Satellite Data
The Landsat-8 satellite is launched by the National Aeronau-
tics and Space Administration (
NASA
) to provide data support
for earth resources, water, forests,
envi
ronment, and urban
planning. The Landsat-8 optical image on 24 March 2014 is
used in this study and consists of nine bands with a spatial
resolution of 30 m. The preprocessing of Landsat-8 data
mainly includes radiation calibration, atmospheric correction,
and geometric correction in
ENVI5.0
software. The radiation
calibration is used to convert the digital number (
DN
) value
of the optical image into the equivalent apparent radiance
data. Then, the Fast Line-of-Sight Atmospheric Analysis of
Hypercubes (
FLAASH
) Atmospheric Correction in the software
is performed based on the processed radiance data. In order to
ensure the geometric accuracy of the image, the optical image
needs to be geometrically corrected by using twenty ground
control points (
GCPs
) with appropriate geometric correction
parameters. The geographical coordinates of
GCPs
is the World
Geodetic System 1984 (
WGS84
).
The
RADARSAT-2
radar satellite operates a C-band multipo-
larized sensor that can acquire multiple resolution images. In
this study, the
RADARSAT-2
radar image on 29 March 2014 in
Single Look Complex format is selected (Table 2). The central
frequency is 5.405 GHz, and the image resolution is about 8
m. The near and far incidence angles are 26.8° and 28.7°, re-
spectively. Preprocessing of
RADARSAT-2
image was performed
primarily in Next
ESA SAR
Toolbox (
NEST
), (version 5.0.16)
and
ENVI
5.0 software including radiation calibration, speckle
removal, and geometric correction. The main purpose of ra-
diation calibration is to convert the
DN
value of the image into
a backscatter coefficient value in dB. Then, the radar image is
filtered by the Enhanced Lee filtering method and geometri-
cally corrected. The correction method is the same as the geo-
metric correction of the optical data and the correction error is
within one pixel. Finally, the
RADARSAT-2
image is resampled
to the same spatial resolution of 30 m as Landsat-8 data.
Table 2. Main parameters of RADARSAT-2 sensor.
Parameters
Values
Acquired time
Universal Transverse Mercator 10:41:47
Incidence angle
26.8°–28.7°
Centre frequency
5.405 GHz
Resolution
About 8 m
Pass direction
Ascending
Method
Modified Particle Swam Optimization Algorithm
The
PSO
algorithm is proposed according to the foraging
behavior of birds. The study found that the individual bird
used the information sharing mechanism to change the flock’s
movement from disorder into order and then obtained the
food. In the optimization problem, food can be regarded as
the optimal solution and the distance between bird and food
can be treated as a function of fitness. Thus, the process of
bird foraging is the process of function optimization. The
individual bird in the search space could be regarded as
individual particle or the potential solution of each optimiza-
tion problem and the collection of these particles is a particle
swarm. Each particle also corresponds to the fitness value of
the optimized function and determines the velocity value of
the flight direction and distance. According to the position in-
formation of the current optimal particle, the particles search
in the solution space through fitness function and adjust the
flight velocity and direction iteratively to make the overall
position of the particle swarm update simultaneously. Eventu-
ally, the optimal swarm position can be found, which is the
optimal solution of the optimization problem.
In this process, each particle updates its position and flight
velocity in the solution space by tracking two best values. One
is the global best value or the optimal solution that the entire
population can find. The other is the individual best value or
the optimal solution that the particle itself can find. In an
N
-
dimensional search space, the position and velocity of
M
par-
ticles are randomly initialized to form an evenly distributed
initial population. The position and velocity of the
i
th par-
ticle in the dimensional space are defined as
X
i
= (
X
i
1
,
X
i
2
, … ,
X
iN
) and
V
i
= (
V
i
1
,
V
i
2
, … ,
V
iN
), respectively,
i
= 1,2, … ,
M
. The
position and velocity of the
i
th
particle in the
D
th
dimensional
space can be expressed as
X
iD
and
V
iD
, respectively, 1
≤
D
≤
N
.
Therefore, when the
i
th particle moves in the
D
-dimensional
space, the individual best value and the global best value can
be expressed as
Pbest
i
= (
Pbest
i
1
,
Pbest
i
2
, … ,
Pbest
iD
) and
Pbest
g
= (
Pbest
g
1
,
Pbest
g
2
, … ,
Pbest
gD
), respectively,
g
∈
[1, 2, … ,
M
]. For
each particle at each moment, a fitness function can be used
to calculate its current fitness and compare its fitness value
with the individual and global best values. Then, the posi-
tions of each particle and the population can be continuously
updated until the optimal solution is found.
For the
i
th
particle with the highest fitness value at the
t
th
moment, the individual optimal position is marked as
pbest
i
and the corresponding global optimal position of the particle
swarm is marked as
gbest
i
. Then, the formula of the posi-
tion and velocity of the particle at the
t
+1
th
moment can be
obtained as follows:
v t
v t c r pbest t
x t
c r gbest
i
k
i
k
i
k
i
k
i
k
+
+ =
+ × ×
−
+ × ×
1
1 1
2 2
1
(
)
( )
(
( )
( ))
(
( )
( ))
t x t
i
k
−
,
(1)
x t
x t v t
i
k
i
k
i
k
+
+
+ =
+
+
1
1
1
1
(
)
( )
(
)
,
(2)
where,
k
is the number of iterations.
r
1
and
r
2
represent the
random number uniformly distributed between 0 and 1. The
learning factor
c
1
and
c
2
are positive constraints. Study has
found that the sum of
c
1
and
c
2
is around 4.0 (Kennedy 2011).
However, although the
PSO
algorithm has a fast conver-
gence speed in the early stage, its search ability is not satisfac-
the convergence speed and reduce the
on. To improve the local search ability
hi and Eberhart (1999) introduced the
elocity term of Equation 1, which can
be rewritten as follows:
v t
v t c r pbest t x t
c r gbest
i
k
i
k
i
k
i
k
+
+ = ×
+ × ×
−
+ × ×
1
1 1
2 2
1
(
)
( )
(
( )
( ))
(
ω
i
k
i
k
t x t
( )
( ))
−
, (3)
where,
ω
is a nonnegative number, which is an important
factor for balancing the local and global search ability of the
algorithm. Studies have shown that the strong local search
ability relates to the small value of inertia weight and the
strong global search ability corresponds to its large value
(Clerc and Kennedy 2002; Trelea 2003).
It can be seen that selecting a suitable inertia weight is es-
sential for balancing global and local search abilities. Some
calibrated and improved methods about inertia weight in-
clude linear degressive inertia weight (
LDIW
) strategy (Shi and
Eberhart 1999), random inertia weight strategy (Eberhart and
Shi 2001), and fuzzy inertia weight strategy (Shi and Eberhart
2001). The
LDIW
strategy can linearly reduce the inertia weight
during the iteration process, which can be expressed as follows:
ω
= (
ω
start
–
ω
end
)(
t
max
–
t
)/
t
max
+
ω
end
,
(4)
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
November 2019
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