By Dr Rajeev Srivastava Principle Sources of Noise Noise Model Assumptions When the Fourier Spectrum of noise is constant the noise is called White Noise The terminology comes from the fact that the white light contains nearly all frequencies in the visible spectrum in equal proportions ID: 533539
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Slide1
Image Restoration: Noise Models
By
Dr. Rajeev SrivastavaSlide2
Principle Sources of NoiseSlide3
Noise Model AssumptionsSlide4
When the Fourier Spectrum of noise is constant the noise is called White Noise
The terminology comes from the fact that the white light contains nearly all frequencies in the visible spectrum in equal proportions
The Fourier Spectrum of a function containing all frequencies in equal proportions is a constantSlide5
Noise Models: Gaussian Noise
Spatial Noise descriptor based on statistical behavior of the grey-level values
Consider the grey-level values as the random variables characterized by a probability density function(PDF)
Gaussian Noise(or Normal Noise)
Where:
z:gray-level
μ:mean of random variable z
:variance of z
Slide6
Noise Models: Gaussian Noise
Approximately 70% of its value will be in the range [(
µ-
σ
), (
µ+
σ
)] and about 95% within range [(
µ-2
σ), (µ+2σ)]Gaussian Noise is used as approximation in cases such as Imaging Sensors operating at low light levelsSlide7
Mean:
μ
=
Variance:
Reyleigh density can be used to approximate skewed histograms
Slide8
Noise Models:
Erlang
(Gamma) Noise
a>0
,b
ϵ
I+
Mean:
μ
=
Variance:
Rayleigh
Noise
arises
in
Laser Imaging
Slide9
Noise Models: Exponential Noise
Special case of
E
rlang
PDF
(b=1)
Where a>0,
Mean:
μ=
Variance:
Slide10
Noise Models: Uniform Noise
The mean and variance are given by
μ=
,
Slide11
Noise Models: Impulse (Salt and Pepper) Noise
If either
unipolar Impulse noise
If
Slide12
Gaussian noise electronic circuit noise and
s
ensor noise due to poor illumination and/or high temperature
Rayleigh density characterize noise phenomenon in range imaging
Exponential and gamma densities laser imaging
Impulse noise occur when quick transients(faulty switching) take place during imaging
Uniform density the least descriptive of practical situations.Slide13
Noise ModelsSlide14
Noise ModelsSlide15
Noise ModelsSlide16
Noise Patterns (Example)Slide17
Image Corrupted by Gaussian NoiseSlide18
Image Corrupted by Rayleigh NoiseSlide19
Image Corrupted by Gamma NoiseSlide20
Image Corrupted by Salt & Pepper NoiseSlide21
Image Corrupted by Uniform NoiseSlide22
Noise Patterns (Example)Slide23
Noise Patterns (Example)Slide24
Periodic
Noise
Slide25
Periodic Noise (Example)Slide26
Estimation of Noise ParametersSlide27
Estimation of Noise Parameters (Example)Slide28
Estimation of Noise Parameters
Once the PDF model is determined, estimate the model parameters (mean
μ
, variance
) or (
a,b
)
Estimate mean and variance compute a and b
Slide29
END