CS654: Digital Image Analysis Lecture 22: Image Restoration - II

Recap of Lecture 21 Image restoration vs. enhancement What is restoration Image restoration model Continuous, discrete formulation Point spread function Noise

Outline of Lecture 22 2D discrete domain modeling Restoration with only noise Restoration with degradation Blind deconvolution Motion Blur Inverse Filtering

Image restoration pipeline Target Images: Gonzalez & Woods, 3 rd edition

2D Discrete Domain Representation Block Circulant matrix

2D Discrete Domain Representation

Image restoration: 1D case Let, What happens if we do

Image restoration DFT :

Restoration in presence of only noise Spatial domain: Frequency domain: Spatial filtering is the choice when additive random noise is present Mean filter Median Filter (order statistics),max, min, mid-point Bandpass, band-reject filters Adaptive filters

Examples

In presence of degradation Degradation (spatial domain) = conv(PSF, image) + noise Degradation (Freq. domain) = H(PSF).H(image) + H(noise) where H=transformation function Image deconvolution Deconvolution filters

Degradation estimation Estimation ObservationExperimentation Mathematical Modeling Blind deconvolution A technique that permits recovery of the target scene from distorted image(s) in the presence of a unknown point spread function (PSF)

Estimation by Observation Spatial domain: Frequency domain: Processed sub-image:

Estimation by Experimentation Scene Acquired Image Degradation function  Impulse response 1.Impulse simulation 2.Degradation function estimation Simulated impulseImpulse response Images: Gonzalez & Woods, 3 rd edition

Estimation by Mathematical Modeling Physical characteristics of atmospheric turbulence Images: Gonzalez & Woods, 3 rd edition

With motion Camera Estimation from Basic Principles Without motion Camera

Uniform linear motion blur

2-D Fourier Transform:

Uniform linear motion blur

Example Images: Gonzalez & Woods, 3 rd edition Input ImageMotion Blurred Image (a=b=0.1, T=1)

Inverse Filtering Simplest approach for image restoration – direct inverse filtering Frequency domain:

Example Full filter CR = 40 CR = 85CR=70 Input image

Thank you Next Lecture: Image Restoration