78 
  
  
379 
E(n) 
= 2.» (3a) 
Var(n) - ge AL (3b) 
The variance of I. is therefore: 
B gaz 
Var I, = 0 (11) = Si/L (4) 
2.2 SAR Image Statistics 
  
From the image pixel statistics derived in par. 2.1 the covariance of the 
image data samples, identified by their row and column coordinates (i.p) 
and j,q), is given by: 
| 2 
E{(I..-m)(I__- z EG, - 
(am gom) e ESSE som (8) 
where, 
m = image mean value = E(S, ;) 
and 
1 
E(I,. 1.3) = MSA S imo 6 
1) PG i 1J TAE: 1j p? (8) 
For uncorrelated speckle, 
1 T ; : 
——ifin.m zo rl)s(id-p)síj- 
d Sn nag o rsen eciog 
Hence with (6), 
1 2 ; ; 
E(lpd m ES. uS + = ESS; = - 7 
Er a (7) 
where EZ is the unspeckled image variance, 
LE hak ae 
ES} = mag (8) 
The image variance is thus given by: 
Eum) -g 2, g 2 
1j S p 
ml+0 2 
here c 2 pen (9) 
W p a 
is the image variance due to speckle. 
A commonly used model describing the statistical properties of an 
unspeckled (i.e. target) image is given by a two dimensional first order 
Gauss-Markov process of which the covariance matrix values are given by: 
= = mi st. 7 A1? 
sd 7 PHS TS 9 m 
where 
e. = image variance = £13: 2) 
Bg = correlation coefficient between row neighbouring pixels 
by © correlation coefficient between column neighbouring pixels. 
The covariance matrix values of an image effected by uncorrelated speckle 
is then given by: