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