insar data coherence estimation using 2d fast fourier transform
Post on 22-Jan-2018
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Kobernichenko V.G. (1), kand. tech. sci. (PhD), professor; Sosnovsky A.V. (1), sen. engineer; Vinogradova N.S. (1), sen. lecturer;
Tsogtbaatar O. (1,2), jun. scientist
(1)IRIT-RTF UrFU, Ekaterinburg(2) Ulan-Baator tech. univ., Mongolia
InSAR data coherence estimation using 2D fast Fourier transform
InSAR signals coherence(ALOS PALSAR data)
low
high
mediate
coherence map interferogram
Coherence map application
damaged areas rejection for subsequent InSAR processing steps facilitation;
as a parameter for adaptive phase noise suppression methods (i.e. Goldstein-Baran spectral filter);
territories classification.
Coherence estimates
1 2
0 2 2
1 2
( , ) ( , )ˆ
( , ) ( , )
z i j z i j
z i j z i jγ
×=
×
∑∑ ∑
&- standard estimate
1 2
3 2 2
1 2
( , ) ( , )ˆ
( , ) ( , )
w i j w i j
w i j w i jγ
×=
×
∑∑ ∑
&
& &1,2 1,2 1,2( , ) ( , ) ( 1, 1)w i j z i j z i j= × − −& &,
( , )1 2
2 2 2
1 2
( , ) ( , )ˆ
( , ) ( , )
jФ i jz i j z i j e
z i j z i jγ
−× ×=
×
∑∑ ∑
)
& - estimated topographic phase (from an external data source)
( , )Ф i j)
,
Coherence estimate degradation caused by phase slope
0 20 40 60 80 100
-2
0
2
0 20 40 60 80 100
-2
0
2
0 20 40 60 80 100
-2
0
2
0ˆ 0.99γ =
0ˆ 0.80γ =
0ˆ 0.21γ =
0γ̂
Coherence estimate degradation caused by phase slope
0 50 100 150 200 250 300 3500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250 300 3500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
With the fixed window size(N=10) With the fixed correlation coefficient (r=0.7)
0γ̂
angle
N=3,10,25
angle
estimate
( , )1 2
4 2 2
1 2
( , ) ( , )ˆ
( , ) ( , )
jФ i jc c
c c
z i j z i j e
z i j z i jγ
−× ×=
×
∑∑ ∑
)
&
{ }( )0
0
21 2( , ) argmax ( , ) ( , )
i i Nj j M
Ф i j F z i j z i j≤ ±≤ ±
= ×)
&
- topographic phase slope estimate in MxN sample window( , )Ф i j)
4γ̂
- normalized SAR images amplitudesiici zzz &&& /=
Phase slope correction in spectral domain
( , ) x yi j
jjФ i j M Ne e
ω ω − × + × − × =)
0
N/2=1, 2, 5, 10, 25
2FFT spectrum peak-to mean ratios
with different window sizeswith different signal correlation coefficients
0,2
0,5
0,8
1,0
N/2 ρ&
2FFT peak-to-mean ratio (N+1)x(N+1) window sizes
and comparison X-band SAR data scenes
2γ̂ 4γ̂
SAR image №1 SAR image №2
0 2ˆ ˆ( )γ γ 4γ̂
Coherence maps:Estimate degradation:
«specks»
and comparison 2γ̂ 4γ̂
and comparison 2γ̂ 4γ̂
γ
σψ
γγ4
2
radi
ans
Phase accuracy dependence on the coherence value for both estimates
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