HRRP classification
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HRRP classification based on multi-scale
fusion sparsity preserving projections
Weilong Dai, Gong Zhang
✉
and Yang Zhang
To improve the accuracy and robustness of high-resolution range
profile (HRRP) target recognition, in this paper, the multi-scale
fusion sparsity preserving projections (MSFSPP) approach is proposed
for feature extraction. Compared with traditional multi-scale feature
extraction method, the proposed MSFSPP approach utilises features
in every scale and their sparse reconstructive relationship to construct
multi-scale fusion features which contain more discriminating infor-
mation. Support vector machine is employed to verify the classification
performance of features extracted by MSFSPP and related feature
extraction methods. Simulation results based on the measured aircraft
datasets show that the proposed MSFSPP approach has outperfor-
mance with a small amount of data.
Introduction: Radar automatic target recognition is an important subject
of radar signal processing. Compared with SAR and ISAR images, high-
resolution range profile (HRRP) is a one-dimensional target signal
which contains a wealth of target information but a relatively small
amount of data [1, 2]. In HRRP recognition system, it is an important
step to extract features which are robust and are easy to recognise.
Traditional HRRP feature extraction methods are mainly concentrated
on single scale, which ignore the global features. Recently, Liu et al.
[3] apply the scale-space theory [4] into HRRP feature extraction,
which takes advantages over single-scale features in respect of recog-
nition. However, features at different scales are recognised indepen-
dently in [3], which results in the isolation of the identification
information between different scales and the expensive complexity of
classification. Considering that HRRP data is typically high-dimensional
and inter-dimension dependently distributed [5, 6], in this paper, we
utilise the internal relationship between multi-scale features to
improve recognition accuracy. Inspired by the idea of sparsity preser-
ving projections (SPP) [7], we propose the multi-scale fusion sparsity
preserving projections (MSFSPP) approach to establish sparse recon-
structive relationship between multi-scale features and reduce the
dimensionality of features. The experimental results based on measured
HRRP datasets of aircrafts validate the superiority of the proposed
approach in accuracy and robustness.
normalised magnitude by two-norm
100 120 140 160 180 200
0
0.05
0.10
0.15
0.20
0.25
0.30
ran
g
e cell
original
scale-0.6
scale-1.2
scale-1.8
scale-2.4
Fig. 1 Multi-scale features with Gaussian kernel
Multi-scale feature extraction of HRRP: According to scale-space
theory, multi-scale presentation of HRRP is realised by the unified
signal sampling under different scale factors. Since the sample of
HRRP is a one-dimensional signal, for an HRRP sample I(g), its 1D
multi-scale extraction is
L(g,
s
) = G( g,
s
) ⊗ I(g) (1)
where ⊗ is the convolution operator, g is spatial coordinate of the HRRP
cells,
s
is the scale factor and G(g,
s
) is the scaling kernel. In this paper,
we choose 1D Gaussian kernel:
G(g,
s
) =
1
2
p
√
s
exp −
g
2
2
s
2
(2)
So multi-scale features of an HRRP can be achieved by adjusting the
parameter
s
. Fig. 1 shows an HRRP’s multi-scale features with
Gaussian kernel. From the figure, it is clear that small-scale features
are prominent in the local and detail information while global and
contour information are better captured in large-scale features. In this
paper, we aim to utilise the sparse reconstructive relationship between
features at all scales to develop a new feature with more discriminating
information. Based on this, we propose an algorithm of multi-scale
fusion feature extraction called multi-scale fusion sparsity preserving
projections (MSFSPP).
Multi-scale fusion sparsity preserving projections: Assume that there
are C classes of targets and the training matrix is Z
o
= [z
1
, z
2
, ...,
z
M
] at original scale, M is the number of training samples of all C
classes. Feature matrices of M HRRP training samples at all S scales
are Z
s
1
, Z
s
2
, ..., Z
s
s
, ..., Z
s
S
(s = 1, 2, ..., S). In this paper,
s
s
is
enumerated in the scale factor set
= {p
1
, p
2
, ..., p
l
} and we set
the factor range between 0.1 and 4 with interval of 0.1. For an HRRP
training sample z
i
[ R
n
(i = 1, 2, ..., M) at original scale, we trans-
form it to different scale spaces and receive z
s
1
,i
, z
s
2
,i
, ..., z
s
s
,i
, ...,
z
s
S
,i
(i = 1, 2, ..., M , s = 1, 2, ..., S). For any feature z
s
s
,i
at
s
s
scale, it can be represented by all-scale features of training samples
except its own. To make the sparse representation more efficient for
feature extraction, a constraint condition is added to the original
sparse representation problem [8] and the equation can be written as
ˆ
r
s
s
,i
= arg min
r
s
s
,
i
r
s
s
,i
1
s.t. z
s
s
,i
= Zr
s
s
,i
e
T
r
s
s
,i
= 1
(3)
where Z = [Z
s
1
, Z
s
2
, ..., Z
s
s
, ..., Z
s
S
] is the matrix composing
of all-scale features of training samples, r
s
s
,i
= [r
s
s
,i,
s
1
,1
, ...,
r
s
s
,i,
s
s
,i−1
, 0, r
s
s
,i,
s
s
,i+1
, ..., r
s
s
,i,
s
S
,M
]
T
is a vector of multi-scale
sparse representation coefficients. r
s
s
,i,
s
k
,j
is the contribution of feature
z
s
k
,j
to reconstructing z
s
s
,i
. In the case of noise, (3) can be represented as
ˆ
r
s
s
,i
= arg min
r
s
s
,
i
r
s
s
,i
1
s.t. Zr
s
s
,i
− z
s
s
,i
≤ 1
e
T
r
s
s
,i
= 1
(4)
where 1 is the noise tolerance. The weight vector
ˆ
r
s
s
,i
can be obtained by
solving (3) or (4). In addition, the sparse reconstructive weight matrix
R [ (
ˆ
r
s
s
,i,
s
k
,j
)
SM×SM
can be defined as follows:
R = [
ˆ
r
s
1
,1
,
ˆ
r
s
1
,2
, ...,
ˆ
r
s
1
,M
, ...,
ˆ
r
s
s
,i
, ...,
ˆ
r
s
S
,M
] (5)
Note that the relationship between samples of different scale spaces is
achieved, which can improve the accuracy of target recognition. Then
we can seek the projections by solving the following function:
min
w
S
s=1
M
i=1
w
T
z
s
s
,i
− w
T
Z
ˆ
r
s
s
,i
2
(6)
with
S
s=1
M
i=1
w
T
z
s
s
,i
− w
T
Z
ˆ
r
s
s
,i
2
= w
T
S
s=1
M
i=1
(z
s
s
,i
− Z
ˆ
r
s
s
,i
)(z
s
s
,i
− Z
ˆ
r
s
s
,i
)
T
w
= w
T
S
s=1
M
i=1
(Ze
s
s
,i
− Z
ˆ
r
s
s
,i
)(Ze
s
s
,i
− Z
ˆ
r
s
s
,i
)
T
w
= w
T
Z
S
s=1
M
i=1
(e
s
s
,i
−
ˆ
r
s
s
,i
)(e
s
s
,i
−
ˆ
r
s
s
,i
)
T
Z
T
w
= w
T
Z
S
s=1
M
i=1
e
s
s
,i
e
T
s
s
,i
−
ˆ
r
s
s
,i
e
T
s
s
,i
−e
s
s
,i
ˆ
r
T
s
s
,i
+
ˆ
r
s
s
,i
ˆ
r
T
s
s
,i
Z
T
w
= w
T
Z(I − R − R
T
+ RR
T
)Z
T
w (7)
where e
s
s
,i
is an SM-dimensional column vector in which the sith
element is equal to 1 and the rest of elements are all equal to 0. To
avoid degenerate solutions, constraining w
T
ZZ
T
w = 1. So the optimal
ELECTRONICS LETTERS 25th May 2017 Vol. 53 No. 11 pp. 748–750
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