Image Restoration: Noise Models By Dr. Rajeev Srivastava

Principle Sources of Noise Image sensors may be affected by Environmental conditions (light levels etc) Quality of Sensing Elements (can be affected by e.g. temperature) Image Acquisition Interference in the channel during transmission e.g. lightening and atmospheric disturbances Image Transmission

Noise Model Assumptions While generating noise models we have to take various assumption, which are as follows Independent of Spatial Coordinates Uncorrelated with the image i.e. no correlation

White Noise 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 constant

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+2 σ )] Gaussian Noise is used as approximation in cases such as Imaging Sensors operating at low light levels

Noise models: Rayleigh noise

Noise Models : Erlang ( Gamma ) Noise

Noise Models: Exponential Noise

Noise Models: Uniform Noise

Noise Models: Impulse (Salt and Pepper) Noise

Applicability of Various Noise Models Gaussian noise electronic circuit noise and sensor 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.

Noise Models

Noise Patterns (Example)

Image Corrupted by Gaussian Noise

Image Corrupted by Rayleigh Noise

Image Corrupted by Gamma Noise

Image Corrupted by Salt & Pepper Noise

Image Corrupted by Uniform Noise

Noise Patterns (Example)

Periodic Noise Arises typically from Electrical or Electromechanical interference during Image Acquisition Nature of noise is Spatially Dependent Can be removed significantly in Frequency Domain

Periodic Noise (Example)

Estimation of Noise Parameters Periodic noise: Fourier spectral components Imaging system is available: study the characteristics of system noise by acquiring a set of images of flat environment under uniform illumination(constant background). Only images are available: estimate the noise PDF from small patches of reasonably constant gray level.

Estimation of Noise Parameters ( Example )

Estimation of Noise Parameters

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