A 2+1D PHASE UNWRAPPING FORA 2+1D PHASE UNWRAPPING FOR

ADVANCED DINSAR DATAADVANCED DINSAR DATA

PROCESSINGPROCESSING

Michele CrosettoMichele Crosetto

OriolOriol Monserrat Monserrat

Purushotham MunigantiPurushotham Muniganti

Monika SawickaMonika Sawicka

Frascati , 26 November 2007

Grazia RossiGrazia Rossi

Laura CalcagniLaura Calcagni

Bruno CrippaBruno Crippa

Proposed procedure

• Processing steps:

• interferogram generation

• 2D phase unwrapping

• interferogram to image transformation:

!FDInSAR = FSlave – FMaster =

= (Fdefo + Fatmo + F tlin)S – (Fdefo + Fatmo + F tlin)M + 2N·p + Fnoise

• Goals:

• detect the 2D unwrapping errors: 2N·p " correct/reject

• compensate for the non-modelled phase component: Fnoise

• control the error propagation in subsequent processing steps

model residual

Proposed procedure

• Approach:

• least squares adjustment + redundant interferograms

• iterative outlier detection & rejection/correction based on:

• size of residuals

• the outliers are unwrapping-related errors, i.e. integer multiple of 2p

• local redundancy of the network of interferograms/images

" with low redundancy no correction/rejection is performed

• error propagation:

• analysis of residuals and local redundancy

• quality index associated with each estimated phase

" used in subsequent processing steps

Simulated data

(1st iteration)

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

interferogram number

resid

uals

[ra

d]

18,63

outlier candidated

• Simulated case:

• 150 interferograms = 150 observations = 150 equations

• 35 images = 34 unknowns

• 20% of unwrapping-related errors

Simulated data

• Simulated case:

• 150 interferograms = 150 observations = 150 equations

• 35 images = 34 unknowns

• 20% of unwrapping-related errors

(2nd iteration)

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

interferogram number

resid

uals

[ra

d]

eliminated

-18,09

outlier candidated

-6,57 unwrapping error

-6,58 -6,33unwrapping error

Simulated data

• Simulated case:

• 150 interferograms = 150 observations = 150 equations

• 35 images = 34 unknowns

• 20% of unwrapping-related errors

(3rd iteration)

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

interferogram number

resid

uals

[ra

d]

eliminated

eliminated

-15,17

outlier candidated

0,37

corrected

2,63

-6,12

12,44

0,07

6,18

12,33

-6,2

-12,85

Simulated data

• Simulated case:

• 150 interferograms = 150 observations = 150 equations

• 35 images = 34 unknowns

• 20% of unwrapping-related errors

(final iteration)

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

interferogram number

resid

uals

[r

ad

]

Re jected observations

Corrected observations

Gardanne mining area

Network:

243 interferograms

53 ERS images

April 1995 – September 2000

Interferogram 987DT = 770 days

Max deformation = 25 rad

4 km

Gardanne mining area

0 [cm] 13

853376-133244

16 km

Gardanne mining areaPoint (853376-133244)

-10

-8

-6

-4

-2

0

2

4

1992 1994 1996 1998 2000 2002 2004 2006

Time [years]

Displacement [cm]

http://webgis.irea.cnr.it/

Residues_853376-133244

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 50 100 150 200

Observation Number

Res

idua

l [R

ad]

Last Solution

First Solution

Gardanne mining area

Sigma0 = 0.19 rad

Point (853376-133244)

-10

-8

-6

-4

-2

0

2

4

1992 1994 1996 1998 2000 2002 2004 2006

Time [years]

Displacement [cm]

Gardanne mining area

0 [cm] 13

850346-131144

Gardanne mining areaPoint (850346-131144)

-15

-10

-5

0

5

1992 1994 1996 1998 2000 2002 2004 2006

Time [years]

Displacement [cm]

http://webgis.irea.cnr.it/

Residues_850346-131144

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 50 100 150 200

Observation Number

Res

idua

l [R

ad]

First solution

Last Solution

Gardanne mining areaPoint (850346-131144)

-15

-10

-5

0

5

1992 1994 1996 1998 2000 2002 2004 2006

Time [years]

Displacement [cm]

Sigma0 = 0.81 rad

Quality index: from global to local

-15

-10

-5

0

5

10

1 6 11 16 21 26 31

image number

ph

ase [

rad

]

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

incidence

0

0.5

1

1.5

2

2.5

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

res_max

0

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

image

standard_deviation

Quality index: from global to local

-15

-10

-5

0

5

10

1 6 11 16 21 26 31

image number

ph

ase [

rad

]

QUALITY INDEX

0

500

1000

1500

2000

2500

3000

3500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

qu

ali

ty_

ind

ex