Frequency Domain Imaging Algorithm Research Articles

An efficient sub-aperture millimeter-wave imaging technique based on boundary-type MIMO array

Millimeter-wave (MMW) 3-D imaging based on multiple-input-multiple-output (MIMO) radar has been widely studied due to its unique advantages in human security screening. However, more research has been done on the use of scanning 1-D MIMO array and the fast imaging methods that match them. This limits the rate of data acquisition and imaging speed to some extent. It is necessary to study frame rate imaging system as well as efficient imaging methods. In this article, a boundary-type MIMO array is designed, based on which an efficient frequency-domain imaging algorithm with sub-aperture is proposed. The proposed algorithm solves the target reflectivity function by dividing the uniform array into two sub-apertures and solving the echo signals of each sub-aperture separately. The final target reflectivity function is obtained by superposing all the solutions. Compared with the advanced RMA, FSA and FωK algorithms, the proposed sub-aperture frequency-domain imaging algorithm (SFA) does not require a large amount of zero-padding to satisfy the requirements of fast Fourier transform (FFT) in all dimensions. It greatly improves the speed of imaging and saves the space required for computation. We derive the theoretical formulation of SFA applied to MIMO array and analyze its computational complexity and phase error. Simulation and experiment verify the efficiency of the proposed SFA.

Frequency-Domain Imaging Algorithm for SA-BiSAR Based on Azimuth Dealiasing

Frequency-Domain Imaging Algorithm for SA-BiSAR Based on Azimuth Dealiasing

Frequency Domain Imaging Algorithms for Short-Range Synthetic Aperture Radar

In order to achieve miniaturization, short-range radar (SRR) generally adopts millimeter-wave (MMW) radar with a frequency-modulated continuous-wave (FMCW) system, which may make the stop–go–stop assumption in traditional synthetic aperture radar (SAR) imaging algorithms invalid. In addition, in order to observe a large enough area, SRR often needs a wide radar beam, which may cause serious range–azimuth coupling when using SRR for SAR imaging. The above two problems may make the traditional SAR imaging algorithm invalid in SRR SAR imaging. Taking the SRR SAR imaging application into account, traditional frequency domain SAR imaging algorithms are analyzed and improved in this paper. Firstly, the intra-pulse motion (IPM) caused by the FMCW system and the two-dimensional coupling (TDC) in the case of a wide beam are analyzed. Subsequently, the applicability of the range Doppler algorithm (RDA), the frequency scaling algorithm (FSA) and the range migration algorithm (RMA) for SRR SAR is analyzed. Then, improvement measures are put forward to address the aliasing and folding phenomena caused by the wide-beam problem in the FSA and RMA, respectively. Finally, the effectiveness of the proposed algorithm is verified using simulation data and real measured data collected using an MMW radar fixed on a slide rail.

An Efficient MMW 3-D Imaging Algorithm for Near-Field MIMO-SAR With Nonuniform Transmitting Array

In this letter, an efficient millimeter-wave (MMW) frequency-domain imaging algorithm is presented for 3-D object reconstruction of the near-field multiple-input–multiple-output synthetic aperture radar (MIMO-SAR) with nonuniform transmitting array. For each single-input–multiple-output (SIMO) case of the MIMO-SAR setup, the precise spectral echo expression is derived by spherical-wave decomposition and fast Fourier transform (FFT) operations. To obtain the linear phase in range direction, the multiorder approximation theory is employed to expand the coupling phases, and thus the target subimage can be reconstructed by utilizing phase compensation, central wavenumber approximation, and inverse FFT. Finally, the fully focused 3-D image for MIMO setup will be realized through accumulating all the SIMO subimages. Compared with the existing representative algorithms, our method avoids complicated interpolation and achieves high-quality fast imaging with only matrix multiplication and a small amount of iteration operations. The experimental results validate the effectiveness of the proposed algorithm.

An improved equivalent acceleration imaging approach for spaceborne sliding spotlight SAR

The traditional hyperbolic range equation model will produce large errors in the spaceborne sliding spotlight synthetic aperture radar with large azimuth time. Although the equivalent acceleration range model (EARM) can deal with the problem of large azimuth scenes well, the interpolation steps from azimuth resampling make the computational burden of algorithm very huge. In response to this problem, this paper improves EARM by dividing the range model into two parts: residual terms of azimuth time and equivalent range expression. The frequency domain imaging algorithm designed for the new range model omits the interpolation step of azimuth resampling. The simulation experiments verify the efficiency and validity of the proposed methodology.

An Efficient mmW Frequency-Domain Imaging Algorithm for Near-Field Scanning 1-D SIMO/MIMO Array

In recent years, millimeter-wave (mmW) 3D imaging technology for scanning 1D single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) array has been extensively studied due to its unique advantages in near-field applications. However, current imaging algorithms for this kind of scheme are not satisfactory, either of low quality since irrational approximations are introduced, or too slow as the back projection method is employed. In this paper, an efficient frequency-domain imaging algorithm is developed to fetch up these shortages. The precise spectral expression of the echo signal within SIMO data is derived through spherical-wave decomposition and fast Fourier transform (FFT) operations. By properly approximating the nonlinear phase, the wavefront curvature is compensated after employing a 1D Stolt interpolation, and then the reflectivity map of the target can be obtained through several multiplications and inverse FFT operations. Image reconstruction for a MIMO array can be realized by coherently summing up all the SIMO focusing results. Both simulation analysis and experimental results demonstrate the effectiveness of the proposed algorithm in imaging quality and computational efficiency.

Airborne Downward-Looking Sparse Linear Array 3-D SAR Imaging via 2-D Adaptive Iterative Reweighted Atomic Norm Minimization

Airborne downward-looking sparse linear array 3-D synthetic aperture radar (DLSLA 3-D SAR) usually uses a sparse and nonuniform linear array that often does not satisfy the Nyquist sampling theorem. Therefore, the cross-track dimensional imaging will fail with the traditional 3-D frequency-domain imaging algorithms. Several grid-based sparse reconstruction (GB-SR) algorithms have been presented to solve this issue. However, they assume that the scatterers are located on the discretized grids; otherwise, the off-grid effect or basis mismatch problem will occur. To address this issue, we propose a novel hyperparameter-free gridless-based sparse reconstruction (GL-SR) algorithm (i.e., 2-D adaptive iterative reweighted atomic norm minimization algorithm called 2-D IRAN) by a combination of the optimal covariance fitting criterion and atomic norm. It is a generalized model, while the other GL-SR algorithms (e.g., GLS, RGLS, and RAM) can be interpreted as the variants of 2-D IRAN. Moreover, since the interior-point method employed in toolboxes has high computational efficiency only for the small-scale matrix optimization problem, a fast implementation of 2-D IRAN via alternating direction method of multipliers (ADMM) is presented for the large-scale matrix optimization problem. Finally, we carry out extensive numerical simulations to demonstrate the advantages and effectiveness of 2-D IRAN for DLSLA 3-D SAR imaging based on the complex 3-D ship model and 3-D distributed scenario.

A 2-D Frequency-Domain Imaging Algorithm for Ground-Based SFCW-ArcSAR

Arc-synthetic aperture radar (ArcSAR) can observe the surrounding ground objects at 360°, with the advantages of a wide imaging range and constant azimuth angular resolution. In this article, based on the stepped frequency continuous wave (SFCW), fourth-order Taylor expansion, and the series-inversion method, the accurate phase expression of the 2-D spectrum is derived, and then, the 2-D frequency-domain imaging algorithm (2-D-FDA) for ArcSAR is realized. In the simulation part, the imaging results of 2-D-FDA are compared with the backprojection algorithm (BPA) and Liao’s method, which is the reference for 2-D-FDA. The simulation results show that the 2-D-FDA is more applicable to process the data obtained from the antenna with the beamwidth larger than 70°. The SFCW-ArcSAR system consists of a vector network analyzer (VNA), a rotating platform, two antennas, and a control computer. Then, the system is used for the outdoor experiment. The experimental results of the corner reflector show that the point target analysis of 2-D-FDA is consistent with those of the BPA and theory. Under the system parameters in this article, the measured azimuth angular resolution is 0.0177 radian, the peak sidelobe ratio (PSLR) in the range direction is −12.46 dB, and the range resolution is 0.48 m on the ground-range plane. The imaging results of the real scenario processed by BPA and 2-D-FDA are consistent, and the ArcSAR image agrees with the optical image of the experimental scene. The effectiveness and correctness of the 2-D-FDA are verified by simulation and experiment.

Hybrid Approaches in Microwave Imaging Using Quantitative Time- and Frequency-Domain Algorithms

In this work we propose two hybrid time-and frequency-domain microwave imagingschemes aimed to improve time-to-solution of quantitative time-domain imaging algorithms and image resolution of quantitative frequency-domain imaging algorithms. The proposed hybrid methods combine discontinuous Galerkin method (DGM) implementations of the time-domain (TD) forward-backward time-stepping (FBTS) algorithm and the frequency-domain (FD) contrast source inversion (CSI) or Gauss Newton Inversion (GNI). Simply put, an initial inversion in one domain (time or frequency) is used as prior information for the other. These schemes, referred to as FD-TD when FD prior is used in a TD algorithm, and TD-FD when TD prior is used in a FD algorithm, are applied to experimental and synthetic data. The results of the hybrid imaging approaches manifest an appreciable improvement relative to the stand-alone of FD and TD algorithms. Specifically, this study demonstrates that low-resolution frequency-domain prior information improves TD convergence. Additionally, we show that early-iteration time-domain solutions improves FD algorithm performance. We hope that these hybridization techniques pave the way for future investigations of optimal strategies for combining TD and FD schemes.

Noninterpolated frequency-domain imaging algorithm for near-field OS-BiSAR in the millimeter-wave band.

This paper presents a frequency-domain imaging algorithm for near-field one-stationary bistatic synthetic aperture radar (OS-BiSAR) in the millimeter-wave (mmW) band. During the image reconstruction process, the interpolation procedure introduced by traditional fast imaging algorithm is avoided. By appropriately decomposing and approximating the nonlinear phase in frequency-domain echo, only multiplication and fast Fourier transform operations are carried out to achieve the lowest computational load. In addition, this method takes the propagation attenuation into consideration, which leads to a better imaging quality than the improved range migration algorithm for distant targets. Both simulation and measurement results validate the effectiveness of the proposed method on high-precision real-time imaging.

Frequency-domain imaging algorithm based on time-frequency-domain perturbation for maneuvering highly squinted FMCW-SAR

Serious range-azimuth coupling and spatial variability of imaging parameters limit the focusing depth of conventional synthetic aperture radar (SAR) imaging methods for maneuvering high-squint frequency modulated continuous wave -SAR. To expand the effective imaging area, an imaging method based on time-frequency-domain perturbation is proposed. First, the slant range model based on data recording parameters is optimized to remove Doppler frequency shift and secondary coupling caused by in-pulse movement. Then, the spatial variability of range cell migration (RCM) is corrected by constructing the time-domain perturbation function to achieve unified RCM correction. In azimuth processing, the linear spatial variability of the first- to third-order Doppler parameters and the second-order space variation of azimuth modulation frequency are removed by the time-frequency perturbation filtering functions. The focus quality of the nonscene center is effectively improved. Finally, the effectiveness of the algorithm is verified by both the simulation data and the measured data.

Geolocation Error Transfer Model and Trajectory Calibration Method for Airborne SAR Considering Motion Compensation Residual Error

Airborne Synthetic Aperture Radar (SAR) location error is affected by the position/speed measurement error of the aircraft, system time error, etc., and also related to the residual error of motion compensation. However, the existing airborne SAR location model rarely considers the effect of residual motion error. Considering that motion and trajectory measurement errors are common in practice, this paper derives a location error transfer model of an airborne SAR image based on the motion compensation and frequency-domain imaging algorithms. The proposed model clarifies the influence of trajectory measurement error on location deviation when residual motion error exists and provides a method of error calibration measurement. The simulation experiments validate the correctness of the proposed location error transfer model. The present method obtains a more accurate error calibration measurement result than the location error model that does not consider the residual motion error, proving the superiority of the proposed model.

New slant range model and azimuth perturbation resampling based high-squint maneuvering platform SAR imaging

Strong spatial variance of the imaging parameters and serious geometric distortion of the image are induced by the acceleration and vertical velocity in a high-squint synthetic aperture radar (SAR) mounted on maneuvering platforms. In this paper, a frequency-domain imaging algorithm is proposed based on a novel slant range model and azimuth perturbation resampling. First, a novel slant range model is presented for mitigating the geometric distortion according to the equal squint angle curve on the ground surface. Second, the correction of azimuth-dependent range cell migration (RCM) is achieved by introducing a high-order time-domain perturbation function. Third, an azimuth perturbation resampling method is proposed for azimuth compression. The azimuth resampling and the time-domain perturbation are used for correcting first-order and high-order azimuthal spatial-variant components, respectively. Experimental results illustrate that the proposed algorithm can improve the focusing quality and the geometric distortion correction accuracy of the imaging scene effectively.

Efficient 3D Image Reconstruction of Airborne TomoSAR Based on Back Projection and Improved Adaptive ISTA

Airborne SAR tomography (TomoSAR) 3D image reconstruction can be realized with combination of 2D imaging algorithms and compressed sensing (CS) algorithms. However, most typical CS algorithms cannot achieve a balance between algorithm efficiency and 3D reconstruction accuracy. Due to difficulties in flight path control of airborne SAR, it is hard to realize registration of SAR images with frequency-domain imaging algorithms because of time-varying baseline. To address these problems, an efficient 3D image reconstruction method for airborne TomoSAR based on back projection (BP) algorithm and improved adaptive iterative shrinkage-thresholding algorithm (IA-ISTA) is proposed. First, 2D images are achieved with BP algorithm on the ground plane. After registration of SAR images, 3D image reconstruction results in the elevation direction are realized with IA-ISTA. Selection criterion of IA-ISTA parameters are given in this paper. At last, final 3D image reconstruction results are achieved after geometrical transformation based on geometric relationship. Both simulated data and measured data of a P-band airborne TomoSAR system are used. 3D image reconstruction results show that the proposed method outperforms traditional methods regarding efficiency and accuracy, which proves the validity and practicality of the proposed method.

A Novel Airborne Dual-Antenna InSAR Calibration Method for Backprojection Imaging Model

The interferometric synthetic aperture radar (InSAR) elevation inversion method based on the backprojection (BP) imaging model simplifies the interferometric processing chain where image registration and phase unwrapping are not required. Meanwhile, BP algorithm is suitable for radar with different imaging modes and geometry. However, the existing calibration methods are all aimed at traditional InSAR which adopts frequency domain imaging algorithm, but the calibration method for backprojection InSAR elevation inversion model has not been published. In this paper, we propose a novel InSAR calibration method which combines Fast Fourier Transform (FFT) estimation method with sensitivity equation method based on backprojection imaging model. FFT is used to process the interferometric phase which has removed the terrain phase of external digital elevation model (DEM) under BP imaging, and the estimation of interferometric parameters is realized through the phase fringe frequency. In the calibration method based on sensitivity equations, the deviations of interferometric parameters are calculated by solving sensitivity equations according to the three-dimensional information of ground control points. FFT estimation method not only generates the initial baseline parameters for sensitivity equation method, which is conducive to obtaining the global optimal solution, but also separates the calibration of phase offset and baseline parameters, which makes it possible to minimize the condition number of sensitivity matrix in sensitivity equation method. Finally, we obtain the calibrated interferometric parameters through iteration of sensitivity equation method and realize high accuracy DEM inversion. Both simulation experiment and airborne dual-antenna InSAR data processing are performed to verify the effectiveness of this method.

Processing of Bistatic SAR Data With Nonlinear Trajectory Using a Controlled-SVD Algorithm

The nonlinear trajectory and bistatic characteristics of general bistatic synthetic aperture radar (SAR) can cause severe two-dimensional space-variance in the echo signal, and therefore it is difficult to focus the echo signal directly using the traditional frequency-domain imaging algorithm based on the assumption of azimuth translational invariance. At present, the state-of-the-art nonlinear trajectory imaging algorithm is based on singular value decomposition (SVD), which has the problem that SVD may be not controlled, and thus may lead to a high imaging complexity or low imaging accuracy. Therefore, this article proposes a nonlinear trajectory SAR imaging algorithm based on controlled SVD (CSVD). First, the chirp scaling algorithm is used to correct the range space-variance, and then SVD is used to decompose the remaining azimuth space-variant phase, and the first two feature components after SVD are integrated to make them be represented by a new feature component. Finally, the new feature component is used for interpolation to correct the azimuth space-variance. The simulation results show that the proposed CSVD can further improve the image quality compared with SVD-Stolt.

A Comparison of Time-Domain and Frequency-Domain Microwave Imaging of Experimental Targets

An existing forward-backward time-stepping (FBTS) time-domain quantitative imaging algorithm is augmented with a discontinuous Galerkin method (DGM) forward solver. The resulting DGM-FBTS imaging algorithm is capable of solving the electromagnetic inverse scattering problem using high-order expansions of the fields and unknown target constitutives, decoupling the solution from the unstructured grid. DGM-FBTS provides a time-domain alternative to our previous development of flexible DGM-based frequency-domain imaging codes, and enables us to present a comparison of the performance of time-domain and frequency-domain imaging algorithms for synthetic and experimental targets. For experimental targets, a procedure for obtaining calibrated time-domain data from frequency-domain broadband VNA-collected data is explained and applied to a system with a reduced number of transmitters and receivers to highlight the potential benefits of time-domain methods. Results highlight the potential capabilities of time-domain experimental imaging using the same hardware configuration used to collect broadband frequency-domain measurements and suggest future work on hybrid frequency- and time-domain imaging algorithms and efforts to improve the computational performance of DGM-FBTS.

Frequency Domain Panoramic Imaging Algorithm for Ground-Based ArcSAR.

The ground-based arc-scanning synthetic aperture radar (ArcSAR) is capable of 360° scanning of the surroundings with the antenna fixed on a rotating arm. ArcSAR has much wider field of view when compared with conventional ground-based synthetic aperture radar (GBSAR) scanning on a linear rail. It has already been used in deformation monitoring applications. This paper mainly focuses on the accurate and fast imaging algorithms for ArcSAR. The curvature track makes the image focusing challenging and, in the classical frequency domain, fast imaging algorithms that are designed for linear rail SAR cannot be readily applied. This paper proposed an efficient frequency domain imaging algorithm for ArcSAR. The proposed algorithm takes advantage of the angular shift-invariant property of the ArcSAR signal, and it deduces the accurate matched filter in the angular-frequency domain, so panoramic images in polar coordinates with wide swath can be obtained at one time without segmenting strategy. When compared with existing ArcSAR frequency domain algorithms, the proposed algorithm is more accurate and efficient, because it has neither far range nor narrow beam antenna restrictions. The proposed method is validated by both simulation and real data. The results show that our algorithm brings the quality of image close to the time domain back-projection (BP) algorithm at a processing efficiency about two orders of magnitude better, and it has better image quality than the existing frequency domain Lee’s algorithm at a comparable processing speed.

An Improved Frequency-Domain Image Formation Algorithm for Mini-UAV-Based Forward-Looking Spotlight BiSAR Systems

Mini-unmanned aerial vehicle (UAV)-based bistatic forward-looking synthetic aperture radar (SAR) (mini-UAV-based BFSAR) is much more attractive than the monostatic one because of the flexibility of the system geometry selection as well as its simplicity of system operation, especially with the mini-UAV platform. However, the trajectory of the mini-UAV needs to be accurately modeled since it is very sensitive to the external environment, and the forward-looking configuration results in more severe spatial variance in image formation processing. In the paper, an improved frequency-domain imaging algorithm based on a very accurate slant range model is proposed for mini-UAV-based BFSAR with spotlight illumination. First, a more accurate slant range expression considering the motion characteristics of the UAV and bistatic spotlight configuration is re-derived. Second, a new range nonlinear chirp scaling (NLCS) operator was derived based on the accurate bistatic slant range model. Third, an improved azimuth NLCS operator in the Doppler frequency domain was established for the spotlight illumination of the transmitter and receiver in mini-UAV based BFSAR systems. Finally, the proposed algorithm is validated by both simulations and real datasets.

Geosynchronous Spaceborne–Airborne Bistatic SAR Data Focusing Using a Novel Range Model Based on One-Stationary Equivalence

Geosynchronous spaceborne-airborne bistatic synthetic aperture radar (GEO-SA-BiSAR) can achieve high-resolution Earth observation with superior system flexibility and efficiency, which offers huge potential for advanced SAR applications. In this article, the echo characteristics of GEO-SA-BiSAR are analyzed in detail, including range history, the Doppler parameters, and spatial variance. The distinct features of GEO-SAR and airborne receiver result in the failure of the traditional bistatic SAR range model and imaging methods. In order to deal with these problems and achieve high-precision data focusing on GEO-SA-BiSAR, this article first proposes a novel range model based on one-stationary equivalence (RMOSE) to accommodate the distinctiveness of the GEO-SA-BiSAR echo, which changes with orbit positions of GEO transmitter. Then, a 2-D frequency-domain imaging algorithm is put forward based on RMOSE, which solves the problem of the 2-D spatial variance of GEO-SA-BiSAR. Finally, simulations are presented to demonstrate the effectiveness of the proposed range model and algorithm.