IEEE Geoscience and Remote Sensing Magazine - December 2022 - 37

applications. A diverse group of refined SBL algorithms
has been extensively researched using tree structure, block
structure, and so on.
With the development of sparse Bayesian methods in CS,
the related technology is gaining rapid popularity in radar
imaging. For SAR imaging, the BCS approaches have been
addressed for imagery improvement in both the resolution
and quality, having two major advantages: 1) they can be
used to alleviate the drawback of necessary parameter tuning,
whereas the regularized methods suffer from the difficulty of
hyperparameter selection, and 2) under certain conditions,
the stable imaging performance of global optimization can
be highly guaranteed compared with other class methods.
Accordingly, BCS is adopted in many applications of SAR
imaging, such as superresolution, sparse aperture imaging,
autofocusing, parametric imaging of a maneuvering target,
and so on. In particular, inspired by model-based BCS, the
TABLE 1. A SUMMARY OF CS ALGORITHMS.
SAR IMAGING APPLICATIONS
CLASSES
Greedy
algorithms
BASIC PRINCIPLE AND
CHARACTERISTIC
Basic principle: Decompose the
sampled data using several atoms,
and iteration is used to retrieve the
useful components of underlying
signal.
Characteristics:
Low complexity and simple
geometric interpretation
Sensitive to the data quality and
quantity, especially when faced with
highly missing or corrupted data
Convex
algorithms
Basic principle: Convex relaxation
is achieved by replacing the L0norm
optimization with some
reasonable approximations, such
as the Lp-norm (0 1 p # 1).
Characteristics:
High precision and robustness to
the data quality and quantity
Sensitive to regularization
parameter tuning
TYPICAL ALGORITHMS
1) MP [85], GP [88],
CoSaMP [84], SP
[89], etc.
2) IHT [94], IST [95],
AMP [96], etc.
3) Model-based CS
[90], Kronecker CS
[91], and structured
CS [92]
1) BP [38], BPDN [39],
etc.
2) IRSL [104], [105];
reweighted L1-norm
[105]; reweighted
L2-norm [104]; etc.
3) Sparse coding,
K-SVD [129], etc.
REPRESENTATIONAL TASKS
Data interpolation: [29], [41], [48],
[108], [159], [171], and [179]
Maneuvering target imaging: [26],
[27], [100], [101], [102], [126], [171],
and [179]
Multidimensional imaging: [48],
[181], and [189]
IMAGING APPLICATION
EXAMPLES
ISAR: [26], [27], [29], [99],
[100], [101], [102], [126], [171],
and [179]
SAR: [41], [107], [108], [199],
and [182]
SAR GMTI: [181] and [189]
3D SAR: [48]
SAR imaging community is also investigating the structured
sparsity model, which is capable of providing more promising
[104] imaging performance.
In summary, Table 1 lists the three class methods, addressing
their characteristics, limitations, and applications.
α
θ1
θ2
a
s
NM
θ3
θ4
FIGURE 4. A graphical representation of a hierarchical model
(a scaled Gaussian mixture). a: sparse signal with the size of N*1;
s: sampling echo data with the size M*1.
β
Data interpolation: [10], [11], [15],
[16], [17], [24], [25], [28], [32], [42],
[49], [51], [52], [53], [54], [116], [118],
[121], [135], [138], [159], [160], [161],
[162], [166], [174], [180], [186], and
[193]
Feature enhancement: [12], [13],
[20], [21], [33], [66], [67], [83], [103],
[109], [110], [111], [117], [118], [119],
[120], [134], [139], [157], [158], [164],
[173], [185], [192], and [194]
Maneuvering target imaging: [46],
[47], [124], and [140]
Phase error correction: [28], [123],
[125], [172], [180], [183], and [187]
Multidimensional imaging: [51],
[52], [53], [54], and [67]
Bayesian
algorithms
Basic principle: Statistical image
formation uses the SBL method; the
posterior approximation is achieved
via various hierarchical models
and an expectation-maximization
solution.
Characteristics:
High accuracy with full posterior
High efficiency with free parameter
tuning
Performance that depends on the
statistical model and solution
SBCS: structured BCS; SVD: singular value decomposition.
DECEMBER 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
37
1) BCS [127], SBL
[128], etc.
2) Multitask BCS [131],
SBCS [93], etc.
3) Bayesian dictionary
learning [106] etc.
Data interpolation: [50], [82], [112],
[114], and [124]
Resolution enhancement: [13],
[113], and [175]
Model error correction: [81] and
[124]
Multidimensional imaging: [50]
and [82]
ISAR: [12], [13], [24], [25], [28],
[32], [42], [130], [138], [161],
[172], [180], [183], [185], and
[186]
SAR: [20], [21], [33], [66], [83],
[107], [109], [110], [111], [115],
[117], [119], [120], [121], [123],
[125], [135], [139], [157], [158],
[159], [160], [164], [174], [187],
[192], and [194]
SAR GMTI: [46], [47], [103],
and [140]
3D SAR: [11], [15], [16], [17],
[48], [49], [52], [53], [54], [67],
[116], [118], [134], [173], [191],
and [193]
ISAR: [13], [81], [112], [113],
[114], [124], and [175]
SAR: [43] and [50]
3D SAR: [50] and [82]
IEEE Geoscience and Remote Sensing Magazine - December 2022

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