Information Technology Reference
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If pattern noise is the irrelative additive noise with mean index zero, then
f
(
u,v
)=
Eg
(
u,v
)
(7)
Where
Eg
(
u,v
) denotes the expectation of
g
(
u,v
). After averaging the
M
images
with noise, we have
M
g
(
u,v
)=
1
M
f
(
u,v
)=
Eg
(
u,v
)
≈
g
i
(
u,v
)
(8)
i
=1
1
M
σ
n
(
u,v
)
σ
g
(
u,v
)
=
(9)
Where
σ
g
(
u,v
)and
σ
g
(
u,v
) denote the variance of
g
and
n
(
u,v
) at the point
(
u,v
) respectively. Eq.9 proves that averaging the
M
images with noise can
reduce the variance of noise to 1/M,compared with that as before. While
M
is
magnifying,
g
(
u,v
) will get closer to the original pixel values. In other words,
g
(
u,v
) will get closer to
f
(
u,v
) as the number of M increasing..
Deduced from the above-mentioned model with additive noise, the noisy image
with multiplicative noise n(u,v) could be defined as
g
(
u,v
)=
f
(
u,v
)+
n
(
u,v
)
∗
f
(
u,v
)
(10)
Where n(u,v) denotes random noise generated by the function of rand() and sub-
jected to equidistribution(0-1). If the noise of image is uncorrelated and irrelative
to the image, then
}
1+
E{n
(
u,v
)
}
≈
E
{
g
(
u,v
)
g
(
u,v
)
1+
E{n
(
u,v
)
}
f
(
u,v
)=
(11)
Since
E
{
n
(
u,v
)
}
= 0, letting
E
{
n
(
u,v
)
}
=
V
,then
M
g
(
u,v
)
1+
V
1
(1 +
V
)
M
f
(
u,v
)
≈
=
g
i
(
u,v
)
(12)
i
=1
Meanwhile, as Eq.8 demonstrates the noise variance after the restoration reduces
to 1
/M
of the original one and the effect of de-noising is perfect to some extent.
Since
V
= 0, the contrast may decrease. In a word, the entire pixel values of
the processed infrared image diminish, compared with the original, because the
number of
V
is not equal to zero. This paper takes five and twenty infrared
images with noise respectively to average for de-nosing, so that we can take a
direct judgment of its superiority with our visual ability. De-noised results by
multi-image average de-nosing algorithm under the three mentioned noises are
showed in Fig.4
Fig.4 indicates that de-noising effects of this method with the three above-
mentioned noises are all satisfactory. But its weakness is that one has trouble in
taking many images of the same object at the same time.However, this method
could be deserved to be adopted if condition allows.
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