Image Restoration · 2020. 10. 28. · Image restoration, constrained least squares filtering CSE 166, Spring 2020 Inverse filtering Wiener filtering Degraded image 28 Motion blur

Image Restoration

Image Processing

CSE 166

Lecture 8

Announcements

• Assignment 3 is due Nov 2, 11:59 PM

• Quiz 3 is Nov 4

• Assignment 4 will be released Nov 2

– Due Nov 9, 11:59 PM

• Reading

– Chapter 5: Image Restoration and Reconstruction

• Sections 5.1, 5.2, 5.3, 5.4, 5.6, and 5.7

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Model of image degradation

• Spatial domain

• Frequency domain

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Noiseimage

Originalimage

Degradedimage

Degradationfunction

Noiseimage

Originalimage

Degradedimage

Degradationfunction

Model of image degradation, then restoration

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Estimate of original imageOriginal image

Noise modeled as different probability density functions

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Adding noise from different models

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Gaussian Rayleigh Gamma

Free ofnoise

Adding noise from different models

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Exponential Uniform Salt andpepper

Free ofnoise

Histograms of sample patches

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Sample “flat” patches from images with noise

Identify closest probability density function (pdf) match:

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Gaussian Rayleigh Uniform

Mean filters

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Additive Gaussian

noise

Geometric mean

filtered

Arithmetic mean

filtered

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X-ray image

Mean filters

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Additivesalt

noise

Additivepeppernoise

Contraharmonicmean filtered

Contraharmonicmean filtered

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Order-statistic filters

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Additivesalt and peppernoise

1x median filtered

3x median filtered

2x median filtered

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Order-statistic filters

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Min filtered

Max filtered

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Comparing filters

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Alpha-trimmed mean filtered

Median filtered

Arithmetricmean

filtered

Geometric mean filtered

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Additive uniform +

salt and peppernoise

Adaptive filters

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AdditiveGaussian

noise

Arithmetricmean filtered

Geometric mean

filtered

Adaptive noise reduction

filtered

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Adaptive filters

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Additivesalt and pepper

noiseMedian filtered

Adaptive median filtered

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Periodic noise

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Conjugate impulses

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Additive sinusoidal noise

DFT magnitude

Notch reject filters

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Notch reject filter

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Filter in frequency

domain

Estimate of original

image

Degraded image

DFT magnitudeConjugate

impulses

Conjugate impulses

Notch reject filter

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Filter in frequency

domain

Estimate of original

image

Degraded image

DFT magnitude

Estimating the degradation function

• Methods

– Observation

– Experimentation

– Mathematical modeling

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Estimation of degradation function by experimentation

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Imaged (degraded) impulseImpulse of light

Estimation of degradation function by mathematical modeling

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Atmospheric turbulence

model

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Estimation of degradation function by mathematical modeling

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Motion blur model

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Image restoration

• Inverse filtering

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Image restoration, inverse filtering

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FullLimited to

radius of 40

Limited to radius of 70

Limited to radius of 85

Image restoration, Wiener filtering

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Inverse filtering Wiener filtering

Full Radially limited

Image restoration, constrained least squares filtering

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Inversefiltering

Wienerfiltering

Degraded image

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Motion blur and

additive noise

Constrained least squares filtering

Less noise

Much less noise

Next Lecture

• Color image processing

• Reading

– Chapter 7: Color Image Processing

• Sections 7.1, 7.2, 7.3, 7.4, 7.5, and 7.6

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