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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
Sub-pixelic Image Registration for SAR Interferometry 
Coherence Optimization 
Riadh Abdelfattah 
Département MASC 
École Supérieure des Communications 
Route de Raoued Km 3,5 
2083, El Ghazala-Ariana, Tunisia 
Email: riadh.abdelfattah@supcom.rnu.tn 
Telephone: +216 1 857 000 
Fax: +216 1 856 829 
Abstract— This paper presents a methodology for the registration of 
an Interferometric Synthetic Aperture radar (InSAR) pair images with 
a sub-pixelic precision performed in the Fourier domain, using the Fast 
Fourier Transform (FFT). We look for the maximum of the modulus of 
the cross-correlation coefficient of both images on a window dimensions 
of 2x2 pixels using an iterative process. This will be possible in the Fourier 
domain, since a shift in the spatial domain is achieved by a multiplication 
with an exponential factor (which is the real shift less than one pixel) in 
the frequency domain. It is shown that the proposed sub-pixelic approach 
allows the coregistration of the images with an accuracy up to a tenth 
of a pixel (and even less). 
I. INTRODUCTION 
SAR interferometry has become one of the most important tech- 
niques of relief mapping [1], [2], [3], [4]. The accuracy of digital ele- 
vation models (DEMSs) produced by SAR interferometry are generally 
comparable to reference DEM [6](obtained from a SPOT stereo pair 
or from an official data base) and ground control points taken over 
the relief. However, this is true under certain conditions of the ground 
scattering characteristics and the acquisition (sensor, baseline, ...) 
geometry which could be measured via the interferometric coherence 
[9], [10], [17]. 
In practice, the coherence has to be estimated on a coregistrated 
images from the combination of several pixels (N independent 
samples correspond to the pixel or to an area around this pixel) 
to limit statistical errors [7], [8]. In order to tend to unbiased 
coherence estimation, a large estimation window is required at low 
interferometric correlation. We must coregistrate one image (the slave 
one) with respect to the other (the master one). As a result of the 
coregistration, we get the best bilinear transform that must be applied 
to the slave image to make it superimposable to the master one. In 
generally, the coregistration process is performed on two steps : a 
coarse one, where the shift (integer number of pixels) between the 
two images in range and azimuth is computed, and than a fine one, 
where the computed shift is less than one pixel. 
In this paper, we present a new procedure for sub-pixelic fine 
coregistration performed in the Fourier domain, using the Fast Fourier 
Transform (FFT). We look for the maximum of the modulus of the 
cross-correlation coefficient of both images on a window dimensions 
of 2x2 pixels using an iterative process. This will be possible in the 
Fourier domain, since a shift in the spatial domain is achieved by a 
multiplication with an exponential factor (which is the real shift less 
than one pixel) in the frequency domain. It is shown that the proposed 
sub-pixelic approach allows the coregistration of the images with an 
accuracy up to a tenth of a pixel (and even less). 
Jean-Marie Nicolas 
Département TSI, École Nationale 
Supérieure des Télécommunications 
46 rue Barrault 
75634 Paris Cedex 13, France 
Email: nicolas@tsi.enst.fr 
Telephone : +33 1 45 81 81 29 
Fax: +33 1 45 81 37 94 
The proposed algorithm is tested on two different areas: a highly 
energetic relief zone (Mustang-Nepal) and a flat zone (Orgeval- 
France). It is shown that on stationary region, the algorithm is well 
adapted and gives important results. However, non stationary regions 
are time consuming and the result is random. 
II. INSAR IMAGE CO-REGISTRATION 
To obtain a high quality DEM from InSAR, the complex images 
need to be registered to sub-pixel accuracy. Image coregistration 
techniques allow the determination of a geometric transformation 
which may exist between two images s and 7n. In general cases, 
image matching depends on three parameters : translation, rotation 
and scaling. For interferometry SAR (InSAR), we generally obtain 
satisfactory results with only sub-pixel translation registration. 
An InSAR image couple is a pair of two SAR images where every 
image is a bidimensional array of single look complex (SLC) data 
(focused data) resulting from the processing of raw data in range and 
in azimuth. These two SLC images result from the raw data focusing. 
Their registration implies compensation of azimuth and range pixel 
displacement. Note that the slant range and azimuth offsets change 
along track and across track in the SAR SLC images. 
The InSAR coregistration process is performed on two steps using 
local statistical information (magnitude or phase) computed with 
selected windows on both images [5], [2], [15] : 
e Coarse matching, where the integer shifts (translation) between 
the two images in range and azimuth are computed. This could 
be done by cross-correlating the amplitudes of the images [5] 
or maximizing a spectral signal to noise ratio (SNR) [2] on a 
selected windows with integer positions [13], [14]. 
Fine matching, where the computed shifts (in range and azimuth) 
are sub-pixelic. 
However, in the case of fine matching, the sub-pixel cross- 
correlation and S/N R maximisation is not robust in the spatial domain 
against correlated noise and disturbances [15], [16], [18]. 
III. SUB-PIXELIC INSAR REGISTRATION 
Let s(xs,ys) and m (2m, Ym) represent the two complex images 
of the InSAR pair to be coregistered. If s(xs,ys) is a translated 
replica of m(x;, y), then the transformation matrix can be written 
as follows: 
s Em Ne + Ex 
(rye oA a fn 
Ys Ym ny + Ey 
  
  
    
    
   
   
     
    
   
   
    
   
   
     
   
    
     
    
    
   
  
   
   
   
   
    
  
  
    
   
   
   
    
    
   
   
   
    
  
  
   
   
  
   
   
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