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There are so many types of low-pass filters. Here gives the common low-pass
filters, such as ideal low-pass filter, Butterworth low-pass filter, Gaussian low-
pass filter and soon. The transfer function models of these low-pass filters are
defined as Table 2.In Table2 below, D 0 denotes the limiting frequency, D ( u,v )=
u 2 + u 2 denotes the distance from point ( u,v ) on the frequency plane to the
origin[8].
Tabl e 2. Several transfer functions of loss-pass filters
Name
Transfer fuction
H ( u, v )= 1 D ( u, v ) ≤ D 0
0 D ( u, v ) >D 0
Ideal lowpass filter
H ( u, v )= E −D 2 ( u,v ) / 2 D 0
Gaussian lowpass filter
n class Butterworth
1
1+[ D ( u,v )
D 0
H ( u, v )=
low-pass filter
] 2 n
Fig. 3. The results de-noised by the different loss-pass filters
Fig. 3 shows the de-noised results after the filtering of the infrared image
which contains multiplicative noise (noise intensity: 0.15), using different low-
pass filters can all nicely remove the high frequency exponents in the image, the
de-noised effects are also very desirable, but they can not avoid the image from
becoming blurred. The image definition is not good. This method is not very
satisfying especially for the fault diagnosis image which has a strict request to
the details
2.4 Multi-image Average De-noising Algorithm
Multi-image average de-nosing algorithm is a method to eliminate noise by aver-
aging several images of the same object. Multi-image average de-nosing algorithm
is an statistical and averaging approach applied on many images of the same ob-
ject to eliminate one's noise. Supposing that the original image is f ( u,v ), n ( u,v )
denotes additive noise, then the image with noise g ( u,v ) could be defined as
g ( u,v )= f ( u,v )+ n ( u,v )
(6)
 
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