47

Keywords: Filtering, SAR, Interferogram, residues, coherence

ABSTRACT: Radar is gaining increasing credibility as a technique for rapid and accurate topographicmapping. Precision and accuracy of elevation and ground displacement assessed from InterferometrySAR (InSAR) depend essentially on phase difference or interferogram quality. The phase noisedegrades the visual quality of the interferogram and increases the error in phase unwrappingresults. Many methods to decrease speckle noise were applied to SAR intensity images, howeverthese can not be applied directly to the interferogram image since intensity SAR information hasa different nature from that of the interferogram.

Interferogram filtering decreases problems in phase unwrapping by minimizing the residuesnumber. Several filters have been proposed in the literature. In this paper, we proposed an improvedvector filter based on an adaptive window. Results are compared to existing filters.

1 INTRODUCTION

InSAR is a relatively new technique in radar remote sensing that allows pairs of radar images to beprocessed to form accurate models of height, or digital elevation models (DEMs).

With InSAR a pair of images is acquired by two antennae, spatially separated by a distance,referred to as baseline (D. Massonnet 1997).

DEM generation from InSAR in an automatic way is a challenging task. Many problems arisewhen the interferogram phase presents jumps and noise caused from decorrelation of the twoimages that form the interferogram. A high noise level of the interferogram makes phase unwrappingnearly impossible without filtering. In this paper we discuss about interferogram noise and presentresults obtained when applying the adaptive vector filter compared to other methods.

2 INTERFEROMETRIC PHASE NOISE

Interferometric phase is modified by an additive noise factor (Lee et al. 1998). The problem isaddressed as decorrelation between the signals received by the two antennae (Franceschetti &Lanari 1999).

We distinguish especially spatial decorrelation due to baseline, thermal decorrelation due to thesystem and temporal decorrelation present in the case of repeat pass interferometry, due to temporalchange of the scene between acquisitions (Franceschetti & Lanari 1999).

Phase noise consists largely of spectral noise associated with coherent signal transmission andreception, additive noise generated in the transmitter and receiver, and noise caused by a loss of

Filtering of InSAR interferograms

Mounira Ouarzeddine, Aichouche Belhadj-Aissa, Mutapha Rebihi & Farid TabaroutUSTHB, Faculté d’electronique et d’informatique, BP N° 32, El Alia, Bab Ezzouar, Alger,Algérie (m.ouarzeddine@lycos.com)

48 M. Ouarzeddine, A. Belhadj-Aissa, M. Rebihi & F. Tabarout

signal coherence (Zebker & Villasenor 1992). The interferometric phase with mean 0 and standarddeviation σv equals 1 is given by:

ϕ = φ + v (1)

whereϕ is the real phaseφ the wrapped phasev is noise

3 PHASE UNWRAPPING

One of the major problems encountered in the implementation of SAR interferometric technique isphase unwrapping. The interferometric phase is known to be modulo 2π. It is called a wrappedphase and has to be unwrapped or calculated back to its real values (Fornaro et al 1996), (Ghiglia& Romero 1994).

To do this we must assume that the variation of the terrain elevation between adjacent pixels,added to unavoidable noise, is not so high to produce phase variations greater that π. Integrating,along an arbitrary path, can easily carry out the phase unwrapping. Every time the difference islower or greater than π then 2π is added or subtracted (Prati et al 1990). Unfortunately it is rare thatan interferogram does not contain noise. Many methods have been proposed to solve the problem(Fornaro et al 1996), (Ghiglia & Romero 1994), but the presence of noise always decreases thequality of the unwrapped phase. Most of algorithms need that the Nyquist criterion is met throughthe most part of the image (C. W. Chen 2001). When this criterion is not fulfilled, a residue exitsand must be avoided or filtered. In Figure 1 we give the following example of residue in theinterferogram image:

0.0

0.0

0.9

0.8

0.1

0.0

0.8

0.8

0.2

0.3

0.6

0.7

0.3

0.4

0.5

0.6

0

0

0

0

+1

0

0

0

0

Figure 1. Example of residue to be filter: Residue is given in bold.

4 QUALITY OF AN INTERFEROGRAM

The complex interferogram is computed according to:

I S S S S e j = = | | | | 1 2*

1 2⋅ ⋅ ⋅ φ (2)

Wheres1 and s2 are two SLC (single look complex) values of the two co-registered images.* stands for the conjugate of a complex variableφ = ϕ1 – ϕ2 is the interferometric phase

The interferogram contains phase information useful for the computation of object space coordinates.This phase can be significant only if the scatters on the surface of the earth have changed neithertheir backscattering behaviour nor their positions relative to each other. This requirement can bechecked using the correlation, which helps to achieve a successful interferometric processing. Thismeasure of the correspondence of both SAR images is called coherence. This means that the phase

49Filtering of InSAR interferograms

between scenes must be statistically similar. The coherence is a measure of the phase noise of theinterferogram. It is estimated by window-based computation of the magnitude |γ| of the complexcross correlation coefficient of the SAR images. The interferometric coherence is defined by:

γ φ γ =

= exp[ ] 0 = | | 11 2

*

1 1*

2 2* 0

⟨ ⋅ ⟩⟨ ⋅ ⟩ ⟨ ⋅ ⟩

≤ ≤S S

S S S Sk j k (3)

⟨ ⟩ stands for ensemble averageAccordingly, when k equals 0 the two images are totally uncorrelated and when k equals 1 (full

correlation), the probability density function (pdf) given by Equation 4 tends to the Dirac function.Curves of the pdf for different values of k are given in Figure 2 (Franceschetti & Lanari 1999).

p kk

k k

k( ) = 1 –

21

1 – cos1 +

cos cos (– cos )

1 – cos

2

2 2

–1

2 2ϕ π ϕ

ϕ ϕϕ

(4)

2.0

1.5

1.0

0.5

0.0

p(φ

)

k = 0.95

k = 0.65k = 0

–π –π /2 0 π/2 ϕπ

Figure 2. Plot of PDF of interferometrical phase noise with coherence (from [1]).

5 ADAPTIVE VECTOR FILTER

Until now no perfect filter exists. Filtering methods encounter the important problem of jumps. Thephase is continuous in [–π, π] interval. To go from a fringe to the other we must cross the contour.This jump causes errors when there is noise and classical filters such as the averaging filter or themedian filter are not efficient.

Given an interferogram image, the vector filter spans the following steps:

1. Calculate the sine and cosine for each pixel.2. Filter the sine and cosine images3. Calculate the interferogram again using the arctangent function

This procedure explores the continuity of the sine and cosine functions to avoid discontinuity in theinterferogram image.

Filtering in step 2 is done using any filter, but this is also a crucial step, because the chosen filtermust not degrade the quality of the phase. We must keep as most as possible the statistical parametersof the pixel. In our case we use an adaptive smooth filter which changes the window size and thenumber of iteration according to fringes quality. If fringes are large then we use a big window. Iffringes are dense then a small window is used. This is to preserve fringes contours. If the fringesare noisy filtering is iterated.

50 M. Ouarzeddine, A. Belhadj-Aissa, M. Rebihi & F. Tabarout

6 RESULTS AND DISCUSSION

The filter has been applied to a couple of ERS1/2 SAR images acquired on the Algiers City. Twoparts have been selected. One of them represents a relatively flat region and the other represents arugged one to estimate the magnitude of filtered residues. The images obtained from the interferometricSAR data are given in grey scale. The abrupt light to dark transitions is 2π to 0 phase transition.

Just a single image is presented in the paper. The image size is 500 by 500 pixels with a 20mresolution. In Figure 3 we give interferograms with their corresponding counter images. The imagein Figure 3a shows a very large contour that cannot be used to help in phase unwrapping step whenwe want to label the phase and then unwrap it.

Figure 3. Interferograms and their corresponding countours. Raw interferogram (a) filtered with smoothfilter (b), filtered with adaptive vector filter (c).

From Figure 3a to Figure 3c, the images present more and more smoothed contours. This is toshow that the vector filter is the one which gives better filtering.

From Figure 3a to Figure 3c, we have applied respectively the smooth filter, the median phaseand the adaptive vector filter.

We see clearly that the raw interferogram is noisy with 46% of residues. In the interferogramfiltered with a smooth filter, residues do not exist unless in the border, because this filter does nottake in account any statistical parameters; we can see from Figure 5 that all the values are close to

51Filtering of InSAR interferograms

each other. Results from such a filtered interferogram are not accurate and hence it is better to avoidit.

From Figures 4 and 5 we can notice that adaptive vector filter is the one that gives a bettercompromise in keeping statistical parameters and filtering residues with 14%. These statistics wereassessed on larger images.

Distribution spatiole Distribution spatiole

Eco

rt t

ype

4

3

2

1

00 5.0 ×104 1.0 ×105 1.5 ×105 2.0 ×105 2.5 ×105

pixels correspondants

Eco

rt t

ype

4

3

2

1

00 5.0 ×104 1.0 ×105 1.5 ×105 2.0 ×105 2.5 ×105

pixels correspondants

Eco

rt t

ype

4

2

0

–2

–4

Distribution en coordonnees polaires· Distribution en coordonnees polaires·

–4 –2 0 2 4Phase en RAD

(a)

Eco

rt t

ype

4

2

0

–2

–4–4 –2 0 2 4

Phase en RAD(b)

Figure 4. Interferogram and their corresponding residues image Raw interferogram (a), interferogramfiltered with vector filter (b).

Figure 5. Interferogram and their corresponding residues image Raw interferogam (a), interferogramfiltered with vector filter (b).

52 M. Ouarzeddine, A. Belhadj-Aissa, M. Rebihi & F. Tabarout

7 CONCLUSION

In this paper we presented comparative results of filtering interferograms using smooth, median,vector and adaptive vector using contour and residues images. We also plotted the standard deviationof different interferograms to better see the distribution of the phase in the [–π, π] interval. Adaptivevector filter gives enhanced fringes and less number of residues. This result is very important inhelping the phase unwrapping step. The processing was carried out with IDL language.

ACKNOWLEDGEMENT

We thank the European space Agency ESA for providing the couple of ERS1/2 images.

REFERENCES

Chen, C.W., “Statistical-cost network-flow approaches to two-dimensional phase unwrapping for radarInterferometry,” PhD thesis, Department of electrical engineering. Stanford university, July 2001.

Fornaro, G., Franceschetti, G., and Lanari, R., Interferometric SAR phase unwrapping using Green’s formulation,IEEE Transactions on Geoscience and Remote Sensing, 34, 720-727, 1996.

Franceschetti, G., Lanari, R., Synthetic Aperture RADAR Processing, CRC Press, 1999.Ghiglia, D.C and Romero L.A., “Robust two dimensional weighted and unweighted phase unwrapping that

uses fast transforms and iterative methods,” Journal of optical society American, vol. 11, no. 1, pp 107-117, January 1994.

Lee, J., Pathanassiou, P., Ainsworth, T., Grunes, M. and Reigber, A., A new technique for Noise Filtering ofSAR interferometric phase images, IEEE Trans. Geosci. Remote Sensing, vol. 36, no. 5, 1998, pp. 1456-1464.

Massonnet, D., “Satellite Radar Interferometry,” Scientific American Article, 1997.Prati, C., Rocca, F., Guarnieri, A., Damonti, E., Seismic Migration for SAR Focusing: Interferometrical

Applications. IEEE Trans. Geosci. Remote Sensing, vol. 28, 1990, pp 627-640,Zebker, H.A. and Villasenor J., Decorrelation in interferometric radar echoes, IEEE Trans. on Geosci. and

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