Restoration improves
image by removing blurring mostly. As image enhancement is subjective process
but image restoration is an objective process.
Restoration attempts to
recover an image that has been degraded by using a prior knowledge of the
degradation phenomenon. Techniques are oriented toward modeling the degradation
and applying the inverse process in order to recover the original image.
It refer to remove or
reduce the degradation that have occurred while the digital image was being
obtained.
Degradation may be
occur due to
1. Sensor noise
2. Blur due to camera
miss focus
3. Relative
object-camera motion
4. Random atmospheric
disturbance
5. Others
Example :-Contrast
stretching is considered an enhancement technique but removal of image blur by
applying a deblurring function is considered a restoration technique.
MODEL
OF THE IMAGE DEGRADATION/RESTORATION PROCESS
Degradation process
operates on a degradation function that operates on an input image with an
additive noise term.
Additive noise term
operates on input image f(x,y) to produce a degraded image g(x,y).Given g(x,y)
some knowledge edge about the degradation function H, and some knowledge about
the additive noise term Æž(x,y) ,the objective of restoration is to obtain an estimate f’(x,y) of the
original image. We want the estimate to be as close as possible to the original
input image and , in general the more we know about H and Æž ,the closer f’(x,y) will be to f(x,y).
If H is a linear , Positive-invariant process then the degraded image is
given in the special domain by
g(x,y)
= h(x,y) * f(x,y) + Æž(x,y)
where h(x,y) is the special representation of the degradation function
and * symbol indicates convolution.
Frequency domain representation
G(u,v) = H(u,v)F(u,v) + N(u,v)
Where the terms in capital letters are Fourier transformation of
corresponding above equation.
These two equations are the basis for most of the restoration material.
Noise Models
Sources of noise in digital images arise during image acquisition and
transmission. Performance of imaging sensors are affecting by a variety of
factors such as environment conditions during image acquisition and quality of
sensing elements itself. For instance acquiring images with a CCD camera, light
levels and sensor temperature are major factors affecting the amount of noise
in the resulting image.
Spacial characteristics
of noise and whether the noise is correlated with the image frequency
properties refer to the frequency content of noise in the fourier sense.For
example when fourier spectrum of noise is constant , the noise usually is
called white noise.
NOISE
PROBAILITY DENSITY FUNCTIONS (Refer to Gonzalez book for formulas and graph)
Gaussian
noise
Because of its
mathematical tractability in both special and frequency domains Gaussian also
called normal noise models are frequently in practice.
This tractability is so
convenient that its often results in Gaussian models being used in situation in
which they are marginally applicable .
The PDF of Gaussian random variable, z is given by
z= gray level
µ= mean of
average value of z σ= standard deviation
Rayleigh Noise
Unlike Gaussian distribution, the Rayleigh distribution
is no symmetric. It is given by the formula.
The mean variance of this
density
It
is displaced from the origin and skewed towards the right
III.
Erlang (gamma) Noise
The mean and variance of this noise is
Its shape is
similar to Rayleigh disruption.
Exponential Noise
Exponential
distribution has an exponential shape.
The PDF of
exponential noise is given as
Where a>0
It is a special
case of Erlang with b=1
V.
Uniform Noise
The PDF of
uniform noise is given by
The mean of this
density function is given by
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