IEEE - Aerospace and Electronic Systems - March 2021 - 63

Kechagias-Stamatis and Aouf
Table 7.

Sparse Representation Classiﬁcation
No

Reference

SAR chip
size

Pre-processing

Data
augmentation

Main features

1

Wei et al. [68]

128x128

-

-

l1;1 À norm

2

Miao and Shan [83]

128x128

-

-

multiple target views (6)

3

Liu and Chen [73]

80x80

normalization

-

l2 À norm, D-S theory of evidence,
maximum belief rule

4

Ren et al. [79]

64x64

-

-

Tikhonov regularization matrix,
learned dictionary

5

Ren et al. [85]

64x64

-

-

weighted regression strategy

6

Chang and You [75]

128x128

normalization, noise filtering,
morphological operations

-

two-stream SRC, score-level
fusion

7

Huang et al. [86]

128x128

-

-

multiple target views (3)

8

Liu et al. [78]

80x80

normalization

-

statistical dictionary learning

9

Zhang [70]

128x128

-

multiresolution

l0;2 À norm

10

Ding and Wen [71]

128x128

-

multiresolution

l0 À norm, l2 À norm minimum
reconstruction error

11

Li et al. [80]

80x80

-

-

analysis dictionary learning

12

Zhang and Liu [72]

128x128

-

multiresolution

l0;2 À norm

13

Zhang et al. [82]

64x64

-

-

multiple target views (6) þ l0 À
norm

Zhang [70] proposed a multistream SRC configuration, where each stream utilizes the target image under
different resolution. The SRC scheme employs a l0;2 À
norm, which is a mixed lp À norm variant that first
applies the l0 À norm on each row of the dictionary
matrix, and then the l2 À norm on the resulting vector.
Ding and Wen [71] also suggest a multiresolution method,
but augment the SRC dictionary by creating multiple SAR
images of lower resolutions originating from the original
templates. Similarly, Zhang and Liu [72] augmented the
templates with multiresolution representations, which
then undergo a Principal Component Analysis (PCA) prior
to the SRC scheme. Liu and Chen [73] weaken the influence of the target aspect angle sensitivity by normalizing
the reconstruction error ek and thus enhance the contribution of the templates with small ek values. Finally, the normalized errors are fused via the Dempster-Shafer theory
[62] and the final target classification relies on the maximum belief rule [74]. Chang and You [75] decoupled the
three main contributors of the SAR imagery, i.e., target
region, shadow, and background, and input the segmented
target (target region and shadow) along with the original
image into two distinct SRC pipelines. Then, both classification results are combined by a score-level fusion for target recognition.
Driven by the conclusion that sparse models learned
from training samples have more advantages than the predefined ones [76], [77], Liu et al. [78] generated a discriminative statistical dictionary learning (DSDL) technique to
MARCH 2021

enhance the SRC performance. The discriminative nature
of the DSDL is further enhanced by manipulating the dictionary entries by minimizing the intraclass differences
and maximizing the interclass differences. Similarly, Ren
et al. [79] proposed a class-oriented dictionary learning
scheme. The latter modifies (4) by adding the Tikhonov
regularization matrix G :
aÃ ¼ arg minky À Xa k22 þg kGak1
a
3
2
0
di;j ðxi;j ; ai;1 Þ Á Á Á
7
6
..
..
..
7:
G¼6
.
.
.
5
4
0
Á Á Á di;j ðxi;j ; ai;nk Þ

(8Þ

(9Þ

Li et al. [80] suggested a hybrid-structured synthesis
dictionary to better reflect the interclass target differences
that incorporate a learned dictionary D s , which is the
same for all templates and reduces the effect of common
features, such as the high similarity caused by specular
reflection. Rather than using the processing costly nonlinear l0 À norm and l1 À norm sparsity regularizers, the
authors employ an analysis dictionary P [81] to create the
coding coefficients of the dictionary by linear projection.
Opposing to the previous methods that utilize a single
target aspect, several SAR ATR pipelines exploit multiple
target aspects. Joint SRC [82] for example, exploits three
target views to increase the completeness of the target's
SAR signature and then utilizes a mixed l0;2 À norm. The
reason for using multiple views is that these are highly

IEEE A&E SYSTEMS MAGAZINE

63
IEEE - Aerospace and Electronic Systems - March 2021

Table of Contents for the Digital Edition of IEEE - Aerospace and Electronic Systems - March 2021
