This letter presents a novel method to resolve the ambiguity in forward-looking radar systems. Traditional methods for ambiguity suppression face challenges with antenna deviations and the ill-conditioning of measurement matrices. To address these limitations, we introduce a deviation-adaptive unfolding network (DAUNet), which integrates perturbed compressive sensing (PCS) and advanced deep learning techniques. The DAUNet efficiently handles the space variance of the measurement matrix by utilizing matrix direct summation and the Kronecker product and modeling the ambiguity suppression as a unified PCS problem. This method incorporates iterative learning processes and a novel neural network architecture to reconstruct ambiguity-free images from multichannel forward-looking radars. Simulation results demonstrate that our approach significantly outperforms the existing methods in handling both point targets and distributed scenarios.

This article presents a robust and efficient method for recovering missing data in sub-Nyquist synthetic aperture radar (SAR) using matrix completion (MC) techniques. Unlike previous MC-based methods that have limitations on the required data properties, such as broadside-looking mode, sparse target scenarios, distributed missing, or low missing data ratios (MDRs), our method is capable of handling consecutively clustered missing data and high MDR, even in the presence of weakened spectrum sparsity caused by squint-looking mode or dense target scenarios. Our approach involves arranging the incomplete SAR echo data from a single range-time sampling instant into a Hankel structured matrix and recovering it using nuclear-norm-based convex relaxation and an augmented Lagrangian multiplier (ALM) method. To address computational complexity, we propose segmenting the SAR echo data into smaller slices and providing guidelines for selecting an appropriate slice size. We demonstrate the effectiveness and accuracy of our method through extensive experiments using simulated data and realistic Radarsat-1 data. The experiments cover various challenging conditions, including squint-looking mode, dense target scenarios, wide-swath coverage, high MDR, and clustered missing. The results highlight the capabilities of our method in handling sub-Nyquist SAR data recovery, even in challenging scenarios. Our proposed method offers a robust and efficient solution for recovering missing SAR data.

Despite the success of compressive sensing (CS) algorithms in sub-Nyquist SAR imaging, they lack a generalized ambiguity-depression capability and suffer from high computational complexity. To address these weaknesses, we propose a novel imaging approach that simultaneously suppresses ambiguity introduced by nonuniform sampling and non-ideal azimuth antenna patterns, while enhancing resolution performance for wide-swath sub-Nyquist SAR imaging. To improve efficiency, we employ the randomized block coordinate descent based on the accelerated fast iterative shrinkage threshold algorithm (FISTA) to obtain the desired ambiguity-free image. In the accelerated FISTA, we incorporate two measures to reduce computational complexity. Firstly, we analytically formulate the update stepsize using the singular-value perturbation theory, Kronecker product technique, and orthogonality of the uniformly discrete Fourier matrix. This enables efficient computation of the Lipschitz constant. Secondly, we expedite the computation of the gradient matrix through efficient frequency domain techniques. Numerical results using both simulated data and realistic SAR echo validate the effectiveness of our proposed method and demonstrate its advantages over existing algorithms.

Due to the unequispaced pulse repetition interval (PRI), the low-oversampling ratio and the range-variant blockage, the echo of the low-oversampled staggered SAR (LS-SAR) is nonuniformly sampled with sub-Nyquist and range-variant rate. However, the existing LS-SAR processing methods lack robustness with regards to the scenario type and the PRI variation mode. In this article, a compressive-sensing-based image reconstruction method for the LS-SAR is proposed. First, a hybrid-domain model (HDM) of the LS-SAR echo is presented. In the HDM, the coupled range cell migration (RCM), the unequispaced PRI, and the conflict blockage are formulated as the matrix multiplications with a 3-D tensor, a 2-D matrix, and a Hadamard product, respectively. Based on the HDM, the image reconstruction is realized through the 2-D fast iterative shrinkage thresholding algorithm (ISTA), in which the gradient is derived by exploiting the properties of the tensor and matrix trace. The fast Fourier transform (FFT) and the nonuniform FFT are implemented to accelerate the computation. Due to good accommodation of the RCM and the LS-SAR sampling characteristics, the proposed method can work well for various PRI variation modes and scenario types. Simulations using the point scatter and the distributed target with wide-swath extension demonstrate the effectiveness as well as the robustness of the proposed method.

Staggered SAR is an advanced radar mode which can get the ability of high azimuth resolution and wide range swath simultaneously. Due to the serious spectrum-aliasing, the azimuth ambiguity occurs in the imaging result and brings the wrong amplitude and phase. To reconstruct the images without ambiguity, traditional model-driven methods and data-driven methods cannot have good performance on removing the artifacts and maintaining the real targets meanwhile. In this paper, we consider this task as a pixels process problem and then propose a pixel-wise deep reinforcement learning method to handle it. The proposed method obtains the best comprehensive performance comparing with other method. In addition, its validity is also verified in experiment.

This paper focuses on processing low oversampling echo data of staggered synthetic aperture radar (SAR). In staggered mode, the non-uniformly sampling and echo data loss cause severe azimuth ambiguity. To solve this problem, we propose a method combining the compressed sensing (CS) tool and the conformal Fourier transform (CFT) algorithm. First, the 2-D-fast iterative shrinkage thresholding algorithm (FISTA) is used to efficiently solve the optimization problem based on CS theory to recovery the missing data. Second, the CFT algorithm is used to accurately compute the spectrum of the non-uniformly sampled echo data. Unlike other methods suiting fast pulse repetition interval (PRI) change only, this method performs well for both fast and slow PRI change. Plus, the proposed method can be well applied to both point and distributed targets. Simulation results demonstrate that the proposed method can effectively and robustly suppress the azimuth ambiguity for staggered SAR data.

Staggered SAR can simultaneously get the ability of high azimuth resolution and wide range swath. However, it also causes pairs of azimuth ambiguities on imaging result because of its non-uniform sampling mode. In this paper, we proposed an innovative ambiguity removal method based on deep learning algorithm with a deep fully convolution and residual neural network. Traditional techniques are constrained in the steps of signal recovering and resampling thus only work at high over-sampling rate. Different from them, the deep learning method doesn't need to record the lost pulses for signal reconstruction and performances well at low over-sampling rate. The simulation results verify the effectiveness of our method and it behaves better than other traditional method.

Staggered SAR is an innovative 2-D imaging system utilizing the digital beam-forming (DBF) technique and the continuous variation of pulse repetition frequency (PRF). However, due to the PRF variation, the echo data in the azimuth is non-uniformly sampled. To achieve good imaging quality, it is indispensable to interpolate the data of the staggered SAR to be uniform before further imaging processing. In order to realize efficient interpolation for different PRF variation schemes, we propose a non-uniform fast Fourier transform (NUFFT)-based interpolation method to resample the non-uniform data of the staggered SAR in this paper. The complexity of the proposed interpolation method is in the order of O(MlogM), where M is the number of azimuth sampling. Simulation is performed based on the echo data of point target from the staggered SAR.

In this letter, an efficient imaging algorithm is proposed for reconstructing the spaceborne/airborne bistatic synthetic aperture radar (SA-BSAR) data acquired with a high squint angle. By utilizing the Taylor expansion and the chain rule for derivatives of composite function, the expression of the SA-BSAR ideal matching filter is converted to a 2-D nonuniform discrete Fourier transform (NUDFT). Due to neither input nor output data of the NUDFT being equispaced, nonuniform fast Fourier transform of type 3 (NUFFT-3) is implemented to speed up the SA-BSAR image reconstruction. The computation complexity of the proposed imaging algorithm is O(MNlogMN), where MN is the number of the image pixels. Simulation results demonstrate the validity of the proposed algorithm.

In this paper, a generalized frequency domain imaging algorithm is proposed for focusing data from the bistatic SAR (BSAR) with arbitrary geometry configurations. The proposed algorithm is derived from the ideal frequency-domain spectrum of arbitrary BSAR, which is achieved from the method of the series reversion (MSR). By implementing the 2-D linear regression, the process of the ideal frequency domain imaging reconstruction of arbitrary BSAR is fitted to be a two-dimensional non-uniform discrete Fourier transform (NUDFT). Then the Non-Uniform Fast Fourier Transform of type 3 (NUFFT-3) is used to compensate of the space-variance of BSAR data. Simulation results demonstrate the validity of the proposed algorithm.

An accurate and concise analytic expression of the two-dimensional spectrum and a modified Omega-K is presented in this paper. The proposed spectrum is obtained by utilizing the curve fitting method and the principle of station phase (POSP) for the general bistatic SAR(GBiSAR). Firstly, the range history of SA-BSAR is fitted into a hyperbola function of the sampling time in least square theory(LST). Then the new function of the range history is easy to perform the POSP to obtain the analytic spectrum. Next, based on the concise two-dimensional spectrum, the modified frequency algorithm Omega-K (MWK) is introduced to deal with the echo of SA-BSAR. Due to the range history's approximation in the derivation of 2D spectrum, the equivalent velocity variable has the non-ignorable space variance for the non-reference points. Therefore, the serious spatial-variant is handled by using the Taylor expansion about the equivalent velocity variable. Then the non-uniform fast Fourier transform is applied to substituting the STOLT interpolation and inverse Fourier transform (IFFT) to enhance focusing performance. Finally, numerical simulations are performed to validate the proposed spectrum and algorithm.

Angular resolution of real aperture radar is limited by the aperture size and wavelength. In this paper, a novel angular superresolution algorithm based on Fourier-Wavelet regularized deconvolution (ForWaRD) is proposed. Orthogonal expansion and scalar shrinkage in a tandem transform domain lie at the core of the ForWaRD. Duo to deconvolution is a noise sensitive process, the method is used to deconvolve and denoise the echo signal simultaneously. We also conclude that optimum performance of this algorithm is simultaneously determined by the Fourier structure of the antenna pattern and the wavelet structure of the surface scatterers. Simulation results show that the algorithm can efficiently enhance the resolution of scanning radar under a low SNR environment.

Near space slow speed SAR owns the ability of sustainable and large-scene imaging. However, the output speed of azimuth image is slow due to the slow speed motion, which is a disadvantage for some applications. In this paper, the terrain observation by progressive scans (TOPS) mode is applied in near space slow speed SAR, and the signal properties are analyzed.

In this paper, we present an accelerated fast factorized back-projection algorithm designed for bistatic SAR data. This method supports a precise bistatic SAR image reconstruction and can attain high execution efficiency. Key to this method is the optimized parallel implementation of the original algorithm that can be executed on GPU. We make effort to a parallelization of factorized back-projection by a reasonable parallel strategy so that it can be implemented by CUDA on GPU. Moreover, we also do some optimization for a further improvement, including memory optimization and phase compute optimization, and when it comes to the translational-invariant data, an extra slant range compute optimization have been done yet. The validity and advantage of proposed approach are verified by simulated X-band bistatic SAR data and experimental data.

In this paper, a frequency domain imaging algorithm is proposed for the spaceborne/airborne bistatic synthetic aperture radar (SA-BSAR) with highly squint angle. The imaging processing is carried out with the following two stages. In the first stage, the space-invariant part of the raw spectrum data is compensated by multiplying with the conjugate of the spectrum from the reference target. In the second stage, the two-dimensional space-variant component, which manifests obvious nonlinear coupling between the range frequency and the Doppler frequency in the high squint case, is effectively corrected by the two-dimensional non-uniform fast Fourier transform (NUFFT) operation. The computation burden of the proposed imaging reconstruction method is O(MN logMN), where MN is the number of the image pixels. Simulation experiments demonstrate the validity of the proposed method.

Focusing bistatic SAR data in frequency domain requires the two dimensional (2D) point target reference spectrum (PTRS). In this paper, a 2D PTRS is derived based on Lof feld's bistatic formula (LBF). The spectrum in this paper combines the influence of the Doppler centroids and frequency modulated rates of the transmitter and receiver on the total Doppler contributions. The essential of this paper is to model the Doppler contributions of the transmitter and the receiver using power series. It can be used in extreme bistatic (like hybrid spaceborne/airborne) and high squint (like bistatic forward-looking) cases. The accuracy of the PTRS is verified using numerical simulation of point target.

In this paper, we present a fast imaging method based on subaperture approximation (SA) technology for 3-D microwave imaging. Compare to 2-D microwave imaging, one of main problems in 3-D microwave imaging is its high computational cost caused by dimension expansion from 2-D to 3-D. This problem limits the application of 3-D microwave imaging. In practice, many 3-D imaging regions contain no targets or are shadowed by other scatterers, which is the sparse character of 3-D imaging regions. Based on this character, we propose a fast imaging method using the SA technology. The basic concept of the SA technology is using subapertures to pick out the regions of interest, then image in the regions of interest. The computational cost of this method is analyzed, and some experimental results are conducted to demonstrate the feasibility of this method. We find that the computational cost of SA 3-D imaging method is far smaller than that of the 3-D BP imaging method.

In this paper, a modified two-step RCMC method is proposed for SA-FBSAR. Comparing with the traditional two-step method, the sequence of the two-dimensional RCMC operations is altered to accommodate the significant nonlinearity of RCM in SA-FBSAR, and the influence of such modification on imaging process is taken into account. Simulation results with point scatterers demonstrate the validity of the proposed RCMC method.

The back projection (BP) algorithm is highly effective in bistatic SAR imaging. But it is time-consuming for the large scene imaging. In this paper, we propose a GPU-based parallel BP algorithm, the range compression and back projection are implemented on the graphics processing unit (GPU) using CUDA language. We also present some optimum methods including memory optimization, phase accumulator reduction and imaging scene segmentation to implement fast and large scene imaging. Numerical experiments demonstrate that the GPU-based method can significantly improve the computational efficiency of the original BP algorithm, about 80 times faster, while the imaging scene size same as the CPU-based BP algorithm.

To better understand the fundamental of the spaceborne/airborne hybrid bistatic SAR (SA-BSAR) image formation, the range cell migration (RCM) of the SA-BSAR is studied in the range-Doppler domain, where the RCM in SA-BSAR can be explicitly expressed in close form. Through the analysis of RCM relationship with target's azimuth and range position, we can find that, because of the system platforms' velocity difference along the azimuth direction, the RCM in SA-BSAR is 2D space variant. Therefore, the fundamental of frequency-domain image formation in SA-BSAR is to process the 2D space-variant RCM correction (RCMC) for nonreferent targets besides the bulk RCMC operation in the frequency domain. Furthermore, appropriate solutions in the frequency domain to remove the RCM in SA-BSAR are proposed and verified with five-point-target simulation.

A frequency domain imaging algorithm for the hybrid spaceborne/airborne BSAR is presented. The key point of deriving the algorithm is the analytical evaluation of the system point target response's 2-D spectrum. To overcome the difficulty of resolving analytical solution for the stationary phase point, the spectrum's phase is approximated by two-order Taylor expanding around the point, which is not only in the neighborhood of the system's corresponding stationary phase point but also can be obtained analytically. Thus the approximated analytical spectrum is pretty close to the actual one. In the imaging algorithm, both range-dependent range cell migration and azimuth-dependent range cell migration are compensated in two steps: Inverse Scaled Fourier Transform which can be realized through the chirp z-transform and phase multiplication. The validity of the algorithm is demonstrated by experiment with the simulated data.