146 CHINESE OPTICS LETTERS / Vol. 8, No. 2 / February 10, 2010
Sub-pixel processing algorithm of the reducing boundary
recursive error in staring FPA micro-scanning imaging
Yan Chen ( ýýý)
∗
, Weiqi Jin (777ÙÙÙ), Lingxue Wang (***ÈÈÈ), and Xia Wang ( ___)
Scho ol of Opto electronics, Beijing Institute of Technology, Beijing 100081, China
∗
E-mail: chenyan340206@yahoo.com.cn
Received April 24, 2009
By analyzing the error distribution rule of the boundary recursive reconstruction algorithm in controlled
micro-scanning, a sub-pixel image processing algorithm is prop osed to reduce the error. The gray statistical
principle is used in the algorithm to optimize the error and acquire the sub-pixel image that approximates
the original image. The simulation result shows that the effect of this algorithm is better than the over-
sample and simple boundary recursive algorithm (BRA), and it results in a goo d effect both in those of
visible light and infrared imaging systems. Therefore, the application of this algorithm will enhance the
p erformance of opto electronic imaging systems.
OCIS co des: 110.4155, 100.3008, 100.3020, 100.2000.
doi: 10.3788/COL20100802.0146.
In the discrete optoelectronic imaging device, the detec-
tor affects the system imaging quality because of the un-
clear imaging caused by the large size of the detector and
the under-sampling caused by the large discrete sampling
space intervals. The system resolution can be effectively
improved by decreasing the detector unit size and in-
creasing the detector duty ratio. However, these meth-
ods are limited by detector technique, sensitivity, optical
system diffraction limit, and the device cost. It is demon-
strated that optical micro-scanning and later image pro-
cessing can decrease the under-sampling effect with high
performance-price ratio, and it has become a feasible way
to develop a high-performance optoelectronic image sys-
tem. This technology has been applied successfully in
the fields of remote sensing, thermal imaging, and mi-
croscopy imaging
[1−3]
.
The sub-pixel imaging technology based on micro-
scanning controls the imaging process by optical micro-
scanning, and combines with later sub-pixel image pro-
cessing to obtain a space resolution smaller than the size
of the detector. This technology has been used in line
scanning and area staring focal plane array (FPA) imag-
ing fields, and its key step is processing the boundary is-
sue. Many current algorithms do not consider the bound-
ary issue and stay only at over-sampling imaging, which
means that they are not really sub-pixel imaging
[4]
. Jin
et al. discussed the b oundary issue in 288 × 4 scanning
thermal imaging system, and put forward the boundary
recursive algorithm (BRA)
[5]
. This algorithm results in
certain effects, but it introduces the error of positive-
negative alternating. Based on Ref. [5], Gao et al. dealt
with the error using the gray statistical principle, and
then greatly improved the image resolution
[6]
. Xu et
al. introduced the BRA to two-dimensional (2D) staring
FPA imaging and realized accurate sub-pixel imaging
[7]
,
but it needs setting fixed boundary or embedded black-
body at the field diaphragm to keep uniformity of the
boundary, which was very difficult to realize in a real
system. Considering of this difficulty, the method in this
letter will not deal with the field diaphragm, and just
analyze the error distribution rule of BRA in 2D staring
FPA imaging, and then put forward a sub-pixel image
processing algorithm that can reduce the error.
According to the order of scanning, controlled micro-
scanning had many models, such as 1 × 1, 2 × 2, 3 × 3, 4
× 4, and so on
[8,9]
. Figure 1 takes the 2 × 2 model to in-
terpret the over-sampling reconstruction of the controlled
micro-scanning. Keeping the imaging scene invariable
makes the FPA move one half of the unit detector to the
right, down, and left, respectively, relative to the target
scene and, gains four under-sampling images A, B, C, and
D. As shown in Fig. 2, the four under-sampling images
are interpolated according to the sampling order to cre-
ate the over-sampling image P . The space sampling rate
is improved, so the over-sampling image P contains more
target scene information, which can improve the image
detail resolution.
In Fig. 2, we note that the over-sampling image P and
the original image O have the following relationship
[10]
P (i, j) =[O(i, j) + O(i, j + 1)
+ O(i + 1, j) + O( i + 1, j + 1)]/4
(i = 1, 2, · · · , 2m; j = 1, 2, · · · , 2n). (1)
Fig. 1. Working model of 2 × 2 controlled micro-scanning.
Fig. 2. Reconstruction of the over-sampling image.
1671-7694/2010/020146-05
c
° 2010 Chinese Optics Letters
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