IEEE Geoscience and Remote Sensing Magazine - September 2022 - 133

SOLVE THE SCATTERING MODEL
Guo, Wang, and Kumar constructed the scattering model
based on the FP Freeman-Durden model, which requires
solving ,, ,, ,, and,
fff **
svd
aa bb for a total of seven model
parameters; Hou adopted the Arii model [91] to characterize
the volume scattering components, adding to the Freeman-Durden
model parameters mv
0 ,
and i meaning that
a total of nine model parameters needs to be solved. As
shown in Figure 14, the method of solving the scattering
model is summarized in two steps: first, the volume scattering
component PV
whether dihedral scattering PD or surface scattering PS
is processed, and then it is determined
is
the dominant scattering mechanism among the remaining
scattering components.
Process PV
The processing of volume scattering component can be
divided in three ways. One is to first solve the volume
scattering component directly. Guo and Kumar, based
on the observation that the surface scattering model
has the same form as the dihedral scattering model, let
fr ,, ,
gs fd
solved ,,and )
rf bb
vg,
a
f ,d
=+ aa
)) )
GC ff rrvg
=+
component, then let /, ;
ba) ,.fd
GC fr r)
= g
a , and r .)
ll = b
))+ ^h At this point, the unknowns to be solved
are ,fs b , b ,)
Second, the volume scattering component is set as a free
parameter. The CP covariance matrix has four observations,
and the value of a or b can be fixed, as detailed in the following
section, by determining whether surface scattering
or dihedral scattering is dominant, which, in turn, reduces
two unknowns. For the Wang model, five unknowns are
left, and one degree of freedom still exists. Therefore, Wang
directly set the free parameter
xf ,2 v
=
problem is how to take the value for x .
Third, we first judge whether the volume scattering component
dominates. Hou investigated whether the parameter
mv
was smaller than the critical value mth
to determine
whether the volume scattering model dominates. If yes, the
dihedral scattering model and the surface scattering model
in the total scattering model degenerate to the basic model,
and only the two parameters mv
and the remaining
and 0i in the volume scattering
model need to be solved, and the solution ends; if
not, we need to proceed according to the following section.
Determine Whether PS or PD Dominates
To determine whether dihedral scattering or surface scattering
dominates in the remaining scattering components
after removing the volume scattering component,
the approaches mainly use the positive or negative of
Re SS
HH VV
^h)
Re SS is positive, then surface scattering dominates;
if Re SS
HH VV
^h)
HH VV
^h)
^^ ^hh h and /, .^h)
ff rr and obtained the volume scattering
ll ^h thus, /,(GC fs
They
nates [92]. Zyl proposed Re SS Re^ff
on this basis [94]. Guo adopted Re SS
HH VV
^h)
HH VV
is negative, then dihedral scattering domi^
HH VVh) =+
sd
$$
criminator and obtained /,Re SS ff f
^h) =+ba+
13vs d
bah
as the dis$$
based
on the correspondence between the FP covariance
matrix and the element positions in the Freeman-Durden
model. In the scattering model written by Kumar,
.
gf Reba bah Hou noted that
according to the written scattering model, the g3
=+ =+^^ ^hhff f
3 sd sd
Re
Re $$ $$
term is
independent of the volume scattering component, while
g
3 02 and g
tering and dihedral scattering dominates, respectively.
sign(Re(SHHSVV))
∗
3 01 can be obtained when the surface scatproposed
by Freeman and Durden, and if
modelGuo
modelKumar
Solar PV first.
Fix the value of β or α.
Let fg . C(γ, γ∗) = fs . C(β, β ∗) + fd . C(α, α ∗)
\fg . g(γ, γ∗) = fs . g(β, β ∗) + fd . g(α, α ∗),
get PV, fg, γ, (γ∗)
modelWang
Take PV as the free parameter.
Let x = 2fv
Judge whether PV is dominant or not.
modelHou
If mv < mth, PV is Dominant, modelV, End,
If mv > mth, PV is Not Dominant, Step B)
(a)
(b)
PD, PS, PV ≥ 0
(c)
FIGURE 14. The method of solving the scattering model. The (a) processing of PV, (b) judging whether PD or PS is dominant, and
(c) processing of the freedom.
SEPTEMBER 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
133
If PD is Dominant, modelβ =1;
If PS is Dominant, modelα = -1,
Determine the corresponding model.
If PD is Dominant, modelD;
If PS is Dominant, modelS,
PV
PD
PS
IEEE Geoscience and Remote Sensing Magazine - September 2022

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