IEEE Geoscience and Remote Sensing Magazine - December 2022 - 46

in the azimuth dimension, benefitting from the parameter
estimation of target rotation [114], [124], [180]. In particular,
the sparse methods have also been extended to the application
of multidimensional imaging, such as InISAR [27];
SAR GMTI [103], [181]; etc. For multichannel imaging, the
joint sparsity constraints are applied to enforce the correlation
among multidimensional data, providing more precise
image reconstruction, such as 3D geometry reconstruction
[116]. The fast solutions, such as AMP [182], ALM [110], and
ADMM [183], have also been investigated to improve computational
efficiency.
The ML-based MC/TC and matrix/tensor representation
[69], [136], [137], [138] techniques, which can be treated
as data-driven methods, are employed in superresolution
radar imaging. In [136] and [137], the MC approaches
are applied to SAR and ISAR imaging from the data of 2D
random sampling. To further improve the sparse imaging
performance, the joint constraints of sparsity and low rank
are used to further reduce the sparse sampling data amount
[68], [69], [138], [145]. Meanwhile, the RPCA approaches
are also used to deal with the complicated clutter [141]
and micromotion components [185]. For the multidimensional
data, the robust tensor representation is further applied
to effectively exploit the most redundant information
for signal enhancement [67], [134], [136], [173]. Last but
not least, a DNN, which is able to adaptively learn highlevel
features from the input data, is also applied to take
advantage of the free model mismatch and high efficiency
compared with model-based methods. In the following
sections, numerical experiments are performed to evaluate
the sparse imaging performance in terms of superresolution,
including resolution enhancement and sparse aperture
imaging.
EXPERIMENTS ON RESOLUTION ENHANCEMENT
The experimental analysis is implemented using the aforementioned
algorithms to demonstrate the effectiveness on
resolution enhancement. The three groups of algorithms-
greedy, convex, and Bayesian-are applied to include the traditional
MP [100], convex L1-norm [12], BCS [13], and SBCS
[113], respectively. The measured ISAR data of Yak-42 aircraft
are used, and the detailed parameters can be found in [81].
The imaging results of superresolution by a factor of four
times are shown in Figure 7. Meanwhile, the conventional
range-Doppler (RD) and BURG algorithms [176] are taken
as references. Figure 7(a) shows that, in the conventional
RD images, the azimuth resolution is coarse, limited by the
CPI of the used pulses. (The pulse number is 32.) For clarity,
the pulse response in one specified range cell is depicted in
Figure 7(g) and (h). It can be seen that the traditional MP
algorithm cannot resolve more adjacent scatterers, apart
from sharpening of the main lobe and suppression of the
sidelobes. In comparison with the BURG algorithm, most
of the sparse algorithms have better superresolution imaging
performance. The convex L1-norm can provide resolution
enhancement by distinguishing more scatters. However,
46
there is little degradation in the image due to an improper
choice for the regularization parameter. The BCS algorithm
can provide very perfect resolution-enhanced images. Meanwhile,
the structured BCS algorithm can further preserve the
target structure.
Then, the sparse imaging performance is evaluated under
different SNR conditions. The SNR is set as 0, 5, 10, 15
and 20 dB. The factor of superresolution is set as four times.
For clarity, the imaging results of 0 dB using the aforementioned
algorithms are shown in Figure 8. In comparison with
the BURG algorithm, most of the sparse algorithms have a
better performance for noise suppression. Among these algorithms,
the BCS and SBCS algorithms have the best imaging
performances, including the superresolution and noise
reduction. Meanwhile, to quantitatively evaluate the sparse
imaging performance, two metrics-the root-mean-square
error (RMSE) and correlation coefficient (CORR)-are employed.
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