Linear Array SAR Research Articles

Sparse recovery algorithm via adaptive grids for linear array SAR 3D sparse imaging

ABSTRACT Compressed sensing (CS) algorithms mostly achieve linear array synthetic aperture radar (LASAR) 3D sparse imaging under the On-Grid strategy, they suffer from the mismatch measurement matrix and decreased imaging quality due to the position-errors among targets and preset scattering units. Aimed at this problem, based on the Off-Grid strategy, a sparse recovery algorithm via adaptive grids (SRAG) is proposed in this paper. First, the proposed algorithm extracts the target scattering units in the imaging scene under the On-Grid strategy. Second, the target scattering units with position-errors are extracted under the non-zero adjacent scattering coefficient criterion, and they are defined as the unfocused scattering units. Third, according to whether the unfocused scattering units’ distance is smaller than the scattering unit spacing, their search-areas of targets’ real positions are set, respectively, and differently. Finally, based on the minimum scattering coefficient residual criterion, we adaptively compensate the unfocused scattering units’ position-errors and re-estimate their scattering coefficients. Both simulation and experimental results indicate that the SRAG algorithm decreases the position-errors effectively, it improves the imaging quality, estimation accuracy of targets’ positions, and scattering coefficients than traditional On-Grid CS algorithms.

Swarm UAV SAR for 3-D Imaging: System Analysis and Sensing Matrix Design

The unmanned aerial vehicle (UAV) is a low-cost and high-efficiency lightweight synthetic aperture radar (SAR)-mounted platform that can be used for a variety of military and civilian missions. Using multiple UAVs to form a swarm can break through the limitations of a single platform and has broad application prospects. In this article, swarm UAV SAR that contains tens or hundreds of UAV platforms is proposed for the first time. The concept and advantages of swarm UAV SAR are investigated, and the mission outlook is given. Afterward, the swarm UAV 3-D linear array SAR (LASAR) is illustrated, which enables high-resolution 3-D imaging in a single flight. Since the antenna array of the swarm UAV 3-D LASAR is sparse, the compressed sensing (CS) algorithm is applied, whose reconstruction performance is closely related to the correlation coefficient of the sensing matrix. Hence, the signal model of swarm UAV 3-D LASAR is derived, and the expression of the sensing matrix is deduced. The sensing matrix design in this article aims at obtaining satisfactory reconstruction performance by optimizing the distribution of the antenna elements, which directly influences the correlation coefficient of the sensing matrix. Considering the limitation of the practical conditions, the sensing matrix design problem is modeled as a constrained integer programming problem. Finally, a sensing matrix design method based on discrete constrained differential evolution (DCDE) algorithm is proposed to solve the optimization problem. Experimental results demonstrate the effectiveness and superiority of the proposed method.

A joint sparse recovery algorithm for coprime adjacent array synthetic aperture radar 3D sparse imaging

ABSTRACT In the linear array synthetic aperture radar (LASAR) three-dimensional (3D) imaging, the spacing between adjacent elements in the uniform linear array (ULA) must satisfy the Nyquist sampling theorem to avoid the grating lobes, which makes the number of elements in the ULA very large. To reduce the elements in the ULA, the coprime adjacent array (CAA) with the same aperture length as the ULA is used when conducting LASAR 3D sparse imaging by compressed sensing (CS) algorithms. However, due to the increased autocorrelation coefficient of the measurement matrix, there exists grating lobes interference in the CAA-SAR imaging results. To solve this problem, we propose a joint sparse recovery (JSR) algorithm for CAA-SAR 3D sparse imaging. Firstly, we conduct sparse imaging on the CAA and its two subarrays, respectively. Secondly, the imaging results of the CAA and its two subarrays are performed image segmentation by the OTSU algorithm to extract their target-areas’ imaging results. Finally, we perform the image fusion by the wavelet transform on the target-areas’ imaging results to obtain the final imaging results. Both simulation and experimental results indicate that the imaging quality and computational efficiency of the JSR algorithm are higher than the random sampling array (RSA) and CAA under the same number of array elements. Besides, under the same aperture length, the JSR algorithm improves the computational efficiency than the ULA without imaging-quality loss.

Fast Bayesian Compressed Sensing Algorithm via Relevance Vector Machine for LASAR 3D Imaging

Because of the three-dimensional (3D) imaging scene’s sparsity, compressed sensing (CS) algorithms can be used for linear array synthetic aperture radar (LASAR) 3D sparse imaging. CS algorithms usually achieve high-quality sparse imaging at the expense of computational efficiency. To solve this problem, a fast Bayesian compressed sensing algorithm via relevance vector machine (FBCS–RVM) is proposed in this paper. The proposed method calculates the maximum marginal likelihood function under the framework of the RVM to obtain the optimal hyper-parameters; the scattering units corresponding to the non-zero optimal hyper-parameters are extracted as the target-areas in the imaging scene. Then, based on the target-areas, we simplify the measurement matrix and conduct sparse imaging. In addition, under low signal to noise ratio (SNR), low sampling rate, or high sparsity, the target-areas cannot always be extracted accurately, which probably contain several elements whose scattering coefficients are too small and closer to 0 compared to other elements. Those elements probably make the diagonal matrix singular and irreversible; the scattering coefficients cannot be estimated correctly. To solve this problem, the inverse matrix of the singular matrix is replaced with the generalized inverse matrix obtained by the truncated singular value decomposition (TSVD) algorithm to estimate the scattering coefficients correctly. Based on the rank of the singular matrix, those elements with small scattering coefficients are extracted and eliminated to obtain more accurate target-areas. Both simulation and experimental results show that the proposed method can improve the computational efficiency and imaging quality of LASAR 3D imaging compared with the state-of-the-art CS-based methods.

A Novel Downward‐Looking Linear Array SAR Imaging Method Based on Multiple Measurement Vector Model with L2,1‐Norm

Downward‐looking linear array synthetic aperture radar (DLLA SAR) is a kind of three‐dimensional (3‐D) radar imaging system. To obtain the superresolution along the crosstrack direction of DLLA SAR, the sparse regularization models with single measurement vector (SMV) have been widely applied. However, the robustness of the sparse regularization models with SMV is unsatisfactory, especially in the low signal‐to‐noise rate (SNR) environment. To solve this problem, we proposed a novel imaging method for DLLA SAR based on the multiple measurement vector (MMV) model with L2,1‐norm. At first, we exchange the processing order between the along‐track (AT) domain and the crosstrack (CT) domain to keep the same sparse structure of the signal in the crosstrack domain so that we can establish the imaging problem as a sparse regularization model based on the MMV model. Moreover, the mixed L2,1‐norm is introduced into the regularization term of the MMV model. Finally, the modified orthogonal matching pursuit (OMP) algorithm is designed for the MMV model with the L2,1‐norm. The simulations verify that the proposed method has better performance in the lower SNR environment and requires lower computation compared with the conventional methods.

An efficient and accurate three-dimensional imaging algorithm for forward-looking linear-array sar with constant acceleration based on FrFT

Linear-array synthetic aperture radar can break through the limitations of traditional SAR on 3-D forward looking imaging, which continues to attract the worldwide attention, especially on 3-D topographic mapping and aircraft blind landing. To overcome the large range migration and strong space-variant characteristic caused by the uniformly accelerated SAR platform, a new 3-D fractional chirp scaling algorithm (FrCSA) for forward looking linear-array SAR with constant acceleration is proposed in this paper. Based on the novel geometry configuration and the equivalent hyperbolic signal model, a chirp scaling operation is employed to compensate the range dependent range cell migration (RCM). Meanwhile, the FrFT tool is introduced to achieve much more accurate focusing. The 3-D imaging results of 3 × 3 × 3 array point scatterers indicate that the proposed method can achieve better focusing capabilities, greater peak side-lobe ratio (PSLR) and integrated side-lobe ratio (ISLR) comparing with the traditional CS algorithm based on FFT.

Multi‐function array SAR system on a spaceborne dual platform

This study proposes a sparse linear array synthetic aperture radar (LASAR) on a spaceborne dual platform. The transmitting elements are placed at the LASAR tips that form a satellite's dual platform, and the receiving elements are placed on the large deformation composite pine which is between the satellite's dual platform. Based on the principle of phase centre of approximation and multiple input multiple output, LASAR with the sparse array could obtain a high-resolution imaging in the cross-along direction, which is crucial to a three-dimensional SAR system. Furthermore, the LASAR system has different modes, such as interferometry and ground moving target indication.

SAR 3D sparse imaging based on CLA

A novel method for synthetic aperture radar (SAR) three-dimensional (3D) sparse imaging based on a coprime linear array (CLA) is proposed. To reduce the geometric resolution loss caused by under-sampled sparse SAR, a jointed sparse imaging approach is used. In this scheme, the coprime sampled data of CLA is separately processed via the iterative reweight least-squares approach, and their recovered results are combined to cancel the false targets and grating-lobes to improve the imaging quality. Both simulated and experimented results demonstrate the effectiveness of the method. It shows that the exploiting of CLA and sparse recovery can significantly reduce the linear array antenna amount and the geometric resolution loss compared with the conventional uniform linear array SAR.

A Fast Sparse Recovery Algorithm via Resolution Approximation for LASAR 3D Imaging

Compressed sensing (CS) algorithms are used for linear array synthetic aperture radar (LASAR) three-dimensional (3D) imaging. However, it is difficult to obtain imaging results with both high computational efficiency and promising imaging quality. Because of the high-dimensional matrix-operations, the computational complexity of several CS algorithms is huge such as the iterative adaptive approach (IAA), bayesian compressed sensing (BCS), and sparsity bayesian recovery via iterative minimum (SBRIM) algorithm. Besides, the greedy pursuit algorithms such as the orthogonal matching pursuit (OMP) algorithm cannot acquire ideal imaging results on account of the preset sparsity of the imaging scene. To solve the problem, we present a fast sparse recovery algorithm via resolution approximation (FSRARA) in this paper. Firstly, the whole imaging scene is divided into 3D scattering units with large spacing, and SBRIM algorithm is used to obtain its low-resolution imaging results quickly. Secondly, the low-resolution imaging results are conducted image segmentation by the fuzzy c-means (FCM) clustering algorithm to extract the possible targets' areas coarsely. Then we re-divide the imaging scene by higher imaging resolution and extract the possible targets' areas according to the coarsely possible targets' areas. FSRARA achieves improved computational efficiency with low-dimensional matrix-operations on the possible targets' areas instead of the high-dimensional one on the whole imaging scene. Meanwhile, FSRARA performs better in suppressing the false targets and sidelobe interference and improves the imaging quality than the SBRIM algorithm. Simulation and experimental results prove that FSRARA improves the computational efficiency by hundreds of times at most than SBRIM algorithm and its computational efficiency is higher than smoothed $L_{0} $ norm (SL0), IAA, and BCS algorithm. Besides, FSRARA improves the imaging quality compared with OMP, IAA, SL0, BCS, and SBRIM algorithms.

Focusing forward-looking linear-array synthetic aperture radar with high speed based on keystone transform and modified nonlinear chirp scaling algorithm

For forward-looking linear-array synthetic aperture radar with high speed, the traditional algorithm neglects its high speed, which leads to poor focusing imaging quality. Due to the high speed movement of the platform, range cell migration (RCM) and two-dimensional spatial variation are more serious. To overcome this problem, an equivalent range model is proposed, which takes the platform’s high speed into consideration. Based on this model, linear range walk correction and second-order keystone transform method are used to eliminate the RCM and range-azimuth coupling, and then a modified nonlinear chirp scaling algorithm based on a circle model is used to improve the focus quality of edge targets. Finally, simulation results are presented to confirm the efficiency of the proposed algorithm.

Azimuth Location Deambiguity for SAR Ground Moving Targets via Coprime Adjacent Arrays

The ground moving target's radial velocity estimation based on the interferometric phase in a multichannel synthetic aperture radar (SAR) system suffers from 2π modulo folding, resulting in the target's azimuth location ambiguity in the SAR image. To address this problem, a novel coprime adjacent arrays SAR (CAA-SAR) is proposed in this paper. The two sparse uniform subarrays constituting the CAA are arranged adjacently with a conjunct element, then a virtual array can be obtained with much more virtual elements and smaller element spacing, which will help to solve the azimuth location ambiguity. After ground clutter suppression, multiple pixels’ samplings are utilized based on the MUSIC algorithm for estimating radial velocity as well as azimuth shift by exploiting all virtual elements of CAA-SAR. Compared with the existing nonuniform linear array SAR method based on Chinese remainder theorem, the CAA-SAR can obtain a better accuracy with the same number of elements in a larger sparse configuration, or use fewer elements to obtain an approximate accuracy in almost the same physical aperture. Compared with the coprime arrays SAR, the CAA-SAR has a better accuracy due to its larger number of unique virtual elements and longer physical aperture. Finally, some results of numerical experiments are provided to demonstrate the effectiveness of the proposed method.

A Chirp Scaling Algorithm for Forward-Looking Linear-Array SAR With Constant Acceleration

For forward-looking linear-array synthetic aperture radar (FLLA-SAR) with constant acceleration, the conventional hyperbolic range model is incorrect, and the range-dependent range cell migration (RCM) cannot be ignored any more. Hence, the traditional chirp scaling (CS) algorithm based on the hyperbolic range model also cannot be used. To overcome these problems, a modified range model for the FLLA-SAR which has taken the platform’s acceleration into consideration is proposed in this letter. Based on the model, an improved CS method is proposed for FLLA-SAR to eliminate the space-variant characteristic of the RCM. Simulation results are presented to validate the range model and the proposed method.

An efficient NLCS algorithm for maneuvering forward-looking linear array SAR with constant acceleration

Forward-looking linear-array synthetic aperture radar (FLLA-SAR), which can overcome the deficiency of the traditional SAR on forward-looking imaging, continues to gain in significance due to the various applications, such as unmanned aerial vehicle (UAV) reconnaissance. To compensate the space-variant characteristic of along-track frequency modulation (FM) rate caused by the high speed maneuvering UAV, an efficient nonlinear chirp scaling (NLCS) algorithm is proposed in this paper. Based on the analysis of novel geometric configuration and the introduction of NLCS operation, the linear-array UAV SAR can reconstruct the 2-D image of the scout area. Finally, the validation of the proposed algorithm is done by exploiting the simulated data based on 3 × 3 array point targets and an airplane scattering model.

DEM Estimation for LASAR Based on Variational Model

This paper discusses the digital elevation model (DEM) estimation problem for the linear array synthetic aperture radar based on the variational model. Compared with the sparse recovery model, the one-to-one mapping between the horizontal grid nodes and the elevations is preserved explicitly, which is important for the topographic surveying and mapping mission. During the research, we find that since the mean square error criterion is insensitive to the amount of the elevation offsets, the numerical method by solving the Euler-Lagrange equation is unreliable and the global optimization method is necessary to solve the variational problem. With the ambiguity function localization and the sliding-window architecture, the global optimal path can be obtained by solving a series of local optimization problems provided that the observation matrix is row full rank. Furthermore, the local optimization problem can be relaxed as a sparse recovery problem and can be solved by a modified orthogonal matching pursuit (OMP) method (named as Var-OMP), whose computational cost is acceptable for the actual data processing. By a series of numerical experiments, we show that the performance of Var-OMP is influenced by both the resolution enhancement factor (L) and the signal-to-noise ratio (SNR). The larger the SNR is, the better the performance is; the smaller L is, the more stable and faster the Var-OMP algorithm is. Compared with the sparse recovery methods, the variational model and the Var-OMP algorithm are more suitable for the DEM estimation application in the face of all kinds of terrains.

Plane-Wave Synthesis and RCS Extraction via 3-D Linear Array SAR

This letter presents an improved back-projection (BP) technique for far-field radar cross section (RCS) feature extraction from near-field measurement. The presented technique can synthesize a plane-wave response from a 2-D near-field planar scanner and obtain a 3-D scattering coefficient image. Due to the 3-D resolving power, it can spatially extract different parts of a complex object, or target’s scattering coefficient from the whole image which may include environment noise such as ground and support. From the 3-D scattering coefficient image, far-field RCS can be obtained as a function of direction and frequency. Simulations of RCS feature extraction for three squares and a 3-D complex-shaped electric-large car model are presented to validate the improved BP method.

Two-dimensional Fast ESPRIT Algorithm for Linear Array SAR Imaging

Two-dimensional Fast ESPRIT Algorithm for Linear Array SAR Imaging

Statistical Analysis of the Effects of Virtual Element Position Errors on Airborne Down-Looking LASAR 3-D Imaging

In order to achieve 3-D imaging with an airborne down-looking linear-array synthetic aperture radar (LASAR), a uniform virtual antenna array may be obtained by aperture synthesis of the cross-track sparse multiple-input-multiple-output array. However, the actual 3-D imaging quality is unavoidably degraded by errors in the virtual element position. In this letter, we investigate the effects of these errors on the forms and the degrees of image quality degradation by decomposing the error-related stochastic processes via an orthogonal transform based on discrete Legendre polynomials. It should be noted that these analyses are helpful for designing a LASAR system and providing a reference for specifying the requisite precision of measurement devices and calibration methods. Finally, we briefly consider the use of calibration methods to eliminate the effects of errors.

Efficient Pseudopolar Format Algorithm for Down-Looking Linear-Array SAR 3-D Imaging

In this letter, a novel 3-D imaging algorithm for down-looking linear-array synthetic aperture radar is presented. The usual algorithms involve either time-consuming interpolations or huge oversampling operations, which adds huge burden to the image formation processor. The proposed algorithm, in contrast, is not only accurate because little approximation has been made but also quite efficient because of two major endeavors that we have made: First, a novel 3-D pseudopolar domain is introduced for the focused data to avoid any oversampling and to make it possible to formulate the image formation process as an interpolation-free image series expansion, and second, convergence acceleration theory in computational mathematics is introduced to accelerate the convergence of the image series expansion. The 3-D imaging capability is evaluated, and the validation of the proposed algorithm is done by exploiting simulated data.

RESOLUTION ENHANCEMENT FOR LASAR 3D IMAGING VIA ℓ<sub>1</sub> REGULARIZATION AND SVA

Linear array SAR (LASAR) has been attracting more and more attention for its capability of obtaining three dimensional (3D) resolutions. However, the low resolution in cross track (CT) direction limited by the length of its linear antenna array has become the bottleneck of its practical applications. To overcome this problem, we present a novel algorithm based on sparse reconstruction (SR) to improve the resolution in CT direction. First, it establishes a 1D real-valued sparse model for LASAR, which deals with the 3D image column by column along CT direction in each equi-range slice. This enables it to handle large scenes. Second, it employs the spatially variant apodization (SVA) to filter bases of the measurement matrix. As a result, the cross coherence gets suppressed as well, and it is helpful to improve the performance of sparse reconstruction algorithms (SRAs). Third, we propose the resolution enhancement ability (REA), which provides a new idea to evaluate how many times the resolution could be improved. Experimental results validate that when the signal to noise ratio (SNR) is 30 dB, LASAR could usually obtain 2 times of resolution improvement in CT direction, while the proposed method further improves the REA by a factor about 2.5. Moreover, the 3D surface terrain simulation shows a great improvement for the digital elevation map (DEM) in resolution enhancement.

SPARSE AUTOFOCUS RECOVERY FOR UNDER-SAMPLED LINEAR ARRAY SAR 3-D IMAGING

Linear array synthetic aperture radar (LASAR) is a promising radar 3-D imaging technique. In this paper, we address the problem of sparse recovery of LASAR image from under-sampled and phase errors interrupted echo data. It is shown that the unknown LASAR image and the nuisance phase errors can be constructed as a bilinear measurement model, and then the under-sampled LASAR imaging with phase errors can be mathematically transferred into sparse signal recovery by solving an ill-conditioned constant modulus linear program (ICCMLP) problem. Exploiting the prior sparse spatial feature of the observed targets, a new super-resolution sparse autofocus recovery algorithm is proposed for under-sampled LASAR 3-D imaging. The algorithm is an iterative minimize estimation procedure, wherein it converts the ICCMLP into two independent convex optimal problems, and joints '1-norm reweights least square regularization and semi-deflnite relax technique to flnd the optimal solutions. Simulated and experimental results conflrm that the proposed method outperforms the classical autofocus techniques in under-sampled LASAR imaging.