The backprojection (BP) algorithm is a precise time-domain technique in synthetic aperture radar (SAR) imaging, known for its robustness in scenarios where frequency-domain algorithms struggle, such as nonlinear flight paths, high-resolution demands, or large imaging swaths. However, the unknown spectral structures of BP images pose significant challenges for frequency-domain autofocus algorithms, including phase gradient autofocus (PGA). This article introduces a novel interpretation of the BP algorithm, and then compares the image spectra between BP and the polar format algorithm (PFA). Our findings indicate that BP image’s spectrum suffers from severe range ambiguity and spectral misalignment, which is the key reason why BP images cannot be directly applied to PGA. To address these issues, we first improve the postprocessing method, and then propose a modified BP algorithm. Both the approaches reconstruct the signal spectrum, thereby facilitating the direct application of PGA. Compared with the postprocessing method, the proposed algorithm is more efficient. Simulation and real data experiments validate the feasibility and efficacy of the proposed method, demonstrating the proposed algorithm’s suitability for autofocusing in the frequency domain.

Higher spatial resolution and larger imaging scene are always the goals pursued by advanced spaceborne synthetic aperture radar (SAR) system. High-resolution and wide-swath SAR imaging can provide more information about the illuminated scene of interest on the one hand but also come with some new challenges on the other. The induced new challenging problems include curved orbit, Earth’s rotation, and spherical ground surface. Most existing image formation algorithms suffer from performance deficiency in these challenging cases, either in focus accuracy or computational efficiency. In this article, an accurate Fourier transform relationship between the phase history domain data and the scene reflectivity function is derived under an arbitrary radar trajectory by exploiting the spherical geometry property of the spaceborne SAR data collection. Using the derived new data model, an image reconstruction algorithm based on Fourier inversion is proposed. The new algorithm has the inherent capability of correcting for the curved orbit and spherical ground surface effect. Meanwhile, the out-of-plane motion effect induced by the Earth’s rotation can also be compensated by a two-step phase correction and data projection procedure embedded in the Fourier inversion reconstruction. The new algorithm inherits the merits of both time domain and frequency domain algorithms and has excellent performance in both focus accuracy and computational efficiency. Both simulation and real data processing results validate the effectiveness of the proposed imaging algorithm.

Phase gratitude algorithm (PGA) is a high-efficient autofocus technique that can estimate and compensate phase errors of SAR (synthetic aperture radar) imagery produced by frequency-domain algorithms. However, from conventional viewpoint, applying PGA on refocusing imagery produced by the time-domain algorithm, i.e., FBP, remains a huge challenge because the spectrum characteristics of FBP imagery are special. In this paper, a modified PGA (MPGA) for spotlight FBP (Filtered Backprojection) imagery is proposed, in which a spectrum correction is performed first to provide advantages for the standard PGA application. Simulations and real data experiments have been carried out to prove the effectiveness and prospect of the proposed approach for refocusing FBP imagery.

The missile-borne SAR works in the forward-squint state, and a higher flight speed will cause a very large relative radial velocity between the target and the antenna phase center (APC). The classic polar format algorithm (PFA) and its improved version do not effectively compensate for the intra-pulse Doppler history resulting from large radial velocity, which leads to defocused images. Therefore this paper proposes a modified version of the PFA, which can solve such image defocus. Compared with the classical PFA, the modified PFA has the same advantages of simplicity and efficiency while implementing higher image quality by compensation of the residual phases caused by large radial velocity. The modified PFA is suitable for hardware implementation, since only fast Fourier transform (FFT) and complex vector multiplications are required in the range dimension processing. In this paper, simulation examples are employed to verify the validity and advantages of the modified PFA.

The Polar Format Algorithm (PFA) is a popular choice for general bistatic synthetic aperture radar (BiSAR) imaging due to its computational efficiency and adaptability to situations with complicated geometries or arbitrary flight trajectories. However, efficient and accurate compensation of two-dimensional (2-D) residual phase errors induced by the wavefront curvature remains challenging when obtaining high quality BiSAR PFA images. In this paper, an analytical expression for the phase errors in the wavenumber domain is derived. With it, the inherent structural characteristics of the phase errors are formulated, where the 2-D phase errors can be reduced to one-dimensional (1-D) phase errors for an optimal coordinate system. Moreover, the mapping relationship between distorted point targets in the optimal imaging coordinates and their actual point targets in the original imaging coordinates is investigated. By exploiting the structural characteristics and the mapping relationship, a highly efficient BiSAR PFA wavefront curvature compensation method is proposed. This allows a reduced-dimensional space-variant filter to be constructed to mitigate the 2-D defocusing effect without compromising the compensation accuracy, with the distortion correction being performed using interpolation. The proposed method significantly reduces the complexity required for residual 2-D phase error compensation while simplifying the distortion correction, resulting in a notable robustness. The effectiveness of the method is demonstrated using point target and scene target simulations.

Wavefront curvature effects grow worse in spotlight Bistatic synthetic aperture radar (BSAR) imagery when reconstructed via polar format algorithm (PFA) under the large-scale scene. The wavefront curvature error, which causes geometric distortion and defocuses to the image, is induced by the faulty hypothesis of the planar wavefront. Due to the approximated or unsegmented wavefront curvature error, conventional compensation algorithms experience different degrees of performance restriction. In this letter, the geometric distortion error and the intact defocus error are separated and analyzed for the first time. Based on the separated phase error model, a modified space-variant post-filtering (MSVPF) algorithm is proposed to correct the wavefront curvature effects of the PFA image. Two major contributions of this algorithm are as follows. First, as no high-order term is ignored in the constructed space-variant filter, the proposed algorithm can compensate for the defocus error with any order. Second, MSVPF employs a separate strategy to correct the space-variant defocus and geometric distortion, which avoids high overlap rate in subimage processing and maintains the computational efficiency of the original SVPF. The effectiveness of the proposed algorithm is demonstrated by numerical simulations.

Based on the principle of planar wavefront assumption, a novel point of view in processing the spotlight synthetic aperture radar (SAR) data is proposed in this letter. After match filtering and motion compensation to the scene center, from the perspective of range cell migration correction (RCMC), two scaling transforms (a range-frequency scaling with a subsequent azimuth-time scaling) are proposed to correct the range cell migration caused by the coupling between the range-frequency and azimuth-time. Moreover, to reduce the spectrum loss (the loss of image resolution), two constant scaling factors are introduced to optimize the range-frequency and azimuth-time scaling transforms, which enable the presented algorithm to realize the flexible and efficient imaging ability. Simulation results are conducted to validate the efficacy of this algorithm.

The phase gratitude algorithm (PGA) is a robust autofocusing approach that can efficiently refocus defocused SAR imagery produced by frequency-domain algorithms. However, from a conventional viewpoint, PGA cannot be extended to refocus SAR imagery produced by time-domain algorithms, such as the Filtered Back Projection (FBP), as the spectrum of the FBP imagery is range ambiguous and azimuth space-variant. In this letter, a novel interpretation of FBP is presented, in which the spectrum structure of the FBP imagery is analyzed in detail. By incorporating the derived spectral information, an efficient spectrum preprocessing is proposed for spectrum restructuring. After this preprocessing, PGA is shown to be able to refocus defocused FBP imagery. The validity and feasibility of the proposed autofocusing approach are demonstrated using both simulated and experimental data.

An alternate transmitting mode (ATM) is an important synthetic aperture radar (SAR) imaging mode as it can provide rich waveform design degrees of freedom to improve the system performance, especially to mitigate range ambiguities. However, the azimuth ambiguity issue caused by the differences between the autocorrelation functions of transmitted waveforms is ignored in existing studies. In this article, a deep understanding of the ambiguities in the ATM allows a correct evaluation of the ambiguity-to-signal ratio and the design of quasi-orthogonal nonlinear frequency modulation (NLFM) waveforms optimized for ambiguity suppression. Moreover, a novel azimuth compensation method is developed to remove the azimuth ambiguities caused by waveform diversity. Finally, detailed simulation experiments are carried out to verify the theoretical analysis.

The filtered backprojection (FBP) algorithm is viewed as a preferred candidate for general bistatic synthetic aperture radar (BiSAR) imaging since it does not pose any restrictions on SAR configurations or flight paths. However, high-efficient autofocus methods such as phase gradient autofocus (PGA) or Mapdrift (MD) cannot be effectively integrated with the FBP algorithm due to the unknown properties of the BiSAR FBP imagery spectrum. In this article, a novel Fourier-based interpretation of the BiSAR FBP algorithm is presented. Based on the new viewpoint, spectral characteristics of the BiSAR FBP imagery in the wavenumber domain, including range spectral ambiguity, space-variant spectral support, and the structural 2-D phase error, are derived in detail. Using these characteristics, a computationally efficient 2-D autofocus approach is proposed. First, a preprocessing is performed to eliminate the range spectral ambiguity and to align the skewed spectrum support, which facilitates the following phase error estimation and correction. Then, an estimation of the 1-D azimuth phase error (APE) is applied by combining multiple estimation results from different subband data. Finally, the 2-D phase error is computed directly from the estimated APE by exploiting the derived analytical structure of the 2-D phase error, which is then applied to restore the BiSAR FBP image. The simulation results are presented to show the effectiveness of the proposed approach.

Video synthetic aperture radar (VideoSAR) possesses the capability of imaging and continuously monitoring the scenario from a wide-aspect interval for enhancing the performance of information interpretation. In this paper, we propose a complete imaging scheme to achieve the unified video coordinate system in high-resolution airborne VideoSAR configuration. Comprehensive postprocessing video imaging (PPVI) framework built on range Doppler algorithm and range migration algorithm is elaborated especially in terms of complex measured data, which is divided into three parts for ensuring the stability of video background: full-aperture imaging, 2-D autofocus technique, and Doppler spectrum segmentation. Experimental results utilizing the measured airborne data have demonstrated the effectiveness of PPVI scheme for sequential VideoSAR formation.

In this article, a new interpretation of the polar format algorithm (PFA) for general bistatic spotlight synthetic aperture radar (SAR) imaging is presented. From the viewpoint of 2-D decoupling, we examine the commonly adopted implementation of the PFA, i.e., the separable 1-D range and azimuth resampling procedures for their roles in range cell migration (RCM) correction, respectively. Utilizing this new formulation, we analyze the effect of range and azimuth resampling on the residual 2-D phase error and reveal the inherent structure characteristics of the residual 2-D phase error in the wavenumber domain. By exploiting the available a priori knowledge on the phase error structure, a structure-aided 2-D autofocus approach to refocus the defocused PFA imagery is proposed. The proposed approach fully exploits the potentiality of the available data and the a priori knowledge about the phase error that need to estimate, so the accuracy of the residual 2-D phase error estimation and correction can be greatly improved. Finally, experimental results are presented to show the effectiveness of the proposed approach.

The filtered backprojection (FBP) algorithm is a popular choice for complicated trajectory synthetic aperture radar (SAR) image formation processing due to its inherent nonlinear motion compensation capability. However, how to efficiently refocus the defocused FBP imagery when the motion measurement is not accurate enough is still a challenging problem. In this paper, a new interpretation of the FBP derivation is presented from the Fourier transform point of view. Based on this new viewpoint, the property of the residual 2-D phase error in FBP imagery is analyzed in detail. Then, by incorporating the derived a priori knowledge on the 2-D phase error, an accurate and efficient 2-D autofocus approach is proposed. This new approach performs the parameter estimation in a dimension-reduced parameter subspace by exploiting the a priori analytical structure of the 2-D phase error, therefore it possesses much higher accuracy and efficiency than the conventional blind methods. Finally, experimental results clearly demonstrate the effectiveness and robustness of the proposed method.

With continuous improvement of the synthetic aperture radar (SAR) resolution, the 2-D defocus effect in SAR image resulting from uncompensated motion error has made autofocus become a new challenging problem. Conventional 2-D autofocus approaches assume that the 2-D phase error is absolutely unknown and estimate them directly. Due to high dimensionality of the unknown parameters, these approaches often suffer from high computational burden and low estimate accuracy. In this paper, we analyze the effect of range migration algorithm (RMA) processing on the 2-D echo phase, and reveal the analytical structure of the residual 2-D phase error in RMA imagery. Then, by exploiting the derived prior knowledge on the phase error structure, an accurate and efficient 2-D autofocus approach is proposed. In the new method, only 1-D error, e.g., azimuth phase error, or residual range cell migration, is required to be estimated directly, while the 2-D phase error is computed directly from the estimated 1-D error by exploiting the analytical structure of the 2-D phase error. The experimental results clearly demonstrate the effectiveness and robustness of the proposed method.

The Doppler shift effect results in some targets shadows in theirs actual position, and a strong correlation exists between adjacent frames of Video Synthetic Aperture Radar (VideoSAR) imagery. Based on the above rationale, a novel approach to moving targets shadow detection for high-frame-rate VideoSAR imagery sequence is presented. First, a fast preprocessing stage is essential in real applications, where the SIFT with RANSAC registration algorithm is employed to compensate for the changing background, and the CattePM model is used to suppress the speckle noise. Then, in order to separate the targets and the background automatically, a threshold segmentation algorithm, called maximizing the Tsallis entropy, is applied. Finally, background difference with three frame difference method implements the precise moving targets extraction. Experimental results utilizing VideoSAR imaging fragment show that multiple moving vehicles are detected effectively and, hence, the validity has been demonstrated.

An improved space-variant postfiltering approach to compensate for the wavefront curvature effect in polar format imagery is presented in this letter. The main contribution of this new method is the construction of a space-variant filter, which is based on exploiting the endomorphism property of the polar format transformation. The new approach provides an accurate and general solution to wavefront curvature compensation under arbitrary radar flight path. Finally, point target simulation has validated the effectiveness of the new approach.

A new approach to process stepped chirps in spotlight synthetic aperture radar is presented in this letter, which is based on exploiting the principle of chirp scaling (PCS). In particular, PCS is integrated into the polar format algorithm (PFA), obtaining a more efficient solution compared with the existing polar interpolation technique. The main contribution of this letter is the implementation of azimuth scaling, in which the bandwidth synthesis is embedded. The algorithm is developed dedicatedly for dealing with stepped chirps. The signal processing flow is investigated in detail, in which no interpolations but only fast Fourier transform and complex multiplications are involved. Point-target simulation has validated the new approach and indicated that it is more efficient than the classic interpolation-based one. The achieved computational gain measured in execution time is around 25%-30%.

In this work, a 2-D subaperture polar format algorithm (PFA) based on stepped-chirp signal is proposed. Instead of traditional pulse synthesis preprocessing, the presented method integrates the pulse synthesis process into the range subaperture processing. Meanwhile, due to the multi-resolution property of subaperture processing, this algorithm is able to compensate the space-variant phase error caused by the radar motion during the period of a pulse cluster. Point target simulation has validated the presented algorithm.