The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
100 
SBAS approach. Then we focus on the results investigated by 
the simplified SBAS method in Nanjing, P. R. China. The last 
section is dedicated to the conclusion, summarizing the main 
findings in the paper. 
2. DESCRIPTION OF THE SBAS-DINSAR 
ALGORITHM 
A detailed discussion on the basic SBAS approach can be found 
in P. Bernardino (P. Berardino, 2002); accordingly, we 
highlight in this section what are the key issues of the algorithm. 
Considering N +1 SAR images relative to the same area, 
acquired at the chronologically ordered times (t 0 , ,7^); 
assuming that each acquisition may be combined with at least 
one other image, also assuming that all the images are co 
registered with respect to an image referred to as master one 
that allows us to identify a common spatial grid. The starting 
point of the SBAS technique is represented by the generation of 
a number, say M, of multilooked DlnSAR interferograms that 
involves the previously mentioned set of N +1 SAR 
acquisitions. Note also that each of these interferograms should 
be calibrated with respect to a single pixel located in an area 
chat can be assumed stable or, at least, with known deformation 
behaviour; this point is referred to as reference SAR pixel or 
reference point. 
Now considering a generic pixel of azimuth and range 
coordinates (x, t) ; the expression of the generic j-th 
interferogram ( j = 1, , M ) computed from the SAR 
acquisitions at times 1 4 and t B , will be the following (Tizzani 
P., 2007): 
5(f)j (x, r) = (j){t B ,x,r)~ (f){t A , X, r) 
\n (1) 
* — W (t B , X, r) - d(t A , x, r)] 
A 
And 
^,x,r) = —-d(t i9 x,r) 
Ä 
d(t 0 ,x,r) = 0 
where A is the radar wavelength, is the unknown 
phase of the image involved in the interferogram generated 
between the time t Q and , d(t A ,X,V) and 
d{t B , X, r) are the radar line of sight (LOS) projections of the 
cumulative surface deformation at the two times t A and t B . 
In order to get a physically sound solution, replace the 
unknowns with the mean phase velocity between time-adjacent 
acquisitions, the new unknowns become: 
A _ &N ~ ( j ) N-1 
t —t ’ 1 t —I 
M ‘0 l N 1 N-l 
take (2) into (1): 
V =[Vj 
j 
Z 0k ~h-ù v k = 30j (3) 
k=ISj+1 
organized in a matrix form, finally leads to the expression 
Bv = 0(f) 
(4) 
Note that in the equation (3) IE and IS corresponding to the 
acquisition time indexes associated with the image pairs used 
for the interferogram generation, note also that we assume the 
master (IE ) and slave (IS ) images to be chronologically 
ordered, i.e., IEj > IS., V/ = 1, , M , in the 
equation(4), B is M x TV matrix. Of course, when solving the 
equation(4), the SVD decomposition is applied to the matrix B , 
and the minimum-norm constraint for the velocity vector V is 
applied in the final solution, to achieve the final solution (f), an 
additional integration step is necessary. 
3. SBAS-DINSAR BASED ON PRIOR KNOWLEDGE 
In fact, deformation in each image pixel has some relations 
between each acquisition, by including a mode for the phase 
behaviour, the above inverse problem can be simplified. 
Assuming a linear relationship between the new model 
parameter vector p and the wanted velocity vector V : 
V = Mp 
(5) 
Where the columns of hi describe the vector component of V , 
substituting this in(4) gives 
BMp — 5(f) 
(6) 
A cubical model for the phase time variation can be written as: