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

(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

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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 Download Presentation

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