ges a) absolute
wrapped noise-
t SNR=0.1, d)
id perpendicular
ly. The satellite
ene centre look
lesis was carried
ise so as to keep
).3, 0.4 and 0.5
n phase images
m the simulated
ion of effect of
S for noise free
shown in Figure
wrapped phase
SNR 7» 0.3
|
SNR=05
Mie HER d
alien el Rs JH
TOLLIT n DR, DN
do if BP FR du
nr DEW T TEE TIT
B: UH
from simulated
simulation, b)
).3, e) SNR=0.4
300 350 400
wrapped phase
LGORITHMS
inwrapped using
ty-guided, mask
least square,
rithm, weighted
The unwrapped
wrapped images
IAPRS & SIS, Vol.34, Part 7, "Resource and Environmental Monitoring", Hyderabad, India,2002
and phase profiles vis-à-vis simulated absolute phase image and
profile. The number patches or discontinuous regions formed
during the process of unwrapping of noisy interferograms are
also evaluated using scatter plot of unwrapped phase vis-à-vis
simulated absolute phase.
5. RESULTS AND DISCUSSION
Profiles of unwrapped phase along with the theoretical
unwrapped phase profile for Goldstein, quality guided
algorithm, Flynn's Minimum Discontinuity approach are
shown in Figures 5, 6, 7 and 8 respectively.
E
xr
*
Unwrapped Phase
fi
a
%
9.
3.
=
a
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2.
=
i
E
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9
3
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ls a il] ere
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i
Unwrapped Phase
Ln
A
BNR=05 |
i
n.
E
@
2.
Ê
=
£z
2
;
“[SNR=04
Figure 5: Profiles of unwrapped phase using Goldstein's branch
cut algorithm a) absolute simulated phase, and from
interferograms with b) SNR=0.1, c) SNR=0.2, d)
SNR=0.3, e) SNR=0.4, f) SNR=0.5
All profiles are extracted at same location aligned in the east-
west direction. Goldstein algorithm provides acceptable results
up to SNR value of 0.3 (Figure 5). Quality guided path
following algorithm provides a similar result, with exception
that it breaks up into different patches separated by lines of
discontinuities. Goldstein’s branch cut algorithm accumulates
the results in form of lines of discontinuities, which appears as
spikes in one-dimensional profile (Figure 6). The quality
guided algorithm results shown Figure 6 uses minimum phase
variance as a quality measure. Breaking up of unwrapped phase
and DEM into a number of surface patches, is a characteristic
of region growing algorithms. Use of height control points for
each of the surface patch is required to join the various surface
patches together into a single integrated region. Preconditioned
conjugate gradient (PCG) algorithm always generates a
smoother surface as compared to other unwrapping algorithms
(Figure 8). The noise even in case of lower SNR is localized
rather than being uniformly distributed as in case of Goldstein
and quality guided path following algorithms. The weighted
multigrid technique yields best unwrapping result up to
SNR=0.3 using minimum phase variance quality measure
(Figure 7) (Pritt, 1996).Thereafter it breaks up into isolated
surface patches, but the number of surface patches are less than
that for quality guided path following algorithm.
A
|)
E
Unwrapped Phase
Unwrapped Phase
&
t
Unwrapped Phase
Unwrapped Phase
k
SNR*05
Unwrapped Phase
Unwrapped Phase
Kx s
Figure 6: Profile of unwrapped phase using quality guided path
following algorithm a) absolute phase, and from
interferogram with b) SNR=0.1, c) SNR=0.2, d)
SNR=0.3, e) SNR=0.4, f) SNR=0.5
Unwrapped Phase
Unwrapped Phase
~ SNR=0.2 SNR=0.3
Unwrapped Phase
2 & a
Unwrapped Phase
à
3k
o
z
A
N
o
mi
x
= le
T
: Peg, uud
{i 184 | X
Unwrapped Phase
Unwrapped Phase
Le ht tn MT
Figure 7: A horizontal profile of unwrapped phase generated
using weighted multigrid algorithm a) absolute
simulated phase, and from interferograms with b)
SNR=0.1, c) SNR=0.2, d) SNR=0.3, e) SNR=0.4, f)
SNR=0.5
Unwrapped Phase
Unwrapped Phase
Unwrapped Phase
SNR=05
Unwrapped Phase
Unwrapped Phase
Figure 8: A horizontal profile of unwrapped phase generated
using preconditioned conjugate gradient (PCG)
algorithm a) absolute simulated phase, and from
interferograms with b) SNR=0.1, c) SNR=0.2, d)
SNR=0.3, e) SNR=0.4, f) SNR=0.5
