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Abstract—This paper introduces a novel estimator of
equivalent number of looks (ENL) that can be applied to any
distribution of texture model, i.e., an estimator that is texture
invariant. The novel estimator is the Development of Trace
Moments (DTM), which cancels the textural variation using trace
moments. Five forms of the DTM estimator using sub-matrices
are presented and compared with each other. The results show
that the full dimensional matrix form seems to be the best in
performance and computational complexity. The experiments
were performed using simulated and real data. The comparisons
among all the existing methods of ENL estimation in the product
model of the clutter, such as K-distribution and G0 distribution,
show the performance of the DTM estimator to be the best if there
are a sufficient number of samples. The global and local ENL
estimations of the real data of San Francisco are analyzed, and the
results agree with the simulated case. This shows that the DTM
always give a good result, especially in the global estimation of
ENL. Therefore, it can be concluded that the DTM estimator is
robust to any distribution model, with low computational
complexity and high accuracy, especially in wide areas with
similar scattering mechanism.
Index Terms—Equivalent number of looks, radar polarimetry,
sub-covariance matrix, trace moments
I. INTRODUCTION
HE EQUIVALENT number of looks (ENL) is an important
parameter of the multilook polarimetric synthetic aperture
radar (Pol-SAR); the ENL describes the degree of
averaging applied to SAR measurements during data formation
and post-processing [1][2]. The ENL influences the accuracy of
the information extracted by methods based upon statistical
modeling of multilook SAR data and is a necessary input
parameter to the important classification and change detection
algorithms for Pol-SAR data [3].
The traditional approach to ENL estimation for single
polarization SAR data has been to manually select a
Manuscript received xxxx; revised xxxx; accepted xxxx.This work was
supported in part by the National Natural Science Foundation of China under
Grant 61372165 and in part by Natural Science Foundation of Hubei Province
under Grant 2012FB06902‖.
The authors are with the school of Electronic Engineering, Naval University
of Engineering. Wuhan 430033, China. (e-mail: liutao1018@ hotmail.com;
seachg@163.com; xizemin@sohu.com; gaojunnj@163.com).
Color versions of one or more of figures in this paper are available on line at
http://ieeexplore.ieee.org.
homogeneous image region, where the assumptions of fully
developed speckle and no texture assure that the scattering
coefficient is circular complex Gaussian. ENL estimation can
be obtained from the statistics of intensity in single polarization
[1][2], including coefficient of variation estimator (CV) and
fractional moment-based estimator (FM) [3]. For full
polarimetric SAR, the common method for estimating the ENL
is obtained by first estimating the ENL of the co-polarization
channels and then averaging the estimated ENL of different
channels [4][5]. To use the correlation of different polarization
channels, Anfinsen et al. put up estimators of ENL involving a
trace moment-based estimator (TM) and a log-determinant
moment-based estimator (ML) via statistics of polarimetric
covariance matrix [3]. The disadvantage of the method is that it
becomes invalid when applied to product models, such as
K-distribution. Anfinsen et al. introduced Mellin transform to a
relaxed Wishart model for Pol-SAR data [6]. Doulgeris then
proposed a texture-corrected ENL estimator via the
log-cumulants methods [7]. This texture-corrected method first
estimates the texture parameters of the K-Wishart model.
Subsequently, the ENL estimation is the numerical solution
from the first-order log-cumulant (FOL) expression. However,
the method requires much time, can be applied only to
K-distribution, and sometimes will be invalid because of its
incorrect estimation of the shape parameters (Fig. 1). On the
other hand, unsupervised estimation methods are used on the
belief that a large enough proportion of the estimation windows
satisfy the statistical assumptions. In this case, the overall
distribution of estimates should be dominated by estimates
computed from truly Wishart distributed samples, and the mode
value can be used as an estimate of the ENL [3]. If the
most-Wishart assumption is not satisfied, the method will fail.
Therefore, it is necessary to find a novel and unsupervised
estimation that can be used to estimate the global ENL of a
SAR image and that is robust for both the Gaussian model and
the product model.
The trace of the covariance matrix has an unambiguous
physical meaning [8], and its statistical properties may lead to
the solution of the ENL estimation for the product model. We
tried to find a novel method for ENL estimation based on trace
moments. The novel estimation method of the ENL that we
obtained, which is based on trace moments, is the Development
of Trace Moments (DTM). The DTM estimator is texture
invariant. It cancels the texture’s influence using trace moments.
In this study, experiments were performed using simulated and
real data. The results show that the novel DTM method is
Texture Invariant Estimation of Equivalent
Number of Looks based on Trace Moments in
Polarimetric Radar Imagery
Liu Tao, Cui Hao-gui, Xi Ze-min, Gao Jun