IEEE Geoscience and Remote Sensing Magazine - March 2021 - 117

MARCH 2021

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

CORRELATION ANALYSIS BASED
ON THE PRODUCT MODEL
The product model was proposed by Ward in 1981 [19]. It
represents the image data as the product of the RCS and the
uncorrelated speckle noise. The speckle is caused by the coherent imaging process, and the RCS is characterized by the
deterministic information of the scene, such as the texture
data. The product model is simple but able to describe the
characteristics of nonuniform regions that have texture. It
has been the most popular model in the field of statistical
modeling of SAR images [2].
Ulaby et al. [20] analyzed the correlation property of
observed SAR images based on the product model, which
represented the SAR image observations as the product of
the average intensity, the normalized texture, and an uncorrelated speckle component, as documented in Figure 2.
To be consistent with the traditional product model, the
product of the average intensity and the normalized texture
component is regarded as the RCS. For the 2D SAR intensity
image I, the product model [19], [20] at a certain pixel ^ x, y h
can be expressed as
I ^ x, y h = v ^ x, y h n ^ x, y h, (1)

Spatial Correlation Analysis of SAR Images

Correlation Due to
Imaging Impulse
Response

Correlation Due to
Fluctuation of a Single
Scatterer

Based on Coherent
Scatterer Model

Correlation Due to
Fluctuation of the
Number of Scatterers

Based on
Product Model

Speckle Correlation
Function

SPATIAL CORRELATION MODELS
In [1], we investigate the development of more than 20 singlepixel statistical distributions based on the Rayleigh speckle
model, the product model, the non-Rayleigh speckle model,
the generalized central limit theorem model, the incoherent
scatterer sum model, the single empirical distribution model, and the finite mixture statistical model. The single-pixel
statistical model is not sufficient to completely describe SAR
clutter, as it does not convey the spatial information of the
image. Therefore, the two-pixel statistical characteristics (the
power spectrum and the correlation function) of the SAR image need further study. This section summarizes the commonly used spatial correlation models of SAR images.
As shown in Figure 1, the correlation analysis of SAR images is mainly divided into two approaches, which include
the following:
1) Correlation analysis based on the product model [20]: The
main idea is to consider the scattered echo as the product of the speckle component and the RCS component.
The correlation function of the scattered echo can also
be -regarded as the product of the correlation functions of
the speckle and the RCS components. In this way, first,
the correlation functions of these two components are
separately modeled, and then the product model is used
to derive the correlation information of an SAR image.

2) Correlation analysis based on the coherent scatterer model
[4], [7]: The purpose here is to model the scattered field
of an SAR image as a random walk and to analyze the
correlation information introduced in the scattering
process. Research shows that the number of scatterers,
the fluctuation of the scattered field of a single scatterer, and the imaging impulse response function are
the main factors affecting the correlation of the observed intensity.
This section will introduce these methods one by one. Figure 2 outlines the main context of the spatial correlation
analysis introduced in this section, which is detailed in
the following.

RCS Correlation
Function

interpretability, which is valuable for the interpretation of
high-resolution SAR images.
In addition, as an important application of SAR image
statistical modeling, this article reviews the main correlated
clutter simulation methods based on the single-pixel statistical models along with their correlation analysis. Clutter
simulation is a forward process for modeling SAR images. It
is an important tool for validating whether the properties of
SAR images have been well understood. It has significant applications for despeckling [21], [22], target detection and recognition [23], [24], interpretation algorithm verification [25],
[26], system design verification, and accuracy evaluation [27],
[28]. It is a vital way to describe SAR clutter based on the statistical characteristics of observed data at a single-pixel and
observed data at a single-pixel and the correlation structures
of these data [29], [30].
The K distribution [4] has been the most widely used
statistical distribution in the study of non-Gaussian clutter models. It can be used to describe sea, forest, and other
scenarios, but it cannot define extremely inhomogeneous
regions. The G 0 distribution [31] is able to depict homogeneous, inhomogeneous, and extremely inhomogeneous
scenes. Therefore, this article reviews four main correlated
clutter simulation methods based on these two classical distribution models: the simulation of correlated K-distributed
clutter based on the product model [2], the simulation of
the correlated G 0 -distributed clutter [30] based on the ITM,
the simulation of the correlated K-distributed clutter based
on the coherent scatterer model [32], and the simulation of
correlated clutter based on the GGCS model.

FIGURE 1. A spatial correlation analysis of SAR images.

117

IEEE Geoscience and Remote Sensing Magazine - March 2021

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