” hydrological observatory in southern Italy. Our results show that the combined SAR + terrain model slightly outperforms the SAR-based model (θNovSAR+Terrain with 0.025 and 0.020 m3 m−3, and 89% compared to θNovSAR with 0.028 and 0.022 m3 m−3, and 86% in terms of RMSE, MAE, and R2). The higher explanatory power for θNovSAR+Terrain is assessed with time-variant SAR phase information-dependent elements of the C2 covariance and Kennaugh matrix (i.e., K1, K6, and K1S) and with local (e.g., altitude above channel network) and compound topographic attributes (e.g., wetness index). Our proposed methodological approach constitutes a simple empirical model aiming at estimating θ for rapid surveys with high accuracy. It emphasizes potentials for further improvement (e.g., higher spatiotemporal coverage of ground-truthing) by identifying differences of SAR measurements between S1 overpasses in the morning and afternoon.

Synthetic aperture radar phase unwrapping using region-growing with polynomial-based phase prediction

Phase unwrapping for interferometric synthetic aperture radar (InSAR) remains a challenge due to the presence of speckle noise and temporal decorrelation in many interferograms. This paper proposes a polynomial-based region-growing phase unwrapping (PBRGPU) approach that is built on the region-growing phase unwrapping (RGPU) approach in Xu and Cumming (Xu and Cumming. 1996. A region growing algorithm for insar phase unwrapping. IGARSS 96. International Geoscience and Remote Sensing Symposium. 31–31 May 1996. Lincoln, NE, USA. doi: 10.1109/igarss.1996.516883 ). The proposed approach iteratively performs phase unwrapping at the edges of multiple seeded regions using a least-squares polynomial phase prediction, which allows for the use of statistically rigorous quality assurance to remove low quality pixels from further processing. Here, a user-specified statistical confidence interval is more intuitive to users than the threshold parameters used by other algorithms. The proposed approach is currently the only phase unwrapping approach to take this strategy with its quality assurance. The proposed approach was found to improve upon the solution quality of the RGPU approach, in some cases achieving a tenfold decrease in root-mean-square error for simulated data. The PBRGPU approach performed well when applied to RADARSAT-2 data collected over Polar Bear Provincial Park (Ontario, Canada). The PBRGPU solutions were consistently on par with or superior to those generated by SNAPHU in terms of accuracy. While the PBRGPU approach does lag behind SNAPHU in terms of the domain of the solution, with SNAPHU unwrapping a significantly larger portion of the interferogram in all test cases, this issue could readily be mitigated through post-processing of the unwrapped interferogram. The proposed approach provides a solid foundation for region-growing algorithms that adapt to local noise levels and integrate all available information rather than relying on preprocessing strategies.

The Impact of SAR Parameter Errors on the Ionospheric Correction Based on the Range-Doppler Model and the Split-Spectrum Method

Interferometric synthetic aperture radar (InSAR) products may be significantly distorted by microwave signals traveling through the ionosphere, especially with long wavelengths. The split-spectrum method (SSM) is used to separate the ionospheric and the nondispersive phase terms with lower and higher spectral sub-band interferogram images. However, the ionospheric path delay phase is very delicate to the synthetic aperture radar (SAR) parameters including orbit vectors, slant range, and target height. In this paper, we get the impact of SAR parameter errors on the ionospheric phase by two steps. The first step is getting the derivates of geolocation with reference to SAR parameters based on the range-Doppler (RD) imaging model and the second step is calculating the derivates of the ionospheric phase delay with respect to geometric positioning. Through the numerical simulation, we demonstrate that the deviation of ionospheric phase has a linear relationship with SAR parameter errors. The experimental results show that the estimation of SAR parameters should be accurate enough since the parameter errors significantly affect the performance of ionospheric correction. The root mean square error (RMSE) between the corrected differential interferometric SAR (DInSAR) phase with SAR parameter errors and the corrected DInSAR phase without parameter errors varies from centimeter to decimeter level with the L-band data acquired by the Advanced Land Observing Satellite (ALOS) Phased Array type L-band SAR (PALSAR) over Antofagasta, Chile. Furthermore, the effectiveness of SSM can be improved when SAR parameters are accurately estimated.

An implicit radar convolutional burn index for burnt area mapping with Sentinel-1 C-band SAR data

Compared with optical sensors, the all-weather and day-and-night imaging ability of Synthetic Aperture Radar (SAR) makes it competitive for burnt area mapping. This study investigates the potential of Sentinel-1 C-band SAR sensors in burnt area mapping with an implicit Radar Convolutional Burn Index (RCBI). Based on multitemporal Sentinel-1 SAR data, a convolutional networks-based classification framework is proposed to learn the RCBI for highlighting the burnt areas. We explore the mapping accuracy level that can be achieved using SAR intensity and phase information for both VV and VH polarizations. Moreover, we investigate the decorrelation of Interferometric SAR (InSAR) coherence to wildfire events using different temporal baselines. The experimental results on two recent fire events, Thomas Fire (Dec., 2017) and Carr Fire (July, 2018) in California, demonstrate that the learnt RCBI has a better potential than the classical log-ratio operator in highlighting burnt areas. By exploiting both VV and VH information, the developed RCBI achieved an overall mapping accuracy of 94.68% and 94.17% on the Thomas Fire and Carr Fire, respectively.

Potential for Absolute Ionosphere and Clock Correction in Noncooperative Bistatic SAR

A method is presented to estimate and compensate the ionospheric and clock-drift perturbations that affect bistatic synthetic aperture radar (SAR) images acquired under a quasi-monostatic acquisition geometry. This is accomplished through multisquint-based processing of the interferometric phase, which allows separating the ionospheric component from the rest of the phase perturbations by processing small azimuth subapertures. It is demonstrated how the absolute, i.e., nondifferential, ionospheric phase can be estimated by exploiting the baseline of the acquisition geometry, which further allows an individual correction of each image of the bistatic pair. A mathematical model of the bistatic SAR phase perturbations, as well as an algorithm for performing their estimation and compensation, is presented. The performance of the method is assessed with end-to-end simulations of bistatic acquisitions over synthetic distributed targets.

Integration of SAR Data Into Monitoring of the 2014–2015 Holuhraun Eruption, Iceland: Contribution of the Icelandic Volcanoes Supersite and the FutureVolc Projects

We report how data from satellite and aerial synthetic aperture radar (SAR) observations were integrated into monitoring of the 2014-2015 Holuhraun eruption in the Barðarbunga volcanic system, the largest effusive eruption in Iceland since the 1783-84 Laki eruption. A lava field formed in one of the most remote areas in Iceland, after the propagation of a ~50 km-long dyke beneath the Vatnajokull ice cap, where the Barðarbunga caldera is located. Due to the 6 month duration of the eruption, mainly in wintertime, daily monitoring was particularly challenging. During the eruption, the European volcanological project FutureVolc was ongoing, allowing collaboration of many European experts on volcano monitoring activities. Icelandic volcanoes are also a permanent Supersite within the Geohazard Supersites and Natural Laboratories (GSNL) initiative, with support from the Committee on Earth Observation Satellite (CEOS) in the form of a large collection of SAR images. SAR data were acquired by Cosmo-SkyMed (CSK) and TerraSAR-X (TSX) satellites and complemented by aerial SAR images. The large set of SAR satellite data significantly contributed to the daily monitoring during the unrest at Barðarbunga caldera, the Holuhraun eruption and the year following the eruption. Detection of surface changes using both SAR amplitude and phase information was conducted throughout the whole duration of the volcano-tectonic event, and in the following months, to quantify and track the evolution of volcanic processes at Holuhraun and geothermal activity at Barðarbunga volcano. Combination of SAR data with other data sets, e.g. satellite optical images and geodetic Global Positioning System (GPS) measurements, was essential for the evaluation of the volcanic hazard in the whole area. International collaboration within the Futurevolc project formed the basis for successful analyses and interpretation of the large SAR data set. Information was provided at Scientific Advisory Board meetings of the Icelandic Civil Protection and used in decision-making, as well as for supporting field-deployment and air-based surveys.

A Multibaseline InSAR Phase Unwrapping Method Using Designed Optimal Baselines Obtained by Motion Compensation Algorithm

Multibaseline (MB) interferometric synthetic aperture radar phase unwrapping (PU) has the advantage of using the baseline diversity to increase the ambiguity intervals of the interferometric phases and overcome the limitation of the phase continuity assumption. One major challenge of the MB PU is that the performance of PU greatly depends on the baseline configuration. In this letter, the motion compensation algorithm is used to modify the baselines of the interferograms. Therefore, optimal baseline configuration can be used in the MB PU to improve the PU performance. Real ALOS/PALSAR data over Himalayan mountain area have been used to verify the performance of the proposed method. The experimental results show that the MB PU with modified baselines becomes more reliable.

Comparison of optimization algorithms for interferometric synthetic aperture radar phase unwrapping based on identical Markov random fields

Phase unwrapping (PU) is one of the key processes in measuring the elevation or deformation of the Earth’s surface from its interferometric synthetic aperture radar (InSAR) data. PU problems may be formulated as maximum a posteriori estimation estimations of Markov random field (MRF). The key issue of this formulation is energy minimization. Iterated conditional mode (ICM), graph cuts (GC), loopy belief propagation (LBP), and sequential tree-reweighted message passing (TRW-S) have been proposed for the energy minimization. Unfortunately, they differ in the formulation of the MRF model for PU, which raises the question of how they compare against each other on the same MRF model for PU. We address this by investigating the four optimization algorithms and comparing them on an identical MRF model, which gives researchers some guidance as to which optimization method is best suited for solving the PU problem. Experiments using simulated and real-data illustrate that the GC algorithm is clearly the winner among the four algorithms in all cases. The ICM algorithm, although very rapid, performs much worse than the other three especially in the terrain with violent changes or discontinuities. The two message-passing algorithms—LBP and TRW-S—perform completely differently. The LBP algorithm performs surprisingly poorly on solving phase discontinuities issue, whereas the TRW-S algorithm does quite well (second only to the GC algorithm).

Interferometric synthetic aperture radar phase unwrapping based on sparse Markov random fields by graph cuts

Phase unwrapping (PU) is one of the key processes in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. It is known that two-dimensional (2-D) PU problems can be formulated as maximum a posteriori estimation of Markov random fields (MRFs). However, considering that the traditional MRF algorithm is usually defined on a rectangular grid, it fails easily if large parts of the wrapped data are dominated by noise caused by large low-coherence area or rapid-topography variation. A PU solution based on sparse MRF is presented to extend the traditional MRF algorithm to deal with sparse data, which allows the unwrapping of InSAR data dominated by high phase noise. To speed up the graph cuts algorithm for sparse MRF, we designed dual elementary graphs and merged them to obtain the Delaunay triangle graph, which is used to minimize the energy function efficiently. The experiments on simulated and real data, compared with other existing algorithms, both confirm the effectiveness of the proposed MRF approach, which suffers less from decorrelation effects caused by large low-coherence area or rapid-topography variation.

Characterizing hydrologic changes of the Great Dismal Swamp using SAR/InSAR

The Great Dismal Swamp (GDS), one of the largest, northernmost peatlands on the Atlantic Coastal Plain, is underlain by a thick water-logged organic soil layer (peat) made up of dead and decaying plant material. The peatland functions as a main sink for a large amount of soil derived organic carbon. The disturbance of this wetland has negatively impacted the ecosystem and contributed to climate change through the release of the stored greenhouse gases. Surface water level and soil moisture conditions are critical information about peatlands, but monitoring these hydrologic changes has been a challenging task. With a lack of in situ soil moisture measurements, we first explored yearlong Soil Moisture Active Passive (SMAP) data to find the close relationship (R-squared value: 0.80) between soil moisture and groundwater table from March 2015 to March 2016. Based on synthetic aperture radar (SAR) backscattering returns and interferometric SAR (InSAR) phase measurements from C-band Radarsat-1 and L-band ALOS PALSAR datasets, we then analyzed the hydrologic changes in the peatlands. We compared averaged C/L-band SAR backscattering intensity (mid 1998–early 2008 for Radarsat-1, late 2006–early 2011 for ALOS PALSAR) with groundwater level changes and found that the SAR backscattering is significantly responsive (R-squared value: 0.76 and 0.67 for Radarsat-1 and ALOS PALSAR, respectively) to soil moisture changes through a three-way correlated relationship of soil moisture, groundwater level, and SAR intensity. Using InSAR coherence observations, we delineated the inundated area (western and northern regions of GDS) during the wet season, subject to double-bounce backscattering. We measured the relative water level changes in the inundated areas through the InSAR phase measurements, and estimated the groundwater level changes corresponding to soil moisture changes using time-series InSAR analysis. Our comprehensive study has demonstrated that time-series SAR backscattering returns and InSAR analysis can be used to gauge soil moisture conditions and to monitor the hydrologic and vegetation changes in the GDS.

Inverse synthetic aperture radar phase adjustment and cross-range scaling based on sparsity

Due to inherent sparsity of ISAR images, compressive sensing theory has been used to obtain a high resolution image. However, before applying sparse recovery methods, the phase error due to the translational motion of target is compensated by autofocusing algorithms and the target rotation rate is estimated by cross-range scaling methods. In this paper, a comprehensive matrix model for a uniformly rotating target that includes the phase error and chirp-rate of the target is derived. Then by using sparsity and minimum entropy criterion, the estimation of residual phase error and the rotation rate is refined. In order to reduce the computational load, we simplify the model and by an iterative method based on adaptive dictionary, the phase error and chirp-rate are estimated separately. Actually, by exploiting a two-dimensional (2D) optimization method and the Nelder–Mead algorithm the phase adjustment is performed and the chirp-rate is estimated by solving a 1D optimization method for dominant range cells of the target. Finally, both simulation and practical data have been used to verify the validity of the proposed approach.

SAR-PC: Edge Detection in SAR Images via an Advanced Phase Congruency Model

Edge detection in Synthetic Aperture Radar (SAR) images has been a challenging task due to the speckle noise. Ratio-based edge detectors are robust operators for SAR images that provide constant false alarm rates, but they are only optimal for step edges. Edge detectors developed by the phase congruency model provide the identification of different types of edge features, but they suffer from speckle noise. By combining the advantages of the two edge detectors, we propose a SAR phase congruency detector (SAR-PC). Firstly, an improved local energy model for SAR images is obtained by replacing the convolution of raw image and the quadrature filters by the ratio responses. Secondly, a new noise level is estimated for the multiplicative noise. Substituting the SAR local energy and the new noise level into the phase congruency model, SAR-PC is derived. Edge response corresponds to the max moment of SAR-PC. We compare the proposed detector with the ratio-based edge detectors and the phase congruency edge detectors. Receiver Operating Characteristic (ROC) curves and visual effects are used to evaluate the performance. Experimental results of simulated images and real-world images show that the proposed edge detector is robust to speckle noise and it provides a consecutive edge response.

Bridge Displacements Monitoring Using Space-Borne X-Band SAR Interferometry

The development of interferometric methodologies for deformation monitoring that are able to deal with long time series of synthetic aperture radar (SAR) images made the detection of seasonal effects possible by decomposing the differential SAR phase. In the case of monitoring of man-made structures, particularly bridges, the use of high-resolution X-band SAR data allows the determination of three major components with significant influence on the SAR phase: the linear deformation trend, the height of structures over terrain, and the thermal expansion. In the case of stable metallic or (reinforced) concrete structures, this last effect can reach a magnitude comparable to or even exceeding the other phase components. In this review, we present two case studies that confirm the feasibility of InSAR techniques for bridge deformation monitoring and our original approach to refine the thermal expansion component.

The Influence of Equatorial Scintillation on L-Band SAR Image Quality and Phase

It is well known that many of the nighttime acquisitions of the L-band Advanced Land Observing Satellite (ALOS) Phased Array-type L-band Synthetic Aperture Radar (PALSAR) instrument over equatorial regions show significant distortions of the image amplitude information. These distortions have the form of amplitude stripes that are roughly aligned with the local geomagnetic field. While ionospheric scintillation has been identified as the source of these distortions, the exact nature of the induced artifacts on synthetic aperture radar (SAR) image quality and SAR signal phase has not yet been studied in sufficient detail. Hence, this paper provides a quantitative analysis of equatorial scintillation effects on SAR image quality and SAR phase. We have performed a statistical analysis of ALOS PALSAR images over equatorial regions to describe the observed distortions and relate them to ionospheric parameters. An ionospheric simulator was developed and validated that is capable of simulating ionospheric distortions based on ionospheric scintillation parameters. Using this simulator, we found that ionospheric scintillation in the equatorial zone can cause significant distortions of SAR image amplitudes, image focus, and SAR signal phase. We determined threshold ionospheric environmental conditions that lead to the formation of these image distortions. Based on these thresholds, we quantified the likelihood of occurrence of ionospheric distortions for the global equatorial belt and for L-band sensors ALOS PALSAR, ALOS-2 PALSAR-2, and NASA-ISRO SAR (NISAR).

ML-based Approaches for Joint SAR Imaging and Phase Error Correction

This paper addresses a series of iterative sparse recovery approaches with application to the synthetic aperture radar (SAR) imaging which suffers from motion-induced model errors. These types of errors result in phase errors in SAR data, which cause defocusing of the reconstructed images. The proposed phase-error correction approaches combine the maximum a posterior (MAP) algorithm and the iterative sparse maximum likelihood-based (SMLA) approaches (referred to as the PE-MAP-SMLA approaches) to solve a joint optimization problem to achieve phase errors estimation and SAR image formation simultaneously. A new PESLIM approach is also proposed that extends the idea of the classical sparse and learning via iterative minimization (SLIM) approach. A closed-form expression for the recursive estimate of the phase errors parameters is derived. A general form of each of these iterative approaches consists of three steps, the first of which is for image formation, the second is for phase errors estimation and the last is for nuisance parameters estimation. The proposed approaches can correct the phase errors accurately, and the reconstruction quality of the SAR images can be improved significantly. Finally, simulation results of 1-D spectral estimation and 2-D SAR imaging examples are generated to show the effectiveness of the proposed approaches.