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IMAGE RESTORATION
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NOISE MODELS
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Principle source of noise in images arise during
imageacquisition (digitization) and/or transmission.Performance of
imaging sensors is affected by number offactors ie
environmental condition during image acquisitions quality of
sensing elements
In case of CCD camera, light levels and sensor temperatureare
major factors affecting the noise.
Frequency domain properties of noise are also very
usefulinformation. For example Fourier spectrum of noise if
isconstant, the noise is usually called white noise.
Thisterminology is used for white light
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(a)Gaussian noise or normal noise:A common noise model. PDF of
Gaussian random variable,Z, is given by:
z gray level mean average value of z std. deviation2 variance70%
of values of Z will be in the range [(-), (+)]95% will be [(-2),
(+2)]99.7% will be [(-3), (+3)]
For 99.7% of the gray level, that are due to Gaussian noise,the
average peak to peak gray level deviation about themean is Peak to
peak = 6.
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For, example if mean gray level of noise in an image is 128,
ands.d. is 10. For 99.7% of the pixels within this image, the
peak-to-peak gray level deviation will be 60 ie images gray
levelvarying between 98 and 158 for 99.7% of pixels.
Rayleigh Noise
Mean and variance are:
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Basic shape is skewed towards right.Quite useful for
approximating skewed histogram.
Erlang (Gamma) Noise
a > 0, b is + ive integer, ! indicate factorial. =b/a,
2=b/a2
Exponential noise
Where, a > 0
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This is a special case of Erlange PDF where b=1This appears in
images acquired using laser asilluminating sources. This is also
known as laserspeckle. In this mean and std deviation is same ie
(1/a).Highest p.d.f is at (0,0).This function is defined beyond the
dynamic range of thetypical digital image.
Uniform noise
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If b>a, gray level b will appear as a light dot in the image.
Gaussian noise is normally due to electronic circuit noise
& sensor noise, to poor illumination or high temp. Rayleigh
noise is helpful in characterization of noise in
range imaging. Exponential & gamma noise is common in laser
images. Impulse is common in phenomena such as quick transient,
faulty switching. Uniform noise is least descriptive of a
practical
phenomena but useful in generating numerous random
functions.
Salt & Peper noise (Impulse noise)
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Image with sinusoidal noise and its spectrum
Periodic Noise
