Fast Factorized Backprojection Algorithm 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.

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.

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 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.

A New Fast Factorized Back Projection Algorithm for Bistatic Forward-Looking SAR Imaging Based on Orthogonal Elliptical Polar Coordinate

Due to the flexible bistatic configuration and complicated moving trajectory of radar platform, time-domain algorithms have significant focusing performance advantages for bistatic forward-looking synthetic aperture radar (BFSAR) applications. In this paper, a new fast factorized back projection (FFBP) based on orthogonal elliptical polar (OEP) coordinate is proposed for BFSAR imaging. Owing to the orthogonality of OEP system, the spectrum of BFSAR subimages can be compacted into the narrowest range and very low Nyquist sampling rate can be utilized in FFBP recursion. Comparing with the conventional FFBP based on original elliptical polar coordinate, the proposed OEP-based algorithm has prominently reduced burden in computation, especially for the BFSAR cases with large baseline geometry. Moreover, a new wavenumber decomposition-based strategy is presented to reveal two-dimensional Nyquist sample requirement without complicated calculation and mathematical derivation, which makes the FFBP process much more easier to design. Promising results from simulations and raw data experiments are presented to validate the advantages of the proposed algorithm.

An Extended Fast Factorized Back Projection Algorithm for Missile-Borne Bistatic Forward-Looking SAR Imaging

In this paper, an extended fast factorized back projection (FFBP) algorithm is proposed to focus the missile-borne bistatic forward-looking synthetic aperture radar (BFSAR) data. It is also based on the subaperture processing technique to reduce the computational burden, but represents the subimages on the elliptical polar coordinates referenced to the tracks of both transmitter and receiver. First, the imaging geometry and signal model of the missile-borne BFSAR are established. Then, considering the special configuration of the missile-borne BFSAR, a novel elliptical polar coordinate system whose origin is determined by the positions of both transmitter and receiver is established. The subaperture processing approach based on this coordinate system is presented. Successively, based on the range error analysis, the sampling requirements of the elliptical polar subimages are derived to provide a tradeoff between the imaging quality and efficiency. Finally, the computational burden of the proposed algorithm is discussed, and the speed-up factor of the proposed algorithm with respect to the direct back projection algorithm is derived. The experimental results with simulated data prove the validity and feasibility of the proposed algorithm.

Wavenumber domain acceleration for stripmap fast factorized backprojection beamforming

Synthetic aperture sonar (SAS) imaging is frequently used in conjunction with autonomous underwater vehicles (AUV's) to perform high resolution wide-area surveys. Wave action and currents perturb the trajectories of AUV's performing these surveys and these perturbations have important ramifications for the SAS beamforming process. Generalized beamforming algorithms operating in the time domain are very flexible with regard to trajectory non-linearities, but they also tend to have a higher computational cost than alternative frequency domain algorithms. Of the generalized beamformers one of the more efficient is fast factorized backprojection (FFBP), which leverages sub-aperture processing and a series of coordinate transformations to improve computational efficiency. FFBP can be used to beamform SAS data, however many SAS systems make use of a real aperture to boost range potential. The existence of a real aperture implies that a frequency domain beamformer could be used to bypass the first few stages of FFBP without loss of generality; however, standard frequency domain SAS beamforming algorithms are not compatible with the FFBP framework. A wavenumber domain beamformer compatible with the early-stage FFBP framework is derived and beamforming results for the modified FFBP algorithm are compared with the standard approach that operates entirely in the time domain.

Simultaneous Range and Cross-Range Variant Phase Error Estimation and Compensation for Highly Squinted SAR Imaging

This paper addresses an autofocusing technique for highly squinted airborne synthetic aperture radar (SAR) imaging. In highly squinted mode, the phase errors resulting by trajectory deviations usually exhibit both range and cross-range variance. To circumvent this problem, a 2-D space-variant phase error model is proposed. Then an autofocusing approach is presented to realize precise SAR reconstruction. This approach mainly consists of three processing steps. First, multiple local images are automatically selected based on sliding window operation in both range and cross-range dimensions. For each local image, weighted squint phase gradient autofocus kernel is applied to estimate the local phase error function. Second, the derived multiple local phase error functions are combined to resolve the 2-D space-variant phase error model using a weighted total least square method. Third, the fast factorized back-projection algorithm with pixelwise phase error correction is utilized to obtain focused image eventually. Experiments on both simulated and real-measured SAR data sets validate the focusing performance of the proposed approach.

Experiment of Azimuth-invariant Bistatic UHF UWB SAR

Bistatic ultrahigh frequency ultrawideband synthetic aperture radar (UHF UWB SAR) has the well ability of the penetrating the foliage, high-resolution imaging and providing the increased information. In the paper, an imaging experiment of the azimuth-invariant bistatic UHF UWB SAR is described and the result is proposed. In August 2015, an along-track bistatic UHF UWB SAR experiment was conducted in China, and the raw data was collected. In this bistatic SAR system, the transmitter and receiver are both carried by a vehicle and separated by an invariable distance. The aim was to investigate the imaging property of the bistatic UHF UWB SAR system. Bistatic image was obtained using the subaperture spectrum-equilibrium method integrated with the fast factorized back projection algorithm (FFBPA). Experiment results prove the validity of the bistatic UHF UWB SAR experiment.

An Adaptive Fast Factorized Back-Projection Algorithm With Integrated Target Detection Technique for High-Resolution and High-Squint Spotlight SAR Imagery

This paper deals with the problem of fast focusing the spotlight synthetic aperture radar (SAR) data in high-resolution and high-squint mode, which has shown its potential capacity in various military SAR applications. Fast factorized backprojection (FFBP) is considered as an ideal methodology for high-resolution and high-squint SAR imagery. However, FFBP performs pixel-by-pixel interpolation, yielding heavy computational burden and limiting its real-time processing. In this paper, target detection technique, which is used as a discrimination tool to retain the target pixels and reject the clutter and noise pixels, is integrated into the subaperture imaging chain during FFBP implementation, aiming to speed up the overall image formation time. Due to the characteristic of spotlight acquisition, an adaptive processing scheme is developed for multiple subaperture images detection. With the integrated target detection technique, only the target pixels need to be interpolated and accumulated coherently. Without loss of focusing performance, the number of interpolations is dramatically reduced. The proposed fast imaging algorithm is named as adaptive FFBP (AFFBP), and it has distinctive superiority for sparse scene reconstruction, such as the maritime target imaging. AFFBP has been successfully applied to two simulated scenes with high and low signal-to-noise ratios (SNRs), and two real measured datasets with squint angle high up to $50^{\circ }$ and $70^{\circ }$ , respectively. All these experiments demonstrate the effectiveness and efficiency improvement of the proposed AFFBP algorithm.

Quasi-Polar-Based FFBP Algorithm for Miniature UAV SAR Imaging Without Navigational Data

Because of flexible geometric configuration and trajectory designation, time-domain algorithms become popular for unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) applications. In this paper, a new quasi-polar-coordinate-based fast factorized back-projection (FFBP) algorithm combined with data-driven motion compensation is proposed for miniature UAV-SAR imaging. By utilizing wavenumber decomposition, the analytical spectrum of a quasi-polar grid image is obtained, where the phase errors arising from the trajectory deviations can be conveniently investigated and the phase autofocusing can be compatibly incorporated. Different from the conventional FFBP based on a polar coordinate system, the proposed algorithm operates in a quasi-polar coordinate system, where the phase errors become spacial invariant and can be accurately estimated and easily compensated. Moreover, the relationship between phase errors and nonsystematic range cell migration (NsRCM) is revealed according to the analytical image spectrum, based on which the NsRCM correction is developed to further improve the image focusing quality for high-resolution SAR applications. Promising experimental results from the raw data experiments of miniature UAV-SAR test bed are presented and analyzed to validate the advantages of the proposed algorithm.

Spectrum-Oriented FFBP Algorithm in Quasi-Polar Grid for SAR Imaging on Maneuvering Platform

In this letter, a new spectrum-oriented fast factorized backprojection (FFBP) algorithm is proposed for synthetic aperture radar (SAR) imaging on a maneuvering platform. Specifically, an analytical SAR image spectrum is derived in a novel quasi-polar coordinate system based on the FFBP, which makes it easy to incorporate with an autocalibration process for both systematic and nonsystematic errors. Different from the conventional FFBP algorithms developed in polar grid, the proposed algorithm devised in quasi-polar gird conducts the motion-induced phase error as a space-invariant component, which will definitely facilitate the phase autofocusing process during the FFBP recursions. Subsequently, a phase autofocusing process is incorporated in the resultant SAR image formation algorithm. Simulations and discussions are presented to show the focusing quality improvement made by the proposed algorithm.

Fast Factorized Backprojection Algorithm for One-Stationary Bistatic Spotlight Circular SAR Image Formation

In this paper, a fast factorized backprojection (FFBP) algorithm is proposed for the one-stationary bistatic spotlight circular synthetic aperture radar (OS-BSCSAR) data processing. This method represents the subimages on polar grids in the slant-range plane instead of the ground plane, which can be accurately referenced to the tracks of both transmitter and receiver. It can not only accurately accommodate the complicated circular track including the motion error, scene topographic information, large spatial variances and significant range-azimuth coupling of the echo data, but also improve the imaging efficiency compared with the backprojection (BP) algorithm. First, OS-BSCSAR imaging geometry is provided, and then the bistatic BP algorithm for the OS-BSCSAR imaging is derived to provide a basis for the proposed FFBP algorithm. Second, based on the subaperture imaging model, the polar grids for calculating the subimages are defined, and the sampling requirements for the polar grids are derived from the viewpoint of the bandwidth, which can offer the near-optimum tradeoff between the imaging quality and the imaging efficiency. Finally, implementation and computational burden of the proposed FFBP algorithm is discussed, and then the speed-up factor of the proposed FFBP algorithm with respect to the bistatic BP algorithm is derived. Experiment results are given to prove the correctness of the theory analysis and validity of the proposed FFBP algorithm.

Precision Imaging of Frequency Stepped SAR with Frequency Domain Extracted HRRP and Fast Factorized Back Projection Algorithm

Novel frequency domain extracted method (FDEM) to obtain high range resolution profile (HRRP) for frequency stepped synthetic aperture radar (SAR) is proposed in this paper, and the mathematical principle and formulas of this new HRRP obtaining idea combined with classical fast Fourier transform (FFT), chirp z transform (CZT), and single point Fourier transform (SPFT) are deduced, analyzed, and compared in detail. Based on the HRRP data, precision imaging processing is completed using a data block partition based fast factorized back projection algorithm. Imaging validations are executed and all results proved that the FDEM has a great capability of antijamming. It is more effective than conventional time domain IFFT method (TDM) and shows a great promise in frequency stepped radar imaging and applications.

Application of fast factorized back-projection algorithm for high-resolution highly squinted airborne SAR imaging

In squinted synthetic aperture radar (SAR) imaging, the range-azimuth coupling requires precise range cell migration correction (RCMC). Moreover, for high-resolution airborne SAR, motion compensation (MOCO) becomes complicated as the squint angle increases, thereby degrading the performance of Doppler-domain imaging algorithms. On the other hand, time-domain back-projection (BP) SAR imaging approaches are considered as optimal solutions to performing precise image focusing and MOCO. Among current BP algorithms, the fast factorized back-projection (FFBP) algorithm is one of the most essential representatives that achieve high-resolution images in an efficient manner. In this paper, the principle and applications of the FFBP algorithm are investigated through the derivation of the azimuth impulse response function (AIRF) of the resulting image. The phenomenon of spectrum displacement induced by motion errors in the BP image is presented and analyzed. Based on rigorous mathematical derivations, a modified FFBP algorithm is proposed to facilitate a seamless integration with motion compensation and accurate imagery of high-resolution highly squinted airborne SAR. Real data results confirm the effectiveness of the proposed approaches.

Fast Time-Domain Imaging in Elliptical Polar Coordinate for General Bistatic VHF/UHF Ultra-Wideband SAR With Arbitrary Motion

In this paper, a fast time-domain imaging algorithm called bistatic fast factorized back projection algorithm (BFFBPA) is proposed for the general bistatic VHF/UHF ultra-wideband synthetic aperture radar. It cannot only accurately dispose the large spatial variant range cell migrations, serious range-azimuth coupling and complicated motion error, but also achieve the imaging efficiency similar to frequency-domain algorithms. It represents subimages in elliptical polar coordinate to reduce the computational load. The imaging geometry with arbitrary motion in this coordinate system is provided, and the bistatic back projection algorithm (BPA) is derived to provide a basis for the proposed BFFBPA. Considering motion errors, the more accurate sampling requirements for elliptical subimages is deduced to offer the near-optimum tradeoff between the imaging quality and efficiency, and the constraint of motion errors for acceptable sampling requirements is discussed. Based on this sampling requirement, the advantage of using elliptical subimage grids for this BFFBPA is analyzed. A phase error correction is performed to reduce the impact of phase errors caused by interpolations in the BFFBPA. The speed-up factor of this BFFBPA with respect to the bistatic BPA is derived. Simulation results and evaluations are given to prove the correctness of the theory analysis and validity of the proposed method.

A coordinate-transform based FFBP algorithm for high-resolution spotlight SAR imaging

This paper proposes a coordinate-transform (CT) implementation for the fast factorized backprojection (FFBP) algorithm (CT-FFBP) to process high-resolution spotlight synthetic aperture radar (SAR) data. Unlike the FFBP utilizing two-dimensional image-domain interpolation for sub-aperture fusion, CT-FFBP finishes the image-projection using CT with the accommodation of chirp-z transform and circular shifting. Without interpolation, CT-FFBP yields enhanced efficiency over the interpolation based FFBP, besides maintaining high precision simultaneously. Both simulation and real-data experiments verifies the efficiency and precision superiorities of the CT-FFBP.

A Novel Fast Factorized Back-projection Algorithm for Synthetic Aperture Radar Imaging

A Novel Fast Factorized Back-projection Algorithm for Synthetic Aperture Radar Imaging