Fast Factorized Back-projection Research Articles

A Fast Factorized Back-Projection Algorithm Based on Range Block Division for Stripmap SAR

Fast factorized back-projection (FFBP) is a classical fast time-domain technique that has garnered significant success in spotlight synthetic aperture radar (SAR) signal processing. The algorithm’s efficiency has been extended to stripmap SAR through integral aperture determination and full-aperture data block processing while retaining its computational efficiency. However, the above method is only operated in the azimuth direction, and the computing efficiency needs to be urgently improved in the actual processing process. This paper proposes a fast factorized back-projection algorithm for stripmap SAR imaging based on range block division. The echo data are divided into multiple subblocks in the range direction, and FFBP processing is applied separately to each full-aperture subblock, further enhancing computational efficiency. The paper analyzes the algorithm’s principles, underscores the necessity of integral aperture determination and full-aperture data block processing, provides specific implementation steps, and applies the algorithm to point target simulation and experimental data from a vehicle-mounted ice radar. The experiments validate the algorithm’s efficiency in stripmap SAR imaging.

A Pulse-by-Pulse Doppler Ambiguity Resolving Algorithm for FLMC-SAR Imaging Based on Fast Factorized Back-Projection

A Pulse-by-Pulse Doppler Ambiguity Resolving Algorithm for FLMC-SAR Imaging Based on Fast Factorized Back-Projection

MuA-SAR Fast Imaging Based on UCFFBP Algorithm with Multi-Level Regional Attention Strategy

Multistatic airborne SAR (MuA-SAR) benefits from the ability to flexibly adjust the positions of multiple transmitters and receivers in space, which can shorten the synthetic aperture time to achieve the required resolution. To ensure both imaging efficiency and quality of different system spatial configurations and trajectories, the fast factorized back projection (FFBP) algorithm is proposed. However, if the FFBP algorithm based on polar coordinates is directly applied to the MuA-SAR system, the interpolation in the recursive fusion process will bring the problem of redundant calculations and error accumulation, leading to a sharp decrease in imaging efficiency and quality. In this paper, a unified Cartesian fast factorized back projection (UCFFBP) algorithm with a multi-level regional attention strategy is proposed for MuA-SAR fast imaging. First, a global Cartesian coordinate system (GCCS) is established. Through designing the rotation mapping matrix and phase compensation factor, data from different bistatic radar pairs can be processed coherently and efficiently. In addition, a multi-level regional attention strategy based on maximally stable extremal regions (MSER) is proposed. In the recursive fusion process, only the suspected target regions are paid more attention and segmented for coherent fusion at each fusion level, which further improves efficiency. The proposed UCFFBP algorithm ensures both the quality and efficiency of MuA-SAR imaging. Simulation experiments verified the effectiveness of the proposed algorithm.

A Novel Multistage Back Projection Fast Imaging Algorithm for Terahertz Video Synthetic Aperture Radar

Terahertz video synthetic aperture radar (THz-ViSAR) has tremendous research and application value due to its high resolution and high frame rate imaging benefits. However, it requires more efficient imaging algorithms. Thus, a novel multistage back projection fast imaging algorithm for the THz-ViSAR system is proposed in this paper to enable continuous playback of images like video. The radar echo data of the entire aperture is first divided into multiple sub-apertures, as with the fast-factorized back projection algorithm (FFBP). However, there are two improvements in sub-aperture imaging. On the one hand, the back projection algorithm (BPA) is replaced by the polar format algorithm (PFA) to improve the sub-aperture imaging efficiency. The imaging process, on the other hand, uses the global Cartesian coordinate system rather than the local polar coordinate system, and the wavenumber domain data of the full aperture are obtained step by step through simple splicing and fusion, avoiding the amount of two-dimensional (2D) interpolation operations required for local polar coordinate system transformation in FFBP. Finally, 2D interpolation for full-resolution images is carried out to image the ground object targets in the same coordinate system due to the geometric distortion caused by linear phase error (LPE) and the mismatch of coordinate systems in different imaging frames. The simulation experiments of point targets and surface targets both verify the effectiveness and superiority of the proposed algorithm. Under the same conditions, the running time of the proposed algorithm is only about 6% of FFBP, while the imaging quality is guaranteed.

Fast Factorized Backprojection Algorithm in Orthogonal Elliptical Coordinate System for Ocean Scenes Imaging Using Geosynchronous Spaceborne–Airborne VHF UWB Bistatic SAR

Geosynchronous (GEO) spaceborne–airborne very high-frequency ultra-wideband bistatic synthetic aperture radar (VHF UWB BiSAR) can conduct high-resolution and wide-swath imaging for ocean scenes. However, GEO spaceborne–airborne VHF UWB BiSAR imaging faces some challenges such as the geometric configuration, huge amount of echo data, serious range–azimuth coupling, large spatial variance, and complex motion error, which increases the difficulty of the high-efficiency and high-precision imaging. In this paper, we present an improved bistatic fast factorization backprojection (FFBP) algorithm for ocean scene imaging using the GEO satellite-unmanned aerial vehicle (GEO-UAV) VHF UWB BiSAR, which can solve the above issues with high efficiency and high precision. This method reconstructs the subimages in the orthogonal elliptical polar (OEP) coordinate system based on the GEO satellite and UAV trajectories as well as the location of the imaged scene, which can further reduce the computational burden. First, the imaging geometry and signal model of the GEO-UAV VHF UWB BiSAR are established, and the construction of the OEP coordinate system and the subaperture imaging method are proposed. Moreover, the Nyquist sampling requirements for the subimages in the OEP coordinate system are derived from the range error perspective, which can offer a near-optimum tradeoff between precision and efficiency. In addition, the superiority of the OEP coordinate system is analyzed, which demonstrates that the angular dimensional sampling rate of the subimages is significantly reduced. Finally, the implementation processes and computational burden of the proposed algorithm are provided, and the speed-up factor of the proposed FFBP algorithm compared with the BP algorithm is derived and discussed. Experimental results of ideal point targets and natural ocean scenes demonstrate the correctness and effectiveness of the proposed algorithm, which can achieve near-optimal imaging performance with a low computational burden.

A Comparison of Processing Schemes for Automotive MIMO SAR Imaging

Synthetic Aperture Radar (SAR) imaging is starting to play an essential role in the automotive industry. Its day and night sensing capability, fine resolution, and high flexibility are key aspects making SAR a very compelling instrument in this field. This paper describes and compares three algorithms used to combine low-resolution images acquired by a Multiple-Input Multiple-Output (MIMO) automotive radar to form an SAR image of the environment. The first is the well-known Fast Factorized Back-Projection (FFBP), which focuses the image in different stages. The second one will be called 3D2D, and it is a simple 3D interpolation used to extract the SAR image from the Range-Angle-Velocity (RAV) data cube. The third will be called Quick&Dirty (Q&D), and it is a fast alternative to the 3D2D scheme that exploits the same intuition. A rigorous mathematical description of each algorithm is derived, and their limits are addressed. We then provide simulated results assessing different interpolation kernels, proving which one performs better. A rough estimation of the number of operations proves that both algorithms can be deployed using a real-time implementation. Finally, we will present some experimental results based on open road campaign data acquired using an eight-channel MIMO radar at 77 GHz, considering the case of a forward-looking geometry.

The Adaptive Streaming SAR Back-Projection Algorithm Based on Half-Precision in GPU

The back-projection (BP) algorithm is completely accurate in the imaging principle, but the computational complexity is extremely high. The single-precision arithmetic used in the traditional graphics processing unit (GPU) acceleration scheme has low throughput and its usage of the video memory is large. An adaptive asynchronous streaming scheme for the BP algorithm based on half-precision is proposed in this study, and then it is extended to the fast back-projection (FBP) algorithm. In this scheme, the adaptive loss factors selection strategy ensures the dynamic range of data, the asynchronous streaming structure ensures the efficiency of large scene imaging, and the mixed-precision data processing ensures the imaging quality. The schemes proposed in this paper are compared with BP, FBP, and fast factorized back-projection (FFBP) algorithms of single-precision in GPU. The experimental results show that the two half-precision acceleration schemes in this paper reduce the video memory usage to 74% and 59% of the single-precision schemes with guaranteed image quality. The efficiency improvements of the proposed schemes are almost one and 0.5 times greater than that of the corresponding single-precision scheme, and the advantage can be more obvious when dealing with large computations.

Factorized Geometrical Autofocus for UWB UHF-Band SAR With a GPS-Supported Linear Track Model

This article describes how to form a SAR image without proper motion quantities. That is within the scope of factorized geometrical autofocus (FGA). The FGA algorithm is a fast-factorized back-projection formulation with adjustable geometry parameters. Subapertures are tuned and merged pair-by-pair (base-2) and step-by-step. With this technique, we can correct an erroneous geometry and form a focused image. The FGA algorithm has been applied on two datasets, acquired by the UWB CARABAS 3 system at UHF-band. The tracks are measured accurately by means of a DGPS. We however adopt and modify a geometry model. Equidistant linear tracks at fixed altitudes are assumed. These tracks are then regulated via a two-stage search strategy and a reverseprocessing procedure. As this is a first experiment at UHF-band, we provide GPS-based length values for the subapertures, to simplify the search. Multiple geometry solutions are tested for each subaperture pair, i.e., at each resolution level. Resulting FGA images are compared to reference images and verified to be focused. This indicates that it is feasible to form a focused image with wavelength resolution at UHF-band, i.e., with minimum support from a motion measurement system.

A Novel CFFBP Algorithm With Noninterpolation Image Merging for Bistatic Forward-Looking SAR Focusing

Fast factorized back-projection (FFBP) has significant advantages for bistatic forward-looking synthetic aperture radar (BFSAR) imaging with arbitrary geometry and complex configuration. Conventional FFBP is generally based on the polar coordinate system (PCS) for recursive processing; however, it involves huge interpolations and causes computational inefficiency. In this article, a novel FFBP is developed for BFSAR focusing based on the Cartesian coordinate system (CCS), which is referred to as Cartesian fast factorized back-projection (CFFBP). In the new algorithm, a two-step spectrum correction is designed to avoid spectrum aliasing, and the Nyquist sampling requirement (NSR) for the BFSAR image spectrum can be decreased significantly. With low NSR in CCS, subimage merging can be implemented with noninterpolation processing, so that the proposed algorithm can achieve high performance in both accuracy and efficiency. Moreover, the practical problem of motion error is particularly considered in algorithm development, and well-adapted data-driven motion compensation (DDMC) is integrated with CFFBP based on which a new Cartesian fast time-domain (CFTD) processing framework is developed for BFSAR application. Promising results from both simulation and raw data experiments are provided and analyzed to validate the high performance of the proposed algorithm.

Efficient Fast Time-Domain Processing Framework for Airborne Bistatic SAR Continuous Imaging Integrated With Data-Driven Motion Compensation

Fast factorized back-projection (FFBP) is a classic fast time-domain algorithm (FTDA), which is not limited by the assumption of azimuth-invariant of echo signal and is suitable for the bistatic synthetic aperture radar (BiSAR) process of arbitrary geometric configuration. However, when the conventional FFBP processing is employed for continuous imaging of multiple full-apertures, the processing efficiency will be decreased significantly, and difficulty will be introduced in motion compensation (MOCO) development. The main contributions in this article include the following two aspects: 1) a new FTDA framework based on FFBP implementation is developed for continuous imaging where echo data are divided into several full-aperture data blocks and then processed separately by FFBP implementation to reduce redundant BP operations for achieving high efficiency and 2) an efficient and effective data-driven MOCO methodology is developed based on the new FTDA framework for high focusing quality. In MOCO, because the phase error functions of subimages are estimated in the phase history domain from different local polar coordinate systems, these phase error functions are actually discontinuous in the spatial domain, which will bring significant discontinuity and defocusing into the final image. To address this problem, the correspondence of error functions between the spatial domain and the wavenumber domain is revealed based on which the phase error functions are reconstructed to remove the discontinuity for high focusing quality. Promising results from both simulation and raw data experiments are provided and analyzed to validate the high performance of the proposed algorithm.

Linear-Array-MIMO SAR Tomography: An Autofocus Approach for Time-Variant and 3-D Space-Variant Motion Errors

Linear-array multiple-input–multiple-output (LA-MIMO) synthetic aperture radar (SAR) can obtain 3-D radar images by only one pass. However, it is sensitive to time-variant measurement errors of curved track and time-variant attitude angles, meaning that autofocus processing for the LA-MIMO SAR tomography is necessary. The existing autofocus methods cannot be used to estimate the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">time-variant</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-D space-variant</i> motion errors (3-D SVME) of the LA-MIMO SAR. To solve this problem, a new autofocus approach based on multiple local autofocusing and the LA-MIMO SAR time-variant motion error estimation is proposed. First, the local motion error estimation based on the fast local spectral analysis (SPECAN) 3-D imaging and the maximum contrast optimization 2-D local autofocusing is performed to estimate the local time-variant motion errors. Then, based on the linear-array motion error model, the time-variant 3-D trajectory deviations of the array center and attitude angles are estimated by the weighted least square estimation (WLSE) to solve the 3-D SVMEs. Last, the 3-D fast factorized backprojection (FFBP) is performed to obtain the well-focused 3-D image of the whole beam. The proposed approach has been applied for the tomography of a new crawler-type unmanned-ground-vehicle (UGV) LA-MIMO SAR. Both the simulation and real data experiments verify the effectiveness of the proposed approach.

An Autofocus Approach for UAV-Based Ultrawideband Ultrawidebeam SAR Data With Frequency-Dependent and 2-D Space-Variant Motion Errors

Unmanned-aerial-vehicle-based (UAV-based) ultrawideband and ultrawidebeam (UWB) synthetic aperture radar (SAR) is very sensitive to atmospheric turbulence and suffers from serious 2-D space-variant motion errors (SVMEs) caused by the ultrawide beam and frequency-dependent phase errors caused by the ultrawideband. This article proposes an autofocus approach for UAV-based UWB SAR data based on the quasi-polar grid fast factorized backprojection (FFBP) imaging framework, multiple subband local autofocus (MSBLA), and trajectory deviation estimation. First, based on an improved weighted phase gradient autofocus (WPGA) method for subband-division local images, MSBLA is introduced to solve the local motion error estimation problem with frequency-dependent phase errors. Then, trajectory deviation estimation based on the weighted least square (WLS) method is performed to solve the 2-D SVME problem. Finally, the subaperture trajectory deviations are fused into a full-aperture trajectory deviation by an improved fusion strategy based on piecewise weighting. This approach is applied to real data from a new UAV-based UWB SAR. The results of both simulation and real data experiments are presented and verify the effectiveness of the proposed approach.

Moving Target Shadow Analysis and Detection for ViSAR Imagery

The video synthetic aperture radar (ViSAR) is a new application in radar techniques. ViSAR provides high- or moderate-resolution SAR images with a faster frame rate, which permits the detection of the dynamic changes in the interested area. A moving target with moderate velocity can be detected by shadow detection in ViSAR. This paper analyses the frame rate and the shadow feature, discusses the velocity limitation of ViSAR moving target shadow detection and quantitatively gives the expression of velocity limitation. Furthermore, a fast factorized back projection (FFBP) based SAR video formation method and a shadow-based ground moving target detection method are proposed to generate SAR videos and detect the moving target shadow. The experimental results with simulated data prove the validity and feasibility of the proposed quantitative analysis and the proposed methods.

Spiral SAR Imaging with Fast Factorized Back-Projection: A Phase Error Analysis.

This paper presents a fast factorized back-projection (FFBP) algorithm that can satisfactorily process real P-band synthetic aperture radar (SAR) data collected from a spiral flight pattern performed by a drone-borne SAR system. Choosing the best setup when processing SAR data with an FFBP algorithm is not so straightforward, so predicting how this choice will affect the quality of the output image is valuable information. This paper provides a statistical phase error analysis to validate the hypothesis that the phase error standard deviation can be predicted by geometric parameters specified at the start of processing. In particular, for a phase error standard deviation of ~12°, the FFBP is up to 21 times faster than the direct back-projection algorithm for 3D images and up to 13 times faster for 2D images.

A Modified Factorized Geometrical Autofocus Method for Wide Angle SAR

Wide-Angle (WA) synthetic aperture radar (SAR) has shown remarkable performance in high-resolution mapping, and its mostly used imaging algorithm, fast factorized back projection (FFBP), is efficient, robust, and of low computational complexity. However, trajectory deviations and the system calibration error, introduced by low measurement accuracy, dramatically degrade FFBP's performance. This article proposes the modified factorized geometrical autofocus (MFGA) method for WA-SAR to address the above problems in FFBP. MFGA implements the phase gradient algorithm on defocus subimages at first. Then, a factorized geometrical error hypothesis between subimages is proposed. And the corresponding defocus factors are classified as three independent parts: image distortion, spectrum migration, and phase error. To deal with those problems, MFGA introduces image registration techniques and a maximum sharpness method to calibrate image distortion and phase error. Moreover, in MFGA, based on minimum entropy and least square method, a Doppler spectrum migration correction algorithm is proposed to correct spectrum migration. In the FFBP chain, MFGA is used on subimages refocus and fusion until obtaining a full-resolution image. In our experiments, we compared MFGA and other time-domain autofocus algorithms using simulated data and real data obtained by helicopter and airship with false trajectory and system calibration parameters. The results show that MFGA performs better in terms of the peak to side-lobe ratio, the azimuth resolution, the refocused images' entropy, and processing time consumption. The better performance demonstrates MFGA's advantages in addressing trajectory deviations and the system calibration error for WA-SAR.

High-Precision Spotlight SAR Imaging with Joint Modified Fast Factorized Backprojection and Autofocus

Fast factorized backprojection (FFBP) takes advantage of high accuracy of time-domain algorithms while also possessing high efficiency comparable with conventional frequency domain algorithms. When phase errors need to be compensated for high-resolution synthetic aperture radar (SAR) imaging, however, neither polar formatted subimages within FFBP flow nor the final Cartesian image formed by FFBP is suitable for phase gradient autofocus (PGA). This is because these kinds of images are not capable of providing PGA with a clear Fourier transform relationship (FTR) between image domain and range-compressed phase history domain. In this paper, we make some essential modifications to the original FFBP and present a scheme to incorporate overlapped-subaperture frame for an accurate PGA processing. The raw data collected by an airborne high-resolution spotlight SAR are used to demonstrate the performance of this algorithm.

A New Fast Factorized Back-Projection Algorithm with Reduced Topography Sensibility for Missile-Borne SAR Focusing with Diving Movement

Time-domain algorithms have significant performance advantages for missile-borne synthetic aperture radar (SAR) focusing with diving movement. However, due to the diving curve trajectory of the missile platform, the range and angular histories of the target become very sensitive to unknown tomography, which provides difficulties for SAR algorithm development. To address this problem, we have proposed a new fast factorized back-projection (FFBP) algorithm with reduced topography sensibility for missile-borne SAR focusing. The new algorithm was designed based on an orthogonal cylindrical coordinate (OCC) system, in which the cross section of a cylinder in the coordinate system is approximately orthogonal to the diving curve trajectory. Owing to the acquisition symmetry of the OCC system, the range and the angular histories of the grid in the OCC geometry become less dependent of the topography in every recursion of FFBP implementation, which can dramatically reduce the adverse effects of unknown topography and achieve high focusing performance. In the simulation, echo signal based on a set of typical parameters from a missile-borne SAR system is generated with unknown tomography. Promising results with 1 m resolution are finally achieved, which demonstrates the performance of the proposed algorithm. The limitation of the algorithm is also discussed in the final part, which will facilitate the development of raw data processes in practical application.

NUFFT-Based Interpolation in Backprojection Algorithms

We consider the interpolation problem associated with the back-projection (BP), fast BP (FBP), and fast factorized BP (FFBP) algorithms exploited in synthetic aperture radar (SAR). The 2-D interpolation required by FBP and FFBP must be properly performed to mitigate the effect of the truncation error and to achieve accurate results, and can be effectively performed by adopting 2-D nonuniform fast Fourier transform (NUFFT) routines.

Data-Driven Motion Compensation for Airborne Bistatic SAR Imagery Under Fast Factorized Back Projection Framework

Due to the independence of azimuth invariance and high implementing efficiency, a fast time-domain algorithm has significant advantages for airborne bistatic synthetic aperture radar (BiSAR) data process with general geometric configuration. In this article, the practical problem of unexpected motion errors of the airborne platform is carefully analyzed under a fast factorized back-projection (FFBP) framework for a general BiSAR process and a coherent data-driven motion compensation (MOCO) algorithm integrated with FFBP is proposed. By utilizing wavenumber decomposition, the analytical spectrum of a polar grid image is obtained where the motion error can be conveniently investigated in image spectrum domain and the coherence between azimuthal phase error (APE) and motion-induced nonsystematic range cell migration (NsRCM) can be perfectly revealed. Then, a new data-driven MOCO method for both APE and NsRCM correction is developed with the FFBP process. Different from the data-driven MOCO in most frequency-domain algorithms, the residual NsRCM introduced by the FFBP process is particularly analyzed and addressed in the MOCO, which significantly improves the image quality in focusing. Promising results from both simulation and raw data experiments are presented and analyzed to validate the advantages of the proposed algorithm for the airborne BiSAR process.

Fast Factorized Backprojection Imaging Algorithm Integrated With Motion Trajectory Estimation for Bistatic Forward-Looking SAR

A bistatic forward-looking synthetic aperture radar (BFSAR) is increasingly in the focus of study, as it breaks through the limitations of imaging on a forward-looking terrain of a moving platform. Fast factorized backprojection (FFBP) is a reliable BFSAR imaging algorithm, with both imaging precision and efficiency being taken into consideration. In FFBP imaging, compensation of the motion errors is important to obtain a well-focused image. To accomplish an accurate motion compensation in image processing, a high-precision navigation system is needed. However, in many cases, because of the accuracy limit of such systems, motion errors are difficult to be compensated correctly, resulting chiefly in resolution decrease in the final images. To deal with such a problem, we propose an FFBP imaging algorithm integrated with motion trajectory estimation for BFSAR. First, a coarse-to-fine residual range cell migration (RCM) correction scheme is applied to ensure the residual RCM within a range resolution. Then, an optimization model with respect to motion trajectory estimation under the criterion of maximum image sharpness is built during FFBP imaging. According to the coarse-to-fine residual RCM correction scheme and the motion trajectory estimation model, a block coordinate descent technique based on steepest descent optimization method integrated with residual RCM correction is proposed to estimate the motion errors in FFBP imaging. We empirically compare the proposed method with several state-of-the-art BFSAR imaging and autofocus algorithms. Simulations on BFSAR data show that the proposed method is more accurate and has similar computational cost.