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operties: 
International Archives of the Photogrammetry, Remote Sensing 
To satisfy these conditions, the proposed regularization 
functional is designed as follows: 
y — dx 2 
a; edet dr. (10) 
| Cx, ||” +r 
where r is the control parameter prevents the dominator from 
becoming zero, A is the modified factor of @ , which ranges 
from 0.01 to 0.3. 
The high-resolution image is solved by employing the 
successive iterations: 
Xp = Xi *[A y -(A' A a, C" O)x,] (11) 
The criterion that is used to terminate the iteration is 
Las E Ze ed (12) 
The iterative steps can be expressed as : 
1. Select a initial value for & and solve the initial image 
using equation (9). 
Using the equation (10) calculate the & of the next 
iterative step. 
3. Solve the iterative image. 
Do 
and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
4. If the two successive iterative images don’t satisfy the 
terminating condition (12), goto the step 2; if the condition 
is satisfied, the last iterative image is the solution. 
5. EXPERIMENTAL RESULTS 
In this section, we illustrate the effectiveness of our proposed 
algorithm for matching errors in solving high-resolution image 
reconstruction problems. 
In the experiments, we constructed high-resolution images 
from four low-resolution images. The low-resolution images 
which were simulated from a original Lena image by 
translating and downsampling a factor of 2 in each dimension 
as{ (0.0,0.0), (0.0,0.5), (0.5,0.0), (0.5,0.5)}, is shown in Figure 
2.The stopping criterion of this proposed algorithm is 
lx —x* 11? / px” Il? < 107° and À was set to 0.15. 
Firstly, RG algorithm was used to enhance a high-resolution 
image using the known sub-pixel shifts. The result is shown in 
figure 3(a). In order to demonstrate the performance of the 
proposed matching-error-considered algorithm, it is assumed 
that the estimation of the sub-pixel shifts is incorrect as 
{ (0.0,0.0), (0.15,0.35), (0.35,0.15), (0.35,0.35)}, and the RG 
algorithm and the proposed algorithm are used to solve the 
solution respectively. The results are shown in Figure 3(b) and 
Figure 3(c). The results visually show that our proposed 
algorithm yields better performance. Figure 3(b) has more 
artifacts because the matching error isn’t considered. However, 
Figure 3(c) has little difference from Figure 3(a), which 
enhanced using correct sub- pixel shifts. So the proposed 
algorithm can lower the effect of the matching error effectively. 
  
Figure 3 (a) enhanced image of RG algorithm using known correct shifts, (b) enhanced image of RG algorithm using incorrect shifts, 
(c)enhanced image of proposed algorithm using incorrect shifts. 
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