IEEE Geoscience and Remote Sensing Magazine - March 2021 - 136

The main simulation process is described in Figure. 14.
The input is an image sample, from which one selects
the single-pixel distribution model and estimates the
model's parameters as well as the correlation structure.
With this information, and using the theoretical relationships presented in [38], one obtains the distribution parameters of the complex Gaussian field scattered
by a single scatterer and of the number of scatterers for
the generalized model. The correlation coefficients of
the Gaussian field and the number of scatterers are also
determined by the correlation coefficient of the real
component and the intensity SAR data, according to
the relationships

t RR ^x h =

t II ^x h =

min " N ^0 h, N ^x h,
t xx ^i, x h , (94)
nN

N m N m t 2xx ^x h + t NN ^x h v 2N
, (95)
2v 2N + n 2N

where t xx ^i, x h , t NN ^x h , t RR ^x h , and t II ^x h are correlation coefficients of the complex Gaussian field, the number of scatterers, the real component, and the intensity
SAR data, respectively; n N and v 2N are the mean and the
variance of the number of scatterers N , respectively;
N ^0 h denotes the number of scatterers at the current position; N ^x h is the number of scatterers at distance x; and
N m = min 6N ^0 h, N ^x h@ .
The corresponding convolution kernels are obtained
according to (78), which can be implemented by a Fourier
transform. Finally, given 1) the distribution parameters
of the complex Gaussian field, 2) the distribution parameters of the number of scatterers, and 3) the convolution
kernels, the generalized model can be used to obtain
data with the same marginal distribution and correlation
structure as the input sample. Figures 15 and 16 show
simulation results based on the GGCS model. The model
performs well on most sea and vegetated clutters (farmland and forests). However, it fails to capture the deterministic patterns, such as urban locales and mountainous
areas, which is expected, as the GGCS model itself is only
for stationary stochastic fields. The authors of [38] discuss
this issue in detail.
CONCLUSIONS
This article reviewed spatial correlation analysis and correlated clutter simulation for SAR images, based on [1]. It
summarized the two main approaches for simulating spatial correlation: one based on the product model and another founded on the coherent scatterer model. The former
is relatively simple and easy to analyze, but it characterizes only the correlation characteristics of the image itself
since it does not involve physical processes, and it does not
support a systematic understanding of SAR images. The
latter starts from the physical modeling of the underlying
scatterers and considers the effect of the number of scatterers, the bottom scatterer, and the imaging function on
136

the spatial correlation of the observed image based on the
imaging process. The analysis of the latter is more sophisticated, as it involves complicated derivations, but it can
explain the correlation characteristics of the images from
the fundamental scattering process, which is helpful for a
deep understanding of SAR images. With the acquisition
of high-resolution and ultrahigh-resolution images, more
and more physical information is contained, and it is important to analyze the main factors that lead to the correlation data in SAR images, such as the spatial resolution,
sampling interval, and size of features. In this case, a more
refined correlation model is necessary, and the advantage
of correlation analysis based on the coherent scatterer
models becomes apparent.
For the correlated clutter simulation problem, four correlated clutter simulation methods based on two classical
distributions, namely, K and G 0 , have been summarized:
a product model-based method, an ITM-based approach, a
coherent scatterer model-based technique, and the GGCS
approach. The first two techniques are directly based on the
statistical characteristics of an image. The latter two start
from the modeling of the underlying scatterers and build
the statistical relationship between the underlying scatterers and the received correlated clutter image. This kind of
physics-based model shows better development prospects
in today's high-resolution SAR image applications. In addition, the existing statistical modeling of SAR images mainly
describes clutter textures, disregarding the boundary and
contour information, which is far from sufficient for SAR
image analysis of complex scenes. Therefore, it is an important direction to enhance the semantic information of the
scene and explore SAR image simulation under the comprehensive influence of high-level semantics and the underlying coherent scattering process.
ACKNOWLEDGMENT
This work was supported, in part, by the Natural Science
Foundation of China, under grants 61991422 and 61822107.
The authors would like to thank Jing-Jing Zhang of the Institute of Electronics, Chinese Academy of Sciences for providing
the E-SAR data acquired over Traunstein, Germany.
AUTHOR INFORMATION
Dong-Xiao Yue (dxyue15@ fudan.edu.cn) received her B.E.
degree in communication engineering from Nanjing University of Posts and Telecommunications, China, in 2015
and the Ph.D. degree in electromagnetic field and microwave technology from Fudan University, Shanghai, China,
in 2020. She is currently with the College of Information
Engineering, Shanghai Maritime University. Her research
interests include statistical analysis for SAR images, Bayesian inversion methods, and deep learning. She is a Student
Member of IEEE.
Feng Xu (fengxu@fudan.edu.cn) received his B.E. degree with honors in information engineering from Southeast University, Nanjing, China, and his Ph.D. degree with
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