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Image Restoration - Focus on Noise. References. Gonzales and Wood second edition Jain. Enhancement - Restoration. Overview. Measured. From [1]. Unknown Approximation. Noise sources. Device noise (often thermal) Digitization process Sampling and quantization Transmission Environment.

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References
References

  • Gonzales and Wood second edition

  • Jain



Overview
Overview

Measured

From [1]

Unknown

Approximation


Noise sources
Noise sources

  • Device noise (often thermal)

  • Digitization process

    • Sampling and quantization

  • Transmission

  • Environment


Noise models
Noise models

  • White noise: autocorrelation is an impulse

  • Colored noise

  • Usually assume that noise is uncorrelated with the image

  • Gaussian: circuit noise, illumination, environment (thermal)

  • Rayleigh: range imaging

  • Uniform: easy to model

  • Others: exponential, impulse (salt and pepper)


Sample pdfs
Sample pdfs

From [1]


Test image
Test image

3 distinct gray levels

From [1]


Additive noise
Additive Noise

Noise is added to the respective gray levels. Hence the multiple lobe histograms

From [1]


Additive noise1
Additive Noise

From [1]


Estimation of noise parameters periodic noise
Estimation of Noise Parameters – Periodic Noise

  • Periodic noise – filter in frequency domain. Appears as pair of impulses. The removal can be automated when the impulses are more pronounced.

From [1]


Noise parameter estimation known model
Noise Parameter Estimation – Known Model

  • Noise parameters can be computed by focusing on small sub-image (patch).

From [1]



Image restoration noise only degradation
Image Restoration – Noise Only Degradation

Use Filters: Spatial Filter

n(x,y) is unknown.

For periodic noise, N(u,v) can be estimated from G(u,v) – spikes at predominant noise frequencies.


Noise reduction filters
Noise Reduction Filters

Noise Reduction Filters




Comparisons of filters
Comparisons of Filters

  • Arithmetic: Smoothing reduces noise. Blurring.

  • Geometric: Smoothing. Less loss of image detail than Arithmetic.

  • Harmonic: Reduces salt noise. No impact on pepper noise.

  • Contraharmonic: Reduces salt and pepper noise. Q>0 reduces pepper noise. Q<0 reduces salt noise. Cannot reduce salt and pepper noise in the same pass.

    Q = 0 yields Arithmetic

    Q = -1 yields Harmonic







Adaptive median filter
Adaptive Median Filter

  • Preserve detail.

  • Smooth non-impulse noise {different from tradition median filter}.

  • Like Adaptive Filter use a window Sxy.

    • The center of the window is replaced by the result

  • Unlike Adaptive Filter, the size of the window is increased.

  • Notation

    zmin = min gray level in Sxy.

    zmax = max gray level in Sxy.

    zmed = median gray level in Sxy.

    zxy = gray level at coordinate (x,y).

    Smax = max allowed size of Sxy.


Adaptive median filter1
Adaptive Median Filter

Level A:

{ is zmed an impulse?}

while window size is less than Smax do

if zmed > zmin AND zmed < zmax, then Go To Level B

else increase the window size

end while

output zxy

Level B:

{ is zxy an impulse?}

if zxy > zmin AND zxy < zmax, then output zxy

else output zmed

  • Algorithm objectives

    • Remove salt and pepper noise

    • Smooth other noise

    • Reduce distortions, e.g. excessive thinning or thickening of boundaries



Periodic noise
Periodic Noise

  • Band reject filters

  • Band pass filters

  • Notch filters


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