InSAR Data Coherence Estimation Using 2D Fast Fourier Transform
- 1. 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
- 2. InSAR signals coherence (ALOS PALSAR data) low high mediate coherence map interferogram
- 3. 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.
- 4. Coherence estimates 1 2 0 2 2 1 2 ( , ) ( , ) ˆ ( , ) ( , ) z i j z i j z i j z i j γ × = × ∑ ∑ ∑ & - standard estimate 1 2 3 2 2 1 2 ( , ) ( , ) ˆ ( , ) ( , ) w i j w i j w i j w i j γ × = × ∑ ∑ ∑ & & & 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 j z i j z i j e z i j z i j γ − × × = × ∑ ∑ ∑ ) & - estimated topographic phase (from an external data source) ( , )Ф i j ) ,
- 5. 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 0 ˆ 0.99γ = 0 ˆ 0.80γ = 0 ˆ 0.21γ = 0 ˆγ
- 6. Coherence estimate degradation caused by phase slope 0 50 100 150 200 250 300 350 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 50 100 150 200 250 300 350 0 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) 0 ˆγ angle N=3,10,25 angle
- 7. estimate ( , ) 1 2 4 2 2 1 2 ( , ) ( , ) ˆ ( , ) ( , ) jФ i j c c c c z i j z i j e z i j z i j γ − × × = × ∑ ∑ ∑ ) & { }( ) 0 0 2 1 2( , ) arg max ( , ) ( , ) i i N j j M Ф i j F z i j z i j ≤ ± ≤ ± = × ) & - topographic phase slope estimate in MxN sample window( , )Ф i j ) 4 ˆγ - normalized SAR images amplitudesiici zzz &&& /=
- 8. Phase slope correction in spectral domain ( , ) x y i j j jФ i j M N e e ω ω − × + × − × = )
- 9. 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
- 10. and comparison X-band SAR data scenes 2 ˆγ 4 ˆγ SAR image №1 SAR image №2
- 11. 0 2 ˆ ˆ( )γ γ 4 ˆγ Coherence maps: Estimate degradation: «specks» and comparison2 ˆγ 4 ˆγ
- 12. and comparison2 ˆγ 4 ˆγ γ σψ γ γ 4 2 radians Phase accuracy dependence on the coherence value for both estimates