IEEE Geoscience and Remote Sensing Magazine - December 2022 - 52

that the final ISAR image by using the true rotational parameters
has the minimum square error of data fidelity. In
this sense, the refined parameter estimator in (21) has the
advantage of reducing the probability of falling into the
local minimum.
In addition, some interesting studies have also been investigated
to improve the optimization convergence [114].
To model ()H j in sparse ISAR imaging, the MP [99] and
MFT [102] dictionaries are used for well-focused image reconstruction
with azimuth scaling. To consider the MTRC, a
modified MP algorithm is proposed using a strategy of 2D
MP [101]. To improve the sparse imaging performance, a
parametric range-azimuth coupling dictionary is constructed
by involving the rotational speed, and the MAP approach
is employed for high-precision image reconstruction [26],
[179]. In addition, the algorithms of jointly sparse autofocusing
and ISAR imaging have also been addressed to resolve
the residual translational phase error owing to the sparse aperture
[26], [124]. Furthermore, there exists some valuable
research on the sparse aperture imaging of maneuvering
targets, addressing the presence of rotational acceleration
and MTRC [28], [114], [180]. The parametric sparse methods
are used to include the rotational parameter estimation
during sparse imaging [179]. For high-maneuvering targets,
the sparse time-frequency methods [190], such as using the
chirp Fourier dictionary [26], [114], are investigated to deal
with the variation of the imaging plane. In addition, the 3D
geometry and motion estimations of maneuvering targets
are also studied for InISAR with a sparse aperture [27]. For
SAR GMTI, similar studies have also addressed, for example,
parametric sparse methods to address the sparse imaging of
a moving target [181].
In the following sections, an experimental analysis of
motion estimation is performed to evaluate the sparse imaging
performance.
EXPERIMENTS ON SPARSITY-BASED AUTOFOCUSING
In this section, numerical experiments are performed using
the same Yak-42 dataset to confirm the effectiveness of the
sparsity-based autofocusing method. Figure 17 shows the
imaging results of sparsity-driven autofocusing [81] under
three different conditions of phase error, including low-order,
high-order, and random forms. (The SNR is set as 10,
5, and 0 dB). It can be seen that a perfect performance of
the phase adjustment can be achieved in the format of random
phase errors and that a well-focused image can also be
obtained under the condition of low SNR (0 dB). Furthermore,
the conventional PGA-based and minimum-entropy
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FIGURE 12. ISAR imaging using the DL algorithms (CRS, and the sparse sampling ratio is 1/4): (a) FCN [62], (b) RMIST [205], (c) ADMM-net
proposed in [206], and (d) ADMM-net proposed in [207].
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IEEE Geoscience and Remote Sensing Magazine - December 2022

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