used to obtain the fitting relationship. Since the coefficient of
the quadratic term in the fitting result is zero, the relationship
can be expressed as:
y
x x
x
x
=
× +
× −
× +
0 001
0 099
0 048
0 707
1 2
1
2
.
.
.
.
(14)
where,
y
represents the volumetric soil moisture content.
x
1
and
x
2
represents the backscatter coefficient in
HH
and
VV
polarizations, respectively.
SVM
algorithm:
SVM
is a machine learning method first
proposed by Cortes and Vapnik (1995) to solve nonlinear
and high-dimensional pattern recognition problems. The
method mainly maps the sample space from low-dimensional
to a high-dimensional feature space. So, the original nonlin-
ear problems can be solved by the linear learning machine
method in the feature space. This part is modeled using
MATLAB
and
SVM
toolboxes to retrieve soil moisture based on
the training data.
BP
neural network: The backscatter coefficients in
HH
and
VV
polarizations are used as input of
BP
neural network. The
surface soil moisture is applied as output data to construct a
three-layer neural network. The numbers of neurons in the
input layer, hidden layer and output layer are 5, 10, and 1, re-
spectively. The number of iterations is set to 1000. A tangent
sigmoid function is selected as the excitation function of the
input layer and hidden layer. The function of the output layer
uses a linear one. The weight and threshold of the network
are initialized, and the
BP
neural network is learned and
trained to explore the implicit relationship between backscat-
ter coefficient and soil moisture based on the field measure-
ments and remote sensing data.
MPSO
-
BP
method: This method selects the same parameter
settings as the three-layer
BP
neural network. Then, the
MPSO
algorithm is used to optimize the weight of the network and
the obtained optimal weight is taken as the initial weight of
the
BP
neural network at the next iteration. The iterative step
is repeated until the output error is within a predetermined
range or reaches a predetermined number of iterations.
The comparison result is shown in Figure 4. The
MPSO
-
BP
method has the highest accuracy with
R
2
of 72.2% and the
RMSE
of 0.033 cm
3
/cm
3
. The multivariate nonlinear regres-
sion method has the lowest accuracy pr
relationship between the backscatter coe
face soil moisture cannot be simply repr
nonlinear expressions.
BP
neural network and
SVM
algorithm
can implicitly express the relationship between backscatter
coefficient and soil moisture. They have good inversion accu-
racy but the stability of the two algorithms is not guaranteed.
The
MPSO
-
BP
method can optimize the neural network and
make the network get a good initial weight at the beginning of
the operation. Therefore, the
MPSO
-
BP
algorithm is relatively
stable and effectively acquire the global optimal value to im-
prove the accuracy of soil moisture retrieval.
Evaluation of Retrieved Accuracies on Different Data Inputs
In this part, the
MPSO
-
BP
algorithm is used to retrieve the
surface soil moisture under vegetation-covered area using
radar and optical data simultaneously. The inversion result
is compared with the method only using a single data source
(optical or radar data) as input to evaluate the validity of the
collaborative inversion of active and passive remote sensing.
Figure 4a and Figure 5 show the validation results of soil
moisture retrieval using optical data (Figure 5b), radar data
(Figure 4a), and both of data (Figure 5a) as inputs in the
MPSO
-
BP
algorithm. As can be seen from Figure 5 and Figure 4a,
the accuracy of surface soil moisture using radar and optical
data simultaneously based on the
MPSO
-
BP
algorithm is much
higher than that of only using a single data source as input
(a) MPSO-BP
(c) SVM
(b) BP
(d) Multiple nonlinear regression
Figure 4. Validation of soil moisture retrieval calculated
from
SAR
images and field measurements using different
inversion methods. The unit of
RMSE
is cm
3
/cm
3
.
794
November 2019
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
