In high-resolution unmanned aerial vehicle (UAV) Synthetic Aperture Radar (SAR) imaging, despite the utilization of inertial navigation system (INS) data for pre-compensation, residual envelope and phase errors may still persist. Residual envelope errors can adversely affect phase error estimation (PEE), consequently degrading autofocus performance. This letter proposes a phase-envelope joint autofocus algorithm for backprojection (BP) imaging. An algorithm framework for alternating iterative estimation of phase and envelope is constructed based on maximizing image sharpness, which can effectively correct phase and envelope errors. In addition, only a small local area is selected for error estimation, significantly reducing memory and time consumption. The effectiveness of the algorithm is verified using X-band UAV SAR raw data.

Forward-looking multi-channel synthetic aperture radar (FLMC-SAR) is an important technical means for achieving forward-looking imaging and enhancing the visibility of the traditional SAR forward blind zone. Its significance extends across various applications, including military reconnaissance, geological exploration, disaster monitoring, and other related fields. However, motion errors, slant range errors, and other factors introduce Doppler errors, making FLMC-SAR imaging and Doppler ambiguity resolving a challenging task. In this paper, leveraging the physical characteristics that the maximum Doppler frequency within the imaging area is provided by targets in the direction of the radar platform’s velocity, we achieve pixel-level Doppler centroid correction. This holds significant implications for Doppler ambiguity resolving, distortion correction, and pixel localization in FLMC-SAR images. Initially, we established the space-time model of FLMC-SAR. Based on this model, we devised a two-step FLMC-SAR imaging processing: time-domain imaging followed by spatial-domain Doppler ambiguity resolving. Within this framework, we analyze the space-time characteristic representation of the maximum Doppler line in the two-dimensional range-Doppler image domain, and the estimation of Doppler error was provided by space-time characteristic. Furthermore, utilizing series inversion, we derived estimations of motion error and slant range error, thereby achieving pixel-level Doppler centroid frequency correction. Extensive simulations and real-data experiments demonstrate that the proposed algorithm is capable of FLMC-SAR imaging for Doppler ambiguity resolving and distortion correction.

The existing Ground Cartesian Back-Projection (GCBP) algorithm is limited by its low effectiveness in spectral compression, which makes it unsuitable for processing high-squint and large-scale strip-map Synthetic Aperture Radar (SAR) data. To address this issue, we propose a novel algorithm called Ground Squint Fast Back Projection (GSFBP) for high-squint strip-map SAR imaging. First, we introduce a Ground Squint Coordinate (GSC) system that replaces the conventional Ground Cartesian Coordinate (GCC) system. The unique geometry of the GSC allows for precise rotation of the two-dimensional wavenumber spectrum without the need for auxiliary operations, significantly easing the constraints related to scene size.Moreover, the GSC framework facilitates seamless sub-image fusion through translation, eliminating the need for interpolation. Building on the original two-step spectral compression method, we have developed a GSC-specific relative spectrum inclination correction function to enhance spectral compression effectiveness. These innovations enable GSFBP to effectively manage large-scale scenes in high-squint SAR imaging. Experimental validation, using both simulated and real measured SAR data, confirms the superiority of the proposed algorithm.

Forward-looking multichannel synthetic aperture radar (FLMC-SAR) has the capability to generate unambiguous 2-D images in the forward-looking direction. In contrast to traditional SAR systems, phase error compensation for FLMC-SAR imaging encounters the following two challenges. On the one hand, the array errors caused by the 3-D attitude angles introduce time-varying phase errors, adding complexity to the compensation. On the other hand, the spatial-domain resources used to resolve Doppler ambiguity affect time-domain SAR imaging, resulting in space-time coupling. In this article, a pulse-by-pulse Doppler ambiguity resolving algorithm for FLMC-SAR imaging based on fast factorized back-projection (FFBP) is proposed to achieve the phase errors compensation. In the proposed method, the processing of imaging and resolving Doppler ambiguity over the full synthetic aperture is decomposed into several pulse-by-pulse processing. Within this pulse-by-pulse processing framework, we modified the BP integral function after incorporating motion compensation (MOCO) and array error compensation, ultimately achieving unambiguous FLMC-SAR imaging results through the processing of “space-time combination.” In addition, the FFBP framework is utilized to accelerate the proposed FLMC-SAR imaging and Doppler ambiguity resolving. Extensive simulations and real-data experiments confirm that the proposed algorithm is capable of addressing time-varying phase errors and achieving unambiguous FLMC-SAR imaging results.

Multichannel forward-looking synthetic aperture radar (FLSAR) imaging presents challenges due to spatiotemporal coupling, especially in wide-beam scenarios. This article introduces a new polar format algorithm (PFA) called the forward-looking polar format algorithm (FL-PFA) for wide-beam FLSAR imaging. The proposed algorithm utilizes a time-space–time hybrid scheme to address the spatiotemporal coupling, matching the spatiotemporal structure of FLSAR echoes. Furthermore, the scheme combines spatial-variant motion compensation (MOCO) and polar format imaging, resulting in an efficient processing flow. For spatial-variant MOCO, this article introduces an adaptive subaperture topography- and aperture-dependent (ASATA) algorithm, offering the advantage of balancing compensation accuracy and efficiency using adaptive optimal subapertures. Subsequently, a novel PFA is proposed to obtain a focused FLSAR image. In the PFA, the azimuth angle wavenumber considers both the spatial-variant quadratic phase and residual motion errors, aligning with the spatial-variant Doppler modulation rate characteristic of FLSAR. By resampling the azimuth angle wavenumber, a well-focused FLSAR image on the polar coordinate grid and more accurate MOCO can be achieved simultaneously. Finally, extensive experiments using simulated and actual synthetic aperture radar (SAR) data demonstrate the superiority of FL-PFA.

Forward-looking multi-channel synthetic aperture radar (FLMC-SAR) is of the capability to achieve unambiguous 2-D images in the forward-looking slight direction. FLMC-SAR imagery usually suffers from relatively low spatial resolution as only limited Doppler diversity can be generated from the synthetic aperture. In this article, a sparsity-driven resolution enhancement algorithm is proposed to improve the resolution FLMC-SAR image of the forward-looking area. Different from conventional beamforming processing to resolve the FLMC-SAR left–right ambiguity, a Bayesian sparsity reconstruction optimization is developed for jointly ambiguity resolving and resolution enhancement in the azimuth angle image domain. The spatial structure of the target in the preliminary image domain is used as the signal sparsity with prior information to solve the constrained optimization problem for FLMC-SAR image resolution enhancement. A local least square estimator of the prior noise and signal statistics in the FLMC-SAR nonisotropic image is established in terms of determining the sparsity weight parameter. Extensive simulation and real FLMC-SAR data experiments confirm that the proposed algorithm is capable of achieving the unambiguous and resolution-enhanced FLMC-SAR image.

High-squint and wide-beam Synthetic Aperture Radar (SAR) imaging is challenging for current popular SAR imaging algorithms because the severe spatial-variant motion error precludes the precise Motion Compensation (MOCO). Especially the azimuth-variant motion error (AVME) would bring not only the azimuth-variant phase error but the non-negligible Nonsystemic Range Cell Migration (NsRCM). This paper proposes a novel SAR imaging algorithm to deal with the NsRCM and the azimuth-variant phase error in high-squint and wide-beam SAR imaging. For Range Cell Migration Correction (RCMC), a Parametric Keystone Transform Algorithm (PKTA) introducing the three-axis trajectory deviations as parameters is developed. It can correct the nominal RCM and the NsRCM through a time-variant scaling transform along slow time. The robust RCMC paves the way to precisely compensate for the azimuth-variant phase error. Following, a fast and precise subaperture MOCO algorithm, which applies the Recursive Discrete Fourier Transform (RDFT), is embedded in the azimuth focus procedure to adjust the azimuth-variant phase error. The proposed algorithm can handle the high-squint and wide-beam SAR data with severe motion errors based on these improvements. Finally, extensive experiments with simulated and real-measured SAR data demonstrate the proposal’s superiority and robustness.

Due to the flexible configuration and maneuvering platform, bistatic synthetic aperture radar (SAR) plays an important role in modern remote sensing applications, but the non-ideal track simultaneously introduces model mismatch and spatial-variant phase problems. This paper proposes a sub-aperture parametric polar format algorithm (PFA) for high-resolution bistatic spotlight SAR imaging. First, a bistatic parametric polar format algorithm is proposed to focus on the generally configured bistatic SAR data. A high-precision range model in the bistatic range and ellipsoid parameter angle coordinate space is established to modify the PFA interpolation kernels. To further enhance the azimuth resolution, the PFA sub-images are fused in the image domain based on the coordinate transformation between the unified Cartesian coordinates and local imaging polar coordinates. During the sub-image fusion, in order to ensure the accurate projection and non-aliasing spectrum, we also consider the geometric deformation of the coarse PFA image and analyze the wavenumber support region along with the Nyquist sampling requirement. This novel sub-aperture method, which is theoretically more efficient than the fast back-projection algorithm, alleviates the limitation of full aperture resolution on PFA’s depth of focus. Finally, our method is applied to the general bistatic spotlight SAR data, involving the level-flight airborne transmitter and the dive hypersonic vehicle-borne receiver, and the results of both points and distributed targets demonstrate its effectiveness and efficiency.

Under the special geometric model of bistatic forward-looking synthetic aperture radar (SAR), the 2-D spatial variation problem makes it difficult for traditional algorithms to achieve well-focused imaging, which limits the imaging area. In this letter, from the perspective of range-azimuth decoupling of signal, dechirping processing and keystone transform are used to realize range-variant phase compensation and range cell migrations (RCMs) correction. Based on the range-azimuth decoupled signal, the overlapped subaperture processing can eliminate the azimuth-variant quadratic chirp rate phase in each range cell. Experimental results demonstrate that the proposed method is suitable for the bistatic forward-looking SAR (BFSAR) system to solve the 2-D spatial variation problem and achieve well-focused imaging.

Current subaperture-based azimuth-variant motion compensation algorithms for synthetic aperture radar (SAR) imagery usually suffer from the challenge of keeping high precision and efficiency simultaneously. In this letter, a novel motion compensation approach is developed to precisely correct the azimuth-variant motion errors. The proposed algorithm applies a time-domain filter to implement the precise Subaperture-to-Pulse correction, providing a promising azimuth-variant phase correction. Extensive experiments demonstrate the superiorities of the proposal with real-measured high-squint SAR data.

Forward-looking multichannel synthetic aperture radar (FLMC-SAR) is an important tool for modern remote sensing applications, which has the capability to reconstruct the high-resolution image of the front area. However, due to the azimuth-variant characteristics of the motion errors over a long aperture, FLMC-SAR data processing is usually a challenging task, especially when involving the motion compensation (MOCO) coupled with Doppler ambiguity resolving. To accomplish an accurate MOCO for FLMC-SAR, a novel parametric azimuth-variant MOCO approach is proposed in this article. Aiming at the coupling problem of MOCO and Doppler ambiguity resolving over the full aperture, we can decouple them through the subaperture division. As a full synthetic aperture is decomposed into several subapertures, the high-order motion errors of the full aperture can be decomposed into the first-order motion errors of the subaperture. On this basis, the mismatch of the space–time spectrum caused by the motion errors can be solved by spectral estimation, yielding Doppler ambiguity resolving for each subaperture. Meanwhile, the azimuth-variant characteristic of motion errors in FLMC-SAR system is characterized by a parametric angle-dependent quadratic phase error (QPE) model. The motion parameters are estimated by a joint multichannel angle estimation-based signal quadratic decomposition method. Immediately, the MOCO for ambiguous targets with different motion errors can be processed separately to improve the imaging performance. Experimental results based on both simulated and real data demonstrate that the proposed method is suitable for FLMC-SAR system.

The success of Deep Learning and its potential use in many safety-critical applicationshas motivated research on formal verification of Neural Network (NN) models. In thiscontext, verification involves proving or disproving that an NN model satisfies certaininput-output properties. Despite the reputation of learned NN models as black boxes,and the theoretical hardness of proving useful properties about them, researchers havebeen successful in verifying some classes of models by exploiting their piecewise linearstructure and taking insights from formal methods such as Satisifiability Modulo Theory.However, these methods are still far from scaling to realistic neural networks. To facilitateprogress on this crucial area, we exploit the Mixed Integer Linear Programming (MIP) formulation of verification to propose a family of algorithms based on Branch-and-Bound (BaB). We show that our family contains previous verification methods as special cases.With the help of the BaB framework, we make three key contributions. Firstly, we identifynew methods that combine the strengths of multiple existing approaches, accomplishingsignificant performance improvements over previous state of the art. Secondly, we introducean effective branching strategy on ReLU non-linearities. This branching strategy allows usto efficiently and successfully deal with high input dimensional problems with convolutionalnetwork architecture, on which previous methods fail frequently. Finally, we proposecomprehensive test data sets and benchmarks which includes a collection of previouslyreleased testcases. We use the data sets to conduct a thorough experimental comparison ofexisting and new algorithms and to provide an inclusive analysis of the factors impactingthe hardness of verification problems.

Traditional synthetic aperture radar (SAR) imaging is limited to achieve the high-resolution image of the side-looking areas. Nevertheless, equipped with a small size linear array across the trajectory, forward-looking multichannel SAR (FLMC-SAR) is capable of reconstructing the high-resolution image of the front area. In FLMC-SAR imaging framework, the left-right Doppler ambiguity is expected to resolve with beamforming approaches using the multichannel system diversity. However, beamforming-based Doppler ambiguity resolving is sensitive to the array deviation angle, which causes a mismatch between the azimuth angle and Doppler frequency. In this article, we propose an array deviation angle calibration and imagery algorithm for FLMC-SAR. The space-time characteristic of FLMC-SAR is explored and the range-dependent array deviation angle model is established. Following the Doppler beam sharpening imaging, strong targets are selected to derive the mismatch of the space-time characteristic. A maximum likelihood estimation of the array deviation angle is developed to modify the matching between the azimuth angle and Doppler frequency. Therefore, the left-right Doppler ambiguity can be solved correctly, yielding high-resolution FLMC-SAR imagery. Extensive simulation and real data experiments are performed to demonstrate the effectiveness of the proposed method.