Much research has recently been devoted to jointly sparse (JS) signal recovery from multiple measurement vectors using $$\ell _{2,1}$$
 regularization, which is often more effective than performing separate recoveries using standard sparse recovery techniques. However, JS methods are difficult to parallelize due to their inherent coupling. The variance based joint sparsity (VBJS) algorithm was recently introduced in Adcock et al. (SIAM J Sci Comput, submitted). VBJS is based on the observation that the pixel-wise variance across signals convey information about their shared support, motivating the use of a weighted
 $$\ell _1$$
 JS algorithm, where the weights depend on the information learned from calculated variance. Specifically, the $$\ell _1$$
 minimization should be more heavily penalized in regions where the corresponding variance is small, since it is likely there is no signal there. This paper expands on the original method, notably by introducing weights that ensure accurate, robust, and cost efficient recovery using both $$\ell _1$$
 and $$\ell _2$$
 regularization. Moreover, this paper shows that the VBJS method can be applied in situations where some of the measurement vectors may misrepresent the unknown signals or images of interest, which is illustrated in several numerical examples.

Reducing Effects of Bad Data Using Variance Based Joint Sparsity Recovery

The ground moving target (GMT) is defocused due to unknown motion parameters in synthetic aperture radar (SAR) imaging. Although the conventional Omega-K algorithm (Omega-KA) has been proven to be applicable for GMT imaging, its disadvantages are slow imaging speed, obvious sidelobe interference, and high computational complexity. To solve the above problems, a SAR-GMT imaging network is proposed based on trainable Omega-KA and sparse optimization. Specifically, we propose a two-dimensional (2-D) sparse imaging model deducted from the Omega-KA focusing process. Then, a recurrent neural network (RNN) based on an iterative optimization algorithm is built to learn the trainable parameters of Omega-KA by an off-line supervised training method, and the solving process of the sparse imaging model is mapped to each layer of the RNN. The proposed trainable Omega-KA network (Omega-KA-net) forms a new GMT imaging method that can be applied to high-quality imaging under down-sampling and a low signal to noise ratio (SNR) while saving the imaging time substantially. The experiments of simulation data and measured data demonstrate that the Omega-KA-net is superior to the conventional algorithms in terms of GMT imaging quality and time.

/pdf/omega-ka-net-a-sar-ground-moving-target-imaging-network-bqmwrf85.pdf

Omega-KA-Net: A SAR Ground Moving Target Imaging Network Based on Trainable Omega-K Algorithm and Sparse Optimization

This paper proposes a spectrum zoom processing based target detection algorithm for detecting the weak echo of low-altitude and slow-speed small (LSS) targets in heavy ground clutter environments, which can be used to retrofit the existing radar systems. With the existing range-Doppler frequency images, the proposed method firstly concatenates the data from the same Doppler frequency slot of different images and then applies the spectrum zoom processing. After performing the clutter suppression, the target detection can be finally implemented. Through the theoretical analysis and real data verification, it is shown that the proposed algorithm can obtain a preferable spectrum zoom result and improve the signal-to-clutter ratio (SCR) with a very low computational load.

/pdf/low-altitude-and-slow-speed-small-target-detection-based-on-58yl04r1tw.pdf

Low-Altitude and Slow-Speed Small Target Detection Based on Spectrum Zoom Processing

Ground moving targets (GMT), due to the existence of velocity in range and azimuth direction, will lead to the deviation from their true position and defocus in the azimuth direction during the synthetic aperture radar (SAR) imaging process. To address this problem and compress the amount of echo data, a sparse SAR imaging method for ground moving targets is proposed. Specifically, we first constructed a two-dimensional sparse observation model of the GMT based on matched filter operators. Then, the observation model was solved by a deep network, GMT sparse imaging network (GMTSI-Net), which was mainly obtained by unfolding an iterative soft threshold algorithm (ISTA)-based iterative solution. Furthermore, we designed an adaptive unfolding module in the imaging network to improve the adaptability of the network to the input of echo data with different sampling ratios. The proposed imaging network can achieve faster and more accurate SAR images of ground moving targets under a low sampling ratio and signal-to-noise ratio (SNR). Simulated and measured data experiments were conducted to demonstrate the performance of imaging quality of the proposed method.

/pdf/sparse-sar-imaging-method-for-ground-moving-target-via-gmtsi-1y9b1mal.pdf

Sparse SAR Imaging Method for Ground Moving Target via GMTSI-Net

When a target is in complex three-dimensional (3-D) motions, inverse synthetic aperture radar (ISAR) images cannot be obtained with any motion compensation algorithms. In this case, selecting optimal coherent processing interval (CPI) (or frame) of the fixed rotational axis is the only way to obtain focused ISAR images. In this article, we focus on selecting optimal CPI for ISAR imaging of maneuvering targets, and a novel method using tracking information is proposed. Without complex computational procedures, the proposed method provides robust performance. The method includes three steps. First, target’s orientation (roll, pitch, and yaw) is estimated by using an extended Kalman filter. Second, the least-square method is adopted to find the best fitted lines of roll, pitch, and yaw angles in different time intervals, and the linearity degrees of the three rotation angles are measured over the imaging intervals. Third, the thresholds of the linearity degrees are set, according to which, optimal CPIs can be selected. The performance of proposed method is demonstrated using both simulated data and measured data. In both cases, optimal CPIs can be selected and well-focused ISAR images can be achieved.

Optimal Coherent Processing Interval Selection for Aerial Maneuvering Target Imaging Using Tracking Information

In order to reduce the amount of echo data and achieve a wider observation swath, a parametric sparse representation method for the motion parameter estimation of ground moving targets is proposed with low pulse repetition frequency (PRF). First, the displaced phase center antenna technique is introduced to cancel the clutters. Second, since range cell migration is not subject to PRF limitations, Hough transform is adopted to estimate the across-track velocities and range positions of moving targets. Then, the parametric method is put forward to estimate the along-track velocities and azimuth positions based on the parametric over-complete chirplet basis matrix, where the basis matrix is determined by the along-track velocities of moving targets. The proposed algorithm can adaptively refine the basis matrix to achieve the optimal sparse representation result. Meanwhile, the azimuth position is obtained by the optimal sparse representation result. Finally, the feasibility and the effectiveness of the proposed method are proved by the simulation results.

Parametric Sparse Representation Method for Motion Parameter Estimation of Ground Moving Target

This paper concerns the problems of huge data and off-grid effect of cross-track direction in downward-looking linear array (DLLA) 3D SAR imaging. Since the 3D imaging needs a great deal of memory space, we consider the methods of downsampling to reduce the data quantity. In the azimuth direction, we proposed a method based on the multiple measurement vectors (MMV) model, which can enhance computational efficiency and elevate the performance of antinoise, to recover the signal. Further, in cross-track direction, since the resolution is restricted by the length of array, as well as platform size, the influence of off-grid effect is more serious than azimuth direction. Continuous compressive sensing (CCS), which can solve the off-grid effect of the classical compressive sensing (CS), is presented to obtain the precise imaging result under the noise scenarios. Finally, we validate our method by extension numerical experiments.

https://downloads.hindawi.com/journals/js/2017/6207828.pdf

Downward-Looking Linear Array 3D SAR Imaging Based on Multiple Measurement Vectors Model and Continuous Compressive Sensing

The storage and transmission of SAR raw data are two basic challenges of high-resolution real-time SAR imaging. To address these problems, a new approach for processing SAR raw data combined with compressed sensing (CS) and Block adaptive tree-structure vector quantization (BATSVQ) is proposed in this paper. For SAR returned signals, CS is engaged to down-sample the radar echoes in the pulse duration. Then, BATSVQ is employed to diminish encode number of every sample value. The compressed data can be transmitted effectively. In the signal receiver, data reconstruction process contains the two ordinal steps according to BATSVQ algorithm and CS reconstruction. Afterward, the Chirp Scaling imaging algorithm is executed to achieve the final SAR image. The simulation results and analysis validate the effectiveness of the proposed method.

https://ieeexplore.ieee.org/iel7/6648511/6663867/06663970.pdf

A novel compressing method of airborne SAR raw data

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Parametric Sparse Representation Method for Motion Parameter Estimation of Ground Moving Target

Downward-Looking Linear Array 3D SAR Imaging Based on Multiple Measurement Vectors Model and Continuous Compressive Sensing

A novel compressing method of airborne SAR raw data