Istanbul 2004 
quality by the 
the filtered 
/ selecting a 
oherence with 
ence on phase 
ering method, 
ering methods 
d in order to 
ng methods: 
g method and 
1ese methods 
so on. All of 
X for INSAR 
d windows for 
es due to the 
considered. 
are presented 
) at the fringe 
nean filtering, 
is calculated: 
1ase of pixel 
of the fringe 
cording to the 
5 gq47 The 
-16 
-30 
13 
  
jases modified 
ering method, 
} = 26, but 
should be: 
ve formula, 
g the median 
1 filtering, we 
terferogram. 
1998) This 
ige, and uses 
ses along the 
lates, whose 
ian the above 
quires phase 
filtering and 
it has to do a 
e. So it is not 
e of difficulty 
a common 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
filtering method for interferogram. It is defined as follows: 
n n 
$2 € ble tel re [se^ 
mn yy = 
Where, Y, (kD presents the complex value of the pixel in 
the main image; V, (k = c.l + h) presents the complex 
value of the corresponding pixel in the slave one; S| 
presents the module of S. (c, h) is the offsets between the. 
main image and the slave one according to the calculated 
pixels; The window is sized 7/7 by n; ¢ is the filtered 
phase. 
If we symbol A = y, (k, I) : |v, (k - cl h) ‚then 
1 m n : 
s-L F5 Ae = sf 
mn yq 
This filtering method is much effective for fringe filtering 
and is used more and more. But, we can find that if the energy 
of the noise is much higher than that of others, the filtering 
result can be affected to lower precision. The sketch map of 
multi-looking filtering is shown in Figure 4. Supposing 4, 
and $, are the phases with noises, whose energies are 
respectively 4 and 4,,but 4, is much higherthan 4,,so 
the result phase 4. will be closeto $,. 
Vector Filtering This is a new filtering method for 
interferogram fringe. It can avoid the affection of coherent 
intensity and has the virtue of fast processing speed, as is the 
  
1h 
Apt P 
75 x 
up À 2 A ~A 
ET dE 
~~ uS rT 
eT zum 
= 3 E 
Te Thee Ee 
Sa 
fhe j$2 
Figure4 Multi-looking Filtering 
amelioration of Multi-looking filtering. 
The Vector Filtering is defined as: 
  
AN 
= 
A B" 
s m 
^ 
A N e J #1 
/ , 7 
/ S 
j eM Fan = 
| Tt \ d 
EL | SERT 7 
| TET Jia 
\ 3d $2 
\ y. 
A 2 
LÉ 
RE — 
Figure Vector filtering 
| n n 
MN i=l [=] 
iPr i 3 
€ (shown in Figure 5) 
Where, ¢ is the result phase; $, , is the phase of pixel 
( kl ) in the filter window. 
The Vector Filtering method can be comprehended in 
another way. Firstly, the interferometric phase $, , is 
mapped to a vector elfe . which can be expressed by 
[Pkt 2 
fa = COS 0. a J sin Pr. : 
That is the interferogram is mapped to a cosine image and a 
sine image. Secondly, the cosine image and the sine image are 
filtered by mean filtering method with the same window size. 
Finally, the phase filtered by Vector Filtering is calculated 
using the following formula: 
COSQ,, and SING, , :e 
  
z d=0 550 
2 
M a=0.5 <0 
2 
¢= sen a>0,b>0 
a 
2x + etant a>0,b<0 
a 
T+ Sen > a<0 
a 
Where, a is the value of the pixel in the cosine image 
  
filtered by mean filtering; D is the value of the pixel in the sine 
image filtered by mean filtering. 
The Vector Filtering not only can avoid the affection of the 
energy, but also has the virtue of fast and high efficiency. So, 
it's a better filtering method for the filtering of interferogram 
fringe. 
3.1 Region Grow Phase Unwrapping 
The second step is phase unwrapping using region grow 
method by selecting a compatible gate value of coherence or 
of fake coherence, as is described as follows: A region is 
grown based on the coherence image or the fake coherence 
image by given a seed pixel, whose coherence or fake 
coherence value is high. Then the phases of different pixels in 
this grown region are unwrapped by the direct-recursive 
algorithm. The phases in other regions are not dealt and 
signed that they are not unwrapped. 
The coherence image is calculated by the following 
Formula: 
  
  
  
  
  
  
  
here iq se srence are re«snectivelv 
Where, po B the coherence, ZZ ute respectively 
* 
the complex value of the master image and of the slave one. Zi 
is the conjugate of Z , . 
Likely, the fake coherence can be calculated by the 
  
f 
m n 
(03 Y cos 9. , Y GC > sin 4, y 
formula: »' — \ i=l j=1 
  
ic