THE PHASE INFORMATION CONTENT OF COMPLEX MULTIFREQUENCY 
MULTIPOLARIZATION SAR IMAGES! 
Luciano Vieira Dutra 
Instituto Nacional de Pesquisas Espaciais - DPI 
Caixa Postal 515 - CEP 12201 
Sao Jose' dos Campos, SP - Brazil 
Shaun Quegan 
The University of Sheffield 
Dep. Of Applied Mathematics - P O Box 597 
Sheffield S10 2UN - England 
ABSTRACT: 
Complex multichannel SAR images carry two types of meaningful information: the channel 
amplitude or intensity (relative energy information) and phase differences among pairs of 
channels. In this work we are mainly concerned with the second case. Phase information is 
considered present when a preferential phase (the mode) can be detected. This phase 
information is discriminatory if it is possible to relate different phases differences to 
distinct objects. A multivariate gaussian assumption for the complex scattering amplitudes 
leads to phase differences distribution in which the mode of the distribution is equal to the 
phase of the complex covariance between channels (when the modulus of the distribution is 
adequately large to ensure significance). Tests were carried out on data gathered over an 
agricultural area in Britain by the Maestro 1989 campaign and it was found that different 
  
HH-VV phases differences can be assigned to distinct agricultural fields, being the mode of 
phase distribution compatible with the phase of complex covariance between these two channels. 
KEY WORDS: SAR, Radar image processing, polarimetry, phase information. 
1.INTRODUCTION 
Polarimetric multifrequency SAR images provide 
five potential information per pixel and per 
frequency. These are three amplitudes and two 
phases differences in the scattering matrix[1]: 
Sm Sam 
= 1 
gaz. Sz (1) 
where f is frequency and reprocity is assumed. 
Phase difference is a distinctive feature of 
polarimetric data and will be the focus of this 
work. It will be investigated how one can define 
and measure phase information and its quality. Can 
this phase difference be used as a feature for 
object classification? 
In a earlier work [2], during the construction of 
MSAR covariance model, under the image formation 
point of view, it was supposed that phase 
differences between two channels are fixed and this 
value, object dependent. This constant phase 
difference appears as the argument of the 
covariance between two channels, when normality and 
extended target assumptions are assumed . How much 
is the case for real data? Practical experiments 
show however that this phase difference is not 
unique, but spread around a most likely value: the 
mode. 
At this point some definition is convenient. Phase 
information is present when there is a narrow 
distribution for phase differences, which means 
that for a particular pair of channels (and a 
certain object) is possible to find a preferential 
value of phase. This is the mode of the 
distribution. This phase information is 
discriminatory if a set of objects in a scene show 
different phase differences, which can be used as 
features to separate them. 
  
Research supported by FAPESP - Brazil. 
608 
A working hypothesis for distributed targets in 
quadpolarized data[3] is that the scattering matrix 
elements obey a zero-mean multivariate complex 
gaussian distribution.: 
p(s) = Flo] °*P (-stcz's) (2) 
where S = (8182,93, ..) 1 ^T ; ; 
(S111-5112-5122-5211 ,...)^. The covariance matrix 
of the complex scattering amplitudes is given by 
Cg(i, 3) -E[S;S;] and E[] denotes expectation. ,On 
2 J A * 
the basis of scattering models, we expect E[S1S 9] 
= E[S»S 3] = 0, and E[S;S ;1=0 , when different 
frequencies are involved. For one frequency, Cg has 
the form: 
2 
on 9 P? 
Cs E 0 a2, 0 (3) 
p 0 0, 
For this distribution, the phase difference 
distribution between two channels i and j has 
PDF[3]: 
p(0) = z (my I E) (4) 
1-Y 
  
  
for 0in the range -1«0&mz, where 
Cy 
d 4€uO; 
is the correlation coeficient of channels i and j 
and 
Y *IX| cos(0 — 4rg(X)) 
mn 
LD 6 AT CC fn (CO (7 0 (80 MH A = 
oO OO 
mt = rt 0 I