Digital Signal Processing Reference
In-Depth Information
netic wave hits an object. The random nature of these interactions can be studied
using their second order moment, called the covariance matrix.
As previously mentioned, polarimetric SAR images can be used for several appli-
cations, in particular land cover classification. Therefore, polarimetric SAR images
classification is an active area of research. Two main approaches appeared in the
corresponding literature. The first approach is to classify pixels thanks to their phys-
ical characteristics. Several matrix decompositions have been proposed: coherent
decompositions, based on the scattering matrix, like the Cameron decomposition
[
6
] or the Krogager decomposition [
14
], in order to characterize pure scatterers.
The distributed scatterers have been studied thanks to incoherent decompositions,
i.e. decompositions of the covariance matrix. Freeman et al. [
10
] proposed such a
decomposition. In [
7
], Cloude et al. proposed the
H
decomposition, based on
the eigendecomposition of the covariance matrix. The second approach is to classify
the images based on their statistical properties: Kong et al. [
13
] derived a distance
measure for single-look complex polarimetric SAR data, which has been extended
by Yueh et al. [
23
] and van Zyl et al. [
20
] for normalized complex POLSAR data. A
distance measure for the multi-look complex case has been proposed by Lee et al.
in [
16
], based on the complex Wishart distribution of the clutter covariance matrix
under the Gaussian assumption.
However, recent POLSAR acquisition systems are now able to acquire very high
resolution images, up to decimetric resolution. Thus, there are fewer scatterers in each
resolution cell and their number varies from one resolution cell to the other. This
leads to a higher heterogeneity, especially in urban areas. Thus, the backscattered
signal can no longer be modeled as a Gaussian process. One commonly used fully
polarimetric non-Gaussian clutter model is the Spherically Invariant Random Vector
(SIRV) model. The polarimetric clutter is no longer modeled as a Gaussian process
but as the product of a Gaussian process and a random variable. This random variable,
called
texture
, represents the local variations of power, hence the heterogeneity.
−
α
10.2 State of the Art
10.2.1 SAR Signal Statistics
Gaussian assumption
In order to reduce the speckle noise in early SAR systems,
a common approach was to average several indepedent estimates of the reflectivity
of each resolution cell. The quantities in each pixel of the resulting so-called multi-
look image are therefore Gaussian-distributed. To obtain the covariance matrix of a
polarimetric scattering vector
k
, corresponding to a pixel of the image, it is neces-
sary to employ an estimation scheme, as the covariance matrix cannot be computed
directly. Several samples
are drawn from the immediate neighbourhood
of the pixel under consideration, with the assumption that they are independent and
identically distributed (i.i.d.). A boxcar neighbourhood is generally used for this.
(
k
1
, ...
k
N
)
