Study on the improvement of instrument's image spatial resolution on the three-axis stabilized platform
2. The basic mathematic model and the algorithm analysis
2.1 The basic mathematic model
For the linear sensor with different relative positions and different over-sampling ratios, the
spatial resolution of the image varies with changes of sampling positions. Given a N ´1 linear
sensor, each pixel’s size is Xe ´Ye and the scanning is along with the X direction with the
over-sampling ratio of t. As examples, one-column positioning and two-column positioning are
discussed in this paper while t equal to 2 and the general final conclusion can be drawn, as
shown in figure 1.
Figure 1 one or two columns positioning sketch
As an example, the conditions of the double sampling and the two-column overlapping
positioning will be used to extract the spatial resolution of the image as shown in figure 2(c). Let
us assume that each detector’s IFOV is IGFOV x d ´IGFOV y d, which is divided into four
sub-blocks, the weight for each sub-block is shown in figure 3(a) and the acquired signals are
future processed to remove dark current, non-linearity, non-uniform, dark pixels and so on. The
final output value of each pixel can be expressed by:
Figure 2 over-sampling sketch for three different modes (double sampling)
Figure 3 two columns double sampling structure sketch
And Sk(i,j) is the kth acquisition value including the A(i,j) sub-block. Assumed that the total
acquisition times in one imaging is M, so the uniform equation can be expressed by:
2.2 The algorithm analysis
In this section, equation 3 solutions and the feasible of methods solution are discussed.
Obviously, ij ij 2M ) )
' = = rank(W rank(W , so 2MN ) ˆ = rank(W , which means that the 2MN
line vectors in matrix W ˆ are not linear correlation. At the same time, the column vector
T
S ˆ can
be presented by the weight matrix W ˆ and the number of column is larger than that of the line,
1) 1)(N 2(M > + + 2MN), so the solution of the equation 3 could be various. Considering the
application, the stable solution vector T A ˆ can be acquired by setting the boundary condition
according to the outer space background properly. Here, during the algorithm realization, we
should pay more attention to the following three aspects: (1) fast algorithm for matrix equation,
(2) boundary condition and (3) analysis of algorithm stability. The relative detail statements can
be found in the reference (Guo, 2003a) .
