COL 9(5), 051003(2011) CHINESE OPTICS LETTERS May 10, 2011
Minimum mean square error method for stripe
nonuniformity correction
Weixian Qian (
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)
∗
, Qian Chen (
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), and Guohua Gu (
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)
440 Institute of Optic-Electronics, Nanjing University of Science and Technology, Nanjing 210094, China
∗
Corresponding author: Developer plus@163.com
Received September 27, 2010; accepted January 6, 2011; posted online April 22, 2011
Stripe nonuniformity is very typical in line infrared focal plane (IRFPA) and uncooled starring IRFPA.
We develop the minimum mean square error (MMSE) method for stripe nonuniformity correction (NUC).
The goal of the MMSE method is to determine the optimal NUC parameters for making the corrected
image the closest to the ideal image. Moreover, this method can be achieved in one frame, making it more
competitive th an other scene-based NUC algorithms. We also demonstrate the calibration results of our
algorithm using real and virtual infrared image sequences. The experiments verify the positive effect of
our algorithm.
OCIS codes: 100.2000, 110.3080.
doi: 10.3788/COL201109.051003.
Stripe no nuniformity is a special kind of nonuniformity
very popular in line infrared focal plane (IRFPA) and
uncooled staring IRFPA. The most common nonunifor-
mity is pixel nonuniformity, which supposes that dif-
ferent pixels have different nonuniformity parameters.
Stripe nonuniformity is defined as all pixels in one stripe
having the same nonuniformity parameters and different
stripes having different nonuniformity parameters. These
differences decide which stripe nonuniformity correction
(NUC) should be considered as a special case
[1,2]
.
NUC techniques have been developed and implemented
to perform the necessary calibration for all infrared (IR)
imaging applications. These co rrection techniques can be
divided into two primary categories: 1) reference-based
correction using calibrated images on startup, and 2)
scene-based techniques that continually recalibrate the
sensor for parameter drifts
[3,4]
.
The most popular reference-based correction meth-
ods are the so-called one-point correction method
and two-point correction method. The drawbacks of
reference-based methods have b e e n well-documented in
literature
[5]
. Hence, researchers have turned to scene-
based NUC algorithms. Scribner et al. discussed
least mean square (LMS)-based nonuniformity correc-
tion algorithm
[3]
, but it blurred the image. Harris et al.
introduced the constant-statistics (CS) constraint NUC
algorithm
[6]
. Howe ver, their method re quired numerous
image sequences for parameter estimation. Moreover,
their algorithm pro duced ghosting artifacts which blurred
the image.
In addition to scene-based NUC algorithms, destrip-
ing algorithms are often used in stripe NUC. T he sim-
plest destriping alg orithm processes image data with a
low-pass filter using discrete Fourier transform
[7]
. The
method is simple, but it often does not remove all stripes
and leads to significant blurring w ithin the image. Some
researchers have removed the stripes using wavelet anal-
ysis, which takes advantage of scaling and directional
properties to detect and eliminate striping patterns
[8]
.
Chen et al. proposed a power filtering metho d to distin-
guish striping-induced frequency components using the
power spectr um, and then r e moved the stripes using a
power finite-impulse response filter
[9]
. Moreover, some
destriping algorithms examine the distribution of digi-
tal numbers for e ach s e ns or, and adjust this distribution
to s ome reference distribution, such as histogram match-
ing and moment matching
[9,10]
. The commo n problem of
these destriping algorithms is that they do not regard the
stripe as the nonuniformity. Hence, they only eliminate
the offset of the stripe nonuniformity and not the gain.
Therefore, these algorithms are no t suitable for the stripe
NUC.
The purpose of this study is to solve the stripe nonuni-
formity problem. In this letter, we develop the minimum
mean square error (MMSE) method for strip e NUC. The
goal of the MMSE method is to determine the optimal
NUC parameters that make the corrected image the clos-
est to the ideal image. However, because the effects of
the destriping algorithms are not satisfactory, we com-
pare our algorithm with the scene-base d NUC algorithm.
The goal of our stripe NUC algorithm is to deter-
mine the optimal correction parameters which can min-
imize the difference between original image (image with
nonuniformity) and ideal image (image without nonuni-
formity). We c all this algorithm the MMSE NUC algo-
rithm. In this letter, the mean squar e error (MSE) is
constructed as
MSE
i,j
= E
n
[d
i,j
(n) − y
i,j
(n)]
2
o
= E
n
[d
i,j
(n) − G
j
x
i,j
(n) − O
j
]
2
o
, (1)
where y
i,j
(n) is the input observation data at pixel (i, j)
in the frame n, x
i,j
(n) is the real scene data without
nonuniformity, G
j
is the str ipe nonuniformity gain pa-
rameter at column j, and O
j
is the stripe nonuniformity
offset para meter at column j, MSE
i,j
is the MSE at time
domain of the pixel (i, j), E is the tempora l mean till
frame n, and d
i,j
(n) is the ideal image at frame n. The
image column number is M and the image row number
is N. Minimizing MSE, we have ∂MSE
i,j
/∂G
j
= 0 and
∂MSE
i,j
/∂O
j
= 0. Set
W
j
=
G
j
O
j
, X
i,j
(n) =
x
i,j
(n)
1
. (2)
1671-7694/2011/051003(3) 051003-1
c
2011 Chinese Optics Letters
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