Synthetic Aperture Radar Autofocus Research Articles

Fast and Accurate Refocusing for Moving Ships in SAR Imagery Based on FrFT

Synthetic aperture radar (SAR) is capable of monitoring the ocean all day, regardless of weather conditions. However, moving ships exhibit azimuth defocus in SAR images, which severely hampers ship recognition performance. Ships typically move in a linear motion at sea. For refocusing linear moving ships, existing SAR autofocus algorithms cannot accurately extract defocus information and require multiple iterations. To overcome the poor focusing quality and high computational complexity of existing refocusing algorithms, this paper proposes a fast and accurate refocusing scheme for moving ships in SAR imagery based on Fractional Fourier Transform (FrFT). Firstly, the azimuth line with the strongest energy in the SAR image is selected as the best azimuth line representing its motion property. Then, according to the entropy variation law of the azimuth line after FrFT, the azimuth line’s optimal rotation order is determined by the proposed minimum entropy search method, which can accurately and quickly obtain defocus information. In the final refocusing module, the scheme provides two ways, i.e., fast or fine refocusing approaches, to generate well-focused images. The fast refocusing approach performs FrFT on each azimuth line at the optimal rotation order of the best azimuth line. The fine refocusing approach takes the optimal rotation order of the best azimuth line as the initial value and further searches for the optimal rotation order of other azimuth lines. In order to verify the effectiveness of the proposed scheme, experiments are carried out on a number of Gaofen-3 SAR images in different acquisition modes. The experimental results show that the proposed fast refocusing approach can achieve the fastest speed, which is 2.1% of the traditional FrFT-based method’s processing time. Moreover, the proposed fine refocusing approach has the best focusing performance, achieving the lowest image entropy among existing methods.

Inverse synthetic aperture radar autofocus imaging of block structure targets with sparse aperture

Inverse synthetic aperture radar (ISAR) autofocus imaging performance is challenged by the residual phase errors that arise from the traditional motion compensation methods with sparse aperture. Moreover, sparse reconstruction algorithms usually ignore the block sparsity in the ISAR image, which cannot recover structured information of the block structure target completely. An imaging method based on joint minimum Tsallis entropy and pattern-coupled sparse Bayesian learning algorithm is proposed to achieve ISAR autofocus imaging of block structure targets with sparse aperture. A pattern-coupled hierarchical complex Gaussian prior is utilized to characterize the correlation among ISAR image pixels in the complex domain. Such a prior model has the potential to encourage block-sparse patterns and achieve ISAR sparse aperture imaging of block structure targets without knowing the block partition prior information. The residual phase errors are estimated based on the minimum Tsallis entropy criterion during the sparse reconstruction of ISAR image to achieve ISAR autofocus imaging, which has the advantage of improving the computational efficiency compared with minimum Shannon entropy criterion. The superiority of the proposed algorithm is verified by the experimental results based on both simulated and measured data.

SAR Image Reconstruction and Autofocus Using Complex-Valued Feature Prior and Deep Network Implementation

Synthetic aperture radar (SAR) plays an important role in remote sensing by providing electromagnetic images of the observation scene. The prior knowledge-based SAR image reconstruction method can reduce the requirement of data sampling ratio and improve image quality. The existing prior knowledge-based method usually uses the magnitude information of SAR images while ignoring the phase information. However, since the echo and backscattering coefficients are complex values, the phase information of SAR images will help improve the reconstruction accuracy in the image reconstruction process. To improve the reconstruction performance, this paper proposes a SAR image reconstruction and autofocus method using complex-valued feature prior. In the proposed method, the complex-valued feature prior is learned from data by a complex-valued feature projection operator (CFPO), which can characterize and extract scene features in Range-Doppler domain and 2D frequency domain. The proposed CFPO enables more efficient use of echo data and helps to improve image reconstruction and autofocus performance. In addition, the proposed method is implemented by an unfolded deep network, which enables data-driven feature learning and efficient computation. The proposed method is verified by simulated and measured data.

A High-Resolution Airborne SAR Autofocusing Approach Based on SR-PGA and Subimage Resampling With Precise Hyperbolic Model

High-resolution airborne synthetic aperture radar (SAR) imaging requires long synthetic aperture time (LSAT). However, the LSAT invalidates the Fresnel approximation in the traditional autofocusing method, leaving a residual signal phase in the motion error. To solve the problem, a signal-reconstruction-based phase gradient autofocus (SR-PGA) and a sub-image resampling (SIR) methods are proposed. They are developed on the hyperbolic model. First, a sub-aperture division strategy divides the full-aperture high-order error into multiple low-order sub-aperture errors. Then, the SR-PGA is developed to estimate the sub-aperture error (SPE), in which the precise deramping is reconstructed to eliminate the residual signal phase in the SPE. Third, the SIR is proposed to eliminate residual Doppler-variant shift of the adjacent sub-images, improving the accuracy of the SPE combination. Finally, simulation and actual data processing verify the effectiveness and validity of the algorithm.

Blind NCS-Based Autofocus for Airborne Wide-Beam SAR Imaging

The improvement in azimuth resolution and/or the increase in the instantaneous beam width can result in a wide-beam autofocus problem in airborne synthetic aperture radar (SAR). Because of the assumption of central-beam approximation, the typical two-step motion compensation (MoCo) method and its extensions are unsuitable for the autofocus of wide-beam SAR imaging. In addition, existing MoCo algorithms for airborne wide-beam SAR imaging require high-precision inertial navigation data. To address these problems, we propose a wide-beam autofocus algorithm based on a blind nonlinear chirp scaling. First, based on the two-step MoCo method, the wide-beam autofocus in this study was modeled as a multiparameter optimization problem for an optimal overall imagery quality. Subsequently, we combine the well-known parametric and nonparametric methods in the SAR autofocus community to convert the multidimensional optimization problem into a two-dimensional optimization problem. Furthermore, we observe that this two-dimensional optimization problem can be further converted into two one-dimensional optimization problems, which can significantly increase the efficiency and robustness of autofocus processing. In addition, the proposed method is a full-aperture algorithm for wide-beam SAR autofocus, which can avoid the problems of image stitching and phase discontinuity compared with well-known subaperture autofocus algorithms (e.g., SATA, PTA, and FD). The processing results of the simulated and measured data verified the effectiveness of the proposed method.

SAF-3DNet: Unsupervised AMP-Inspired Network for 3-D MMW SAR Imaging and Autofocusing

The sparse imaging method based on compressed sensing (CS) is widely used in the field of millimeter-wave (MMW) synthetic aperture radar (SAR) imaging. However, 3D sparse imaging is limited by the difficult parameter tuning, the huge computational load, and the low processing efficiency. In addition, due to the motion errors and model mismatch, it is difficult to obtain well-focused results without error correction techniques. To address these issues, we propose a deep learning framework that integrates 3D sparse imaging and autofocusing, named 3D Sparse Autofocusing Network (SAF-3DNet) for MMW SAR data processing. The network is constructed based on an auto-encoder, which can optimize parameters without effective ground truth. The backbone structure of the encoder is expanded by approximate message-passing (AMP), and the operators in the frequency domain are used to replace the traditional matrix-vector CS model, which avoids large-scale matrix multiplication and other operations, and greatly improves the operation efficiency. In addition, the 2D phase error estimation in the cross-range plane is embedded into the sparse imaging models, enabling simultaneous 3D imaging and autofocusing. The decoder is designed as a mapping from the autofocusing results to the echo data. Experimental results based on both simulated and measured data demonstrate the proposed SAF-3DNet can achieve well-focused 3D reconstruction within an ephemeral time, which expresses the potential of 3D MMW SAR real-time and high-quality imaging.

SAE-Net: A Deep Neural Network for SAR Autofocus

The sparsity-driven technique is a widely used tool to solve the synthetic aperture radar (SAR) imaging problem. However, it always encounters sensitivity to motion errors. To solve this problem, this article proposes a new deep neural network architecture, i.e., the sparse autoencoder network (SAE-Net). The proposed SAE-Net is designed to implement SAR imaging and autofocus simultaneously. In SAE-Net, the encoder transforms the SAR echo into an imaging result, and the decoder regenerates the SAR echo using the obtained imaging result. The encoder is designed by the unfolded alternating direction method of multipliers (ADMM), while the decoder is formulated into a linear mapping. The joint reconstruction loss and the entropy loss are utilized to guide the training of the SAE-Net. Notably, the algorithm operates in a totally self-supervised form and requires no other training dataset. The methodology was tested on both synthetic and real SAR data. These tests show that the proposed architecture outperforms other state-of-the-art autofocus methods in sparsity-driven SAR imaging applications.

Autofocus Methods for Moving Target Imaging in Synthetic Aperture Radar

To use moving target signatures in synthetic aperture radar (SAR) for classification and identification, it is desirable to obtain a well-focused image from the blurred moving target signature. While a substantial amount of research has been done on solving the constant chirp rate defocusing of a moving target, this often leaves significant blurring in the moving target signature of a real target. This work aims at improving previous work on autofocus, specifically considering higher order motion terms, including those due to range walk and small rotations. Additionally, we aim to reduce the reliance on bright well-separated point scatterers. We apply SAR autofocus methods normally used for full imagery to moving targets: minimum entropy and phased gradient autofocus, and include recent innovations that allow these methods to handle range walk. Finally, we add a novel range-varying autofocus stage. We use SAR imagery of a truthed moving pickup truck collected with the MIT Airborne Radar Testbed (ARTB) to compare autofocus algorithms.

AFnet and PAFnet: Fast and Accurate SAR Autofocus Based on Deep Learning

Autofocus plays a key role in synthetic aperture radar (SAR) imaging, especially for high-resolution imaging. In the literature, the minimum-entropy-based algorithms (MEA) have been proved to be robust and have been widely applied in SAR. However, this kind of method needs hundreds of iterations and is computationally expensive. In this paper, we proposed a non-iterative autofocus scheme based on deep learning and minimum-entropy criterion. It’s an unsupervised framework, which utilizes entropy as the loss function. In this scheme, deep neural networks are utilized for feature extraction and parameter estimation. Based on this scheme, two autofocus models (autofocus network and progressive autofocus network) are proposed. After training, the network learned the rules of autofocus from a large number of examples. Experimental results on real SAR data show that the proposed methods have focusing quality close to the state-of-the-art but with real-time focusing speed.

STLS-LADMM-Net: A Deep Network for SAR Autofocus Imaging

Synthetic aperture radar (SAR) can provide high-resolution electromagnetic backscattering images of the illuminated area, playing a significant role in various applications. However, achieving focused SAR images is challenging under sparse sampling and phase error conditions. By exploiting the sparsity or compressibility priors, the state-of-the-art sparsity-driven SAR imaging methods can reconstruct images under the condition of sparse sampling. However, the handcrafted priors used in these methods limit the imaging performance, and the iterative solution schemes reduce the computational efficiency. Besides, the measurement inaccuracy introduced by the phase error also degrades the reconstruction performance of the sparsity-driven imaging methods. To address these issues, a deep network for SAR autofocus imaging is proposed, which alternately performs image reconstruction and phase error estimation. When performing image reconstruction, the sparsity-cognizant total least-square (S-TLS) model is introduced to handle the problem of measurement inaccuracy, contributing to robust reconstruction performance under the condition of phase error. During the implementation of the deep network, a feature transform operator is used to realize data-driven prior knowledge learning and overcome the limitations of handcrafted priors. Moreover, the deep network approach can significantly improve computational efficiency. Experiments on simulated and real data verify the effectiveness and efficiency of the proposed method.

Fast SAR Autofocus Based on Ensemble Convolutional Extreme Learning Machine

Inaccurate Synthetic Aperture Radar (SAR) navigation information will lead to unknown phase errors in SAR data. Uncompensated phase errors can blur the SAR images. Autofocus is a technique that can automatically estimate phase errors from data. However, existing autofocus algorithms either have poor focusing quality or a slow focusing speed. In this paper, an ensemble learning-based autofocus method is proposed. Convolutional Extreme Learning Machine (CELM) is constructed and utilized to estimate the phase error. However, the performance of a single CELM is poor. To overcome this, a novel, metric-based combination strategy is proposed, combining multiple CELMs to further improve the estimation accuracy. The proposed model is trained with the classical bagging-based ensemble learning method. The training and testing process is non-iterative and fast. Experimental results conducted on real SAR data show that the proposed method has a good trade-off between focusing quality and speed.

Synthetic aperture radar autofocus based on phaseless measurements

We introduce a new framework for compressed sensing (CS) in synthetic aperture radar (SAR) imaging in the case of model error. Conventional CS-based autofocus methods solve a joint optimization problem to achieve both model error parameter estimation and SAR image formation simultaneously. Owing to the possibly nonconvex feature of the joint optimization problem, however, these algorithms may get stuck in local optima having large phase errors and thus fail to reconstruct the image. In contrast, we use phaseless measurements and pose imaging as a convex optimization problem. To solve the convex problem, we use the alternating direction method of multipliers-based approach, which is computationally efficient and easy to implement. The results from simulations with both point targets and extended targets validate the effectiveness of the proposed method.

Polar Format-Based Compressive SAR Image Reconstruction With Integrated Autofocus

In this article, we develop a polar format-based algorithm for recovering synthetic aperture radar (SAR) imagery from sparsely/randomly sampled data in the presence of motion compensation/phase errors. Our method integrates conventional SAR autofocus algorithms into an $\ell _{1}$ norm penalized image recovery problem. We demonstrate the effectiveness of this approach using a real airborne SAR data set covering a large scene.

Simplified and approximation autofocus back‐projection algorithm for SAR

Due to accuracy limited inertial measurement unit systems, residual synthetic aperture radar (SAR) motion errors need to be compensated by autofocus method. Back-projection (BP) algorithm is a time-domain imaging process suitable for arbitrary trajectory and imaging on digital elevation model. However, traditional SAR autofocus algorithm requires a Fourier transform relationship between image domain and phase history domain. This study introduces an autofocus algorithm based on phase-error estimation. By selecting the image sharpness as target cost function, the exact phase error is directly estimated in closed form by solving the fourth-order polynomial with simplified approach. Another straightforward approximation autofocus method is also proposed to simplify calculation with high accuracy. The vast storage requirement for filtered BP data is reduced through a trade between time and space. Computer simulation and airborne experimental results validate the efficiency and efficacy of the proposed method.

Compressive Sensing Based SAR Imaging and Autofocus Using Improved Tikhonov Regularization

For synthetic aperture radar (SAR) imaging, the compressive sensing (CS) coupled with total variation (TV)-based algorithm is known as an effective focusing technique using under-sampled dataset. However, the performance of the CS-TV method can be degraded by drawbacks of TV in terms of noise sensitivity and computational efficiency. In this paper, a novel approach to CS-SAR imaging is proposed based on improved Tikhonov regularization (ITR) coupled with an adaptive strategy using iterative reweighted matrix to solve the CS reconstruction problem of SAR images with sparsity. The proposed method can provide different degrees of performance of SAR autofocus with changes to the value of certain parameters of ITR. The proposed scheme outperforms conventional CS-based methods with respect to image quality, noise robustness, and computational complexity of the algorithm owing to the additional sensitivity of the proposed objective function. From the simulation results, we verify that the proposed autofocus method is highly efficient in forming SAR images from non-uniformly under-sampled dataset in terms of both image quality and computational efficiency.

Blind Gain and Phase Calibration via Sparse Spectral Methods

Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some cases, sparse structure in the unknown signal alleviates the ill-posedness of BGPC. Recently, there has been renewed interest in solutions to BGPC with careful analysis of error bounds. In this paper, we formulate BGPC as an eigenvalue/eigenvector problem and propose to solve it via power iteration, or in the sparsity or joint sparsity case, via truncated power iteration. Under certain assumptions, the unknown gains, phases, and the unknown signal can be recovered simultaneously. Numerical experiments show that power iteration algorithms work not only in the regime predicted by our main results, but also in regimes where theoretical analysis is limited. We also show that our power iteration algorithms for BGPC compare favorably with competing algorithms in adversarial conditions, e.g., with noisy measurement or with a bad initial estimate.

Robust Two-Dimensional Spatial-Variant Map-Drift Algorithm for UAV SAR Autofocusing

Autofocus has attracted wide attention for unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) systems, because autofocus process is crucial and difficult when the phase error is spatially dependent on both range and azimuth directions. In this paper, a novel two-dimensional spatial-variant map-drift algorithm (2D-SVMDA) is developed to provide robust autofocusing performance for UAV SAR imagery. This proposed algorithm combines two enhanced map-drift kernels. On the one hand, based on the azimuth-dependent phase correction, a novel azimuth-variant map-drift algorithm (AVMDA) is established to model the residual phase error as a linear function in the azimuth direction. Then the model coefficients are efficiently estimated by a quadratic Newton optimization with modified maximum cross-correlation. On the other hand, by concatenating the existing range-dependent map-drift algorithm (RDMDA) and the proposed AVMDA in this paper, a phase autofocus procedure of 2D-SVMDA is finally established. The proposed 2D-SVMDA can handle spatial-variance problems induced by strong phase errors. Simulated and real measured data are employed to demonstrate that the proposed algorithm compensates both the range- and azimuth-variant phase errors effectively.

Theory of data‐driven SAR autofocus to compensate for refraction effects

There are challenges in attempting to acquire sufficient atmospheric measurements that are required in order to model the physical atmospheric refraction effects for all transmission pulses within a typical synthetic aperture radar (SAR) collection interval. In particular, atmospheric turbulence can induce spatial variations of the air density, temperature, and other physical variables along the synthetic aperture, which can have differing effects on the local refraction-induced bending and delay of each of the transmission pulses. The primary goal of the current investigation is to develop an alternate approach based on data-driven techniques in order to develop methods for automatically correcting such refraction-induced defocus effects on SAR image data. This alternate methodology applies two-dimensional maximum likelihood signal-theoretic techniques in order to estimate and compensate for the refraction-induced phase errors of the input defocused SAR imagery, thus yielding improved scene refocus wherein the majority of the refraction-induced defocusing effects have been corrected. The efficacy of this data-driven approach is demonstrated through the injection of known bending and delay effects applied to measured Ku-band SAR data.

A Coarse-to-Fine Autofocus Approach for Very High-Resolution Airborne Stripmap SAR Imagery

An autofocus operation is an indispensable procedure to obtain well-focused images for synthetic-aperture radar (SAR) systems without precise navigation devices. Three challenges have been faced in the very high-resolution (VHR) airborne SAR autofocus due to the long cumulative time: the varying along-track velocity, the residual range cell migration (RCM), and the range-dependent phase errors with higher order components. When it comes to the stripmap mode, the autofocus becomes more complicated, since the scenario with a few strong scatterers is more likely to be encountered with a moving beam. Combining the merits of parametric and nonparametric autofocus algorithms, a robust motion error estimation method is proposed in this paper. First, we perform a stripmap multiaperture mapdrift autofocus operation to extract the along-track velocity and the most range-invariant errors, removing the residual RCM at a subaperture scale. Second, one referential center block is selected to retrieve the residual range-invariant error, which can eliminate the residual RCM globally in the range dimension. With a global high-quality input, the residual range-variant phase errors can be retrieved precisely utilizing a center-to-edge local maximum-likelihood weighted phase gradient autofocus kernel at last. Experiments on real VHR airborne stripmap SAR data are performed to demonstrate the robustness of the proposed method.

Sparse representation-based algorithm for joint SAR image formation and autofocus

Inaccuracies in the observation model of the synthetic aperture radar (SAR) due to inaccuracies of the velocity and position of the platform or atmospheric turbulence cause degradations in reconstructed images which necessitate the use of autofocus algorithms. In this paper we propose a novel signal processing algorithm for joint SAR image formation and autofocus in a synthesis dictionary based sparse representation framework. Proposed algorithm can be applied broadly to scenes that exhibit sparsity with respect to any dictionary. This is done by extending our previously developed sparse representation-based SAR imaging framework to joint SAR image formation and autofocus. To this end, the phase error vector is separated from the unknown phase of the complex-valued back-scattered field. Phase error vector is estimated using a MAP estimator and compensated through an iterative algorithm to produce focused images. We demonstrate the effectiveness of the proposed approach on synthetic and real imagery.