1. Co-Registration of SAR Image Pairs for Interferometry

2. Current Progress & Preliminary Results
An InSAR Co-registration Module “PurSAR”
InSAR co-registration
Coherence Evaluation
Interferogram Generation
DEM Processed by ASF SAR Processor + “PurSAR” + ERDAS
Experiments & Analysis

3. Co-registration Module “PurSAR”
Coarse co-registration
Cross-correlation by FFT
Finding coarse tie points
Coarse image shift
Fine co-registration
Finding and filtering sub-pixel tie points
4 and 6 parameters transformation
Nearest neighbor, linear, cubic, and SINC interpolators
Coherence computation
Interferogram generation

4. Coarse co-registration
Defining the grids
Cross-correlation computation
Filtering cross-correlation peaks by peak-to-rms ratio
Finding the matching points and discarding the outliers
Determining the x and y shifts
Shift of the slave image

5. Fine co-registration Defining the grids
SINC up-sampling the small windows surrounding the grid points
Cross-correlation computation
Filtering cross-correlation peaks by peak-to-rms ratio
Finding the matching points and discarding the outliers
Set 4-par & 6-par transformation equations by least square
Re-sampling the slave image by nearest neighbor, linear, cubic, and SINC interpolators
SINC interpolators: normalized, windowed, and doppler centroid shifted

6. Coherence, Interferogram, and DEM
Coherence evaluation
Coherence image computation
Coherence statistics: average, histogram, etc
Coherence table: re-sampling algorithms vs. coherence magnitude
Coherence comparison with ASF SAR Processor
Interferogram computation
DEM generation
Importing co-registered SAR image pair into ERDAS
Type in the orbit information
Processing the SAR images into DEM in ERDAS Radar
DEM evaluation

7. Experiments
Comparison among airborne RTV SAR DEM, LIDAR and Aerial DEM
ERS InSAR processing and coherence evaluation

8. Patch 2-AR-Roof

12. Armory (Building/Roof)

13. Armory-EW (Building/Roof)

14. Armory-NS (Building/Roof)

15. ERS InSAR processing and coherence evaluation

16. ERS Data description InSAR pair: a.cpx (master) and b.cpx (slave)
Location: Fairbanks, Alaska
Size: 5000 rows and 1000 columns; cut from a standard scene (about 25000x5000)
Format: Single-look complex
Processed by ASF SAR Processor
The right image is only the magnitude for a.cpx

17. Coarse Co-registration
Pair: a.cpx and b.cpx
Grids: 5x3 = 15 points
Peak-to-RMS Ratio = 0.004
Searching window size = 256
Use only magnitude as input for cross-correlation computation
All 15 points have good peaks and no outlier
Shifts: 2 in x-direction (range); 1 in y-direction (azimuth)
b.cpx  b_shift.cpx

18. 15 Pairs of Matching Points

19. Cross-correlation Peak for Point (700, 300)

20. Fine Co-registration Pair: a.cpx and b_shift.cpx
Grids: 5x5 = 25 points for better performance
Up-sampling ratio = 11
Up-sampling interpolator: SINC
Peak-to-RMS Ratio = 0.003
Searching window size = 33 before up-sampling
Cross-correlation with only magnitude
Cross-correlation with complex data

21. Cross-correlation with Only Magnitude ---- Matching Points

22. Cross-correlation with Only Magnitude ---- Point (500, 100)

23. Cross-correlation Section with Only Magnitude ---- Point (500, 100)

24. Cross-correlation with Only Magnitude
All 25 points have good peaks
A beautiful sub-pixel peak for Point (500, 100)
Azimuth direction section
Solid lines
Up-sampled cross-correlation
1/11th sub-pixel matching accuracy
Dash lines
Original pixel cross-correlation
Mostly zero after coarse co-registration

25. Cross-correlation with Complex Data ---- Point (500, 100)

26. Cross-correlation with Complex Data
Only 3 points passed the filter
No obvious single peak
Noise added by including phase data
So better to use only magnitude for sub-pixel co-registration for this SAR pair; but not always

27. 6-par Transformation

28. Discarding the Outliers

29. 6-par Transformation & Discarding the Outliers
5 outliers were filtered out
6-parameter transformation equations
Coefficients for y are much less significant than those for x
So 4-parameter transformation is OK
NofPoints = 25
X = *x *y
StDev of X =
Y = *x *y
StDev of Y = 20

30. 4-par Transformation

31. Discarding the Outliers

32. 4-par Transformation & Discarding the Outliers
NofPoints = 25
X = x *x
StDev of X =
Y = y *x
StDev of Y =
NofPoints = 20

33. 2D Separable SINC Function

34. Re-sampling
Re-sampling the slave image b_shift.cpx by nearest neighbor, linear, cubic, and SINC interpolators
b_shift.cpx 
b_nearest_4par.cpx
b_linear_4par.cpx
b_cubic_4par.cpx (bicubic)
b_sinc2_4par.cpx (SINC length = 2) …
b_sinc20_4par.cpx (SINC length = 20)

35. Coherence Image ---- a.cpx vs. b.cpx

36. Coherence Image ---- a.cpx vs. b_shift.cpx

37. Coherence Image ---- a.cpx vs. b_sinc4_4par.cpx

38. Coherence Statistics (I)
Image Pair for Coherence Computation
Average Coherence
a.cpx + b_corr.cpx (Co-registered and Re-sampled by ASF SAR processor)
0.695
a.cpx + b.cpx (before any co-registration)
0.191
a.cpx + b_shift.cpx (after coarse)
0.613
a.cpx + b_nearest_4par.cpx
a.cpx + b_linear_4par.cpx
0.661
a.cpx + b_cubic_4par.cpx (bicubic)
0.680

39. Coherence Statistics (II)
Image Pair for Coherence Computation
Average Coherence
a.cpx + b_sinc2_4par.cpx
0.691
a.cpx + b_sinc4_4par.cpx
0.701
a.cpx + b_sinc6_4par.cpx
a.cpx + b_sinc8_4par.cpx
0.700
a.cpx + b_sinc10_4par.cpx
0.699
a.cpx + b_sinc14_4par.cpx
a.cpx + b_sinc20_4par.cpx
0.696

40. Coherence Analysis
ASF SAR Processor uses 4 or 6-point cubic convolution for re-sampling
It is better than nearest neighbor, linear, and bicubic interpolation
However, a 4-point SINC interpolator gives the better coherence than it
The speed of computer has increased a lot, and the price has lowered significantly during the last 10 years; So SINC interpolation can be used practically
The longer SINC is not always better for interpolation, due to the noise

41. Interferogram ---- a.cpx and b_sinc4_4par.cpx
Single look  Multi look

42. Interferogram ---- Spherical Earth Correction

43. Interferogram ---- Phase Unwrapped

44. InSAR DEM in Slant Range

45. Final InSAR DEM