With regard to inverse synthetic aperture radar (ISAR) imaging, traditional range-Doppler (RD) algorithm is inapplicable to sparse aperture. Although compressive sensing (CS) algorithm can overcome this problem, the imaging resolution is not high enough. When deep learning (DL) is applied to ISAR imaging, some problems may also occur, such as network complexity, the selection of labels in network training, the influence of noise and sparse aperture, and the loss of weak scattering points in network test. In order to solve the above problems, a joint fast iterative shrinkage-thresholding algorithm (FISTA) and Visual Geometry Group Network (VGGNet) high-resolution imaging method is proposed in this paper. In the proposed method, FISTA is presented to reduce the impact of noise and sparse aperture. The high-resolution processing network (HRPN) is built based on VGGNet. Then, combined with peak extraction technology, the random ideal scattering points are utilized to construct the training/validation set. Meanwhile, the training process of HRPN is analyzed theoretically, and the network test strategy is designed by the differences between the test set and the training/validation set. Extensive experiments based on both simulated and measured data demonstrate that the proposed method has good imaging performance and small network complexity.

Accurate translational motion compensation (TMC) is the key procedure of inverse synthetic aperture radar (ISAR) imaging. Under the condition of sparse aperture, the correlation of adjacent pulses is severely destroyed, which brings a few challenges to TMC and imaging. Thus, this paper proposes a novel TMC method for ISAR imaging. In this technique, the signal model of joint phase adjustment and ISAR imaging is established first. Then, the process of TMC is designed. That is, after range alignment with improved global minimum entropy (IGME), the range joint fast orthogonal matching pursuit (RJFOMP) algorithm is applied to ISAR imaging, and the minimum entropy method (MEM) is adopted to estimate the phase error. Meanwhile, the joint optimization of phase adjustment and ISAR imaging is realized through the cyclic iteration. Extensive experiments based on both simulated and measured data demonstrate that the proposed TMC method is effective for two modes of motion errors, which are named as coherent mode (CM) and non-coherent mode (NCM), respectively. When RJFOMP is used for joint phase adjustment and ISAR imaging, it has excellent imaging performance under noisy and sparse conditions.

In view of inverse synthetic aperture radar (ISAR) imaging, sparse aperture not only affects the imaging quality of traditional range Doppler (RD) algorithm but also increases the difficulty of translational motion compensation (TMC). For the purpose of reducing the influence of motion errors on the target imaging, reweighted alternating direction method of multipliers (RADMM) is proposed to realize the joint processing of phase adjustment and ISAR imaging. Combined with pattern-coupled sparse structure (PCSS) information of the target, the reweighted $l_1$ norm minimization problem is established first. Then, the minimum entropy method is adopted to estimate the phase error, and the iterative process of RADMM is deduced. Finally, the experimental results based on two sets of measured data demonstrate the validity of the proposed algorithm under the conditions of noise and sparse aperture.

In terms of the target with micromotion parts, the readability of inverse synthetic aperture radar (ISAR) image of the main body is influenced by micro-Doppler (m-D) effects. Some facts, such as radar working modes and electromagnetic environment, may lead to sparse aperture, which further induces high side lobes and makes the removal of m-D effects more difficult. To jointly eliminate m-D effects and the interference introduced by sparse aperture, a novel m-D effects removed ISAR imaging algorithm is proposed. In this technique, sparse ISAR imaging with the removal of m-D effects can be established as an optimization model of joint low-rank and sparse representation, which is a quadruple constraint optimization problem, including the low rank of the high-resolution range profile (HRRP) of the main body, the sparsity of the HRRP of micromotion parts, the sparsity of the imaging result of the main body, and the noise constraint of the echo signal. Furthermore, the matrix factorization method is theoretically presented to simplify the optimization process of the nuclear norm, and the alternating direction method of multipliers is utilized to solve all constructed models efficiently. Experimental results based on both simulated and measured data demonstrate the superiority of the proposed algorithm.

To realize inverse synthetic aperture radar imaging with limited bandwidth and short coherent processing interval, in view of pattern-coupled sparse structure of imaging targets, a two-dimensional joint sparse imaging algorithm, namely two-dimensional reweighted alternating direction method of multipliers (2D-RADMM), is proposed. The main idea of the proposed algorithm contains two aspects: one is expanding one-dimensional RADMM (1D-RADMM) to 2D-RADMM by matrix processing, so as to reduce the computation and memory usage. The other is designing different pattern-coupled modes to further improve the imaging performance. Extensive experiments based on two sets of measured data demonstrate that compared with traditional unweighted algorithms, the proposed algorithm has excellent imaging quality under noisy and sparse conditions, and its imaging time is <2 s, which can be suitable for the real-time inverse synthetic aperture radar imaging.

For inverse synthetic aperture radar (ISAR) imaging of targets with micromotion parts, the removal of micro-Doppler (m-D) effects is the key procedure. However, under the condition of a sparse aperture, the echo pulse is limited or incomplete, giving rise to the difficulty of eliminating m-D effects. Thus, a novel m-D effects removal algorithm is proposed, which can effectively eliminate m-D effects, as well as the interference introduced by noise and sparse aperture in the ISAR image of the main body. The proposed algorithm mainly includes two processing steps. First, combined with the cut-off point determined by the normalized singular value difference spectrum, the rough estimation of the main body is achieved by singular value decomposition (SVD). Then, the variational mode extraction (VME) is extended to complex variational mode extraction (CVME). The constrained variational problem constructed by bandwidth and spectral overlap constraints is solved by the alternating direction method of multipliers (ADMM), and the precise estimation of the main body is obtained. Experimental results based on both simulated and measured data demonstrate that the proposed algorithm can acquire the high-resolution ISAR image of the main body under noisy and sparse conditions.