1. EE465: Introduction to Digital Image Processing
Image Deblurring
Introduction
Inverse filtering
Suffer from noise amplification
Wiener filtering
Tradeoff between image recovery and noise suppression
Iterative deblurring*
Landweber algorithm
EE465: Introduction to Digital Image Processing

2. EE465: Introduction to Digital Image Processing
Where does blur come from?
Optical blur: camera is out-of-focus
Motion blur: camera or object is moving
Why do we need deblurring?
Visually annoying
Wrong target for compression
Bad for analysis
Numerous applications
EE465: Introduction to Digital Image Processing

3. Application (I): Astronomical Imaging
The Story of Hubble Space Telescope (HST)
HST Cost at Launch (1990): $1.5 billion
Main mirror imperfections due to human errors
Got repaired in 1993
EE465: Introduction to Digital Image Processing

4. Restoration of HST Images
EE465: Introduction to Digital Image Processing

5. EE465: Introduction to Digital Image Processing
Another Example
EE465: Introduction to Digital Image Processing

6. The Real (Optical) Solution
Before the repair
After the repair
EE465: Introduction to Digital Image Processing

7. Application (II): Law Enforcement
Motion-blurred license plate image
EE465: Introduction to Digital Image Processing

8. EE465: Introduction to Digital Image Processing
Restoration Example
EE465: Introduction to Digital Image Processing

9. Application into Biometrics
out-of-focus iris image
EE465: Introduction to Digital Image Processing

10. Modeling Blurring Process
• Linear degradation model
y(m,n)
x(m,n)
h(m,n) +
blurring filter
additive white Gaussian noise
EE465: Introduction to Digital Image Processing

11. Blurring Filter ExampleFT
Gaussian filter can be used to approximate out-of-focus blur
EE465: Introduction to Digital Image Processing

12. EE465: Introduction to Digital Image Processing
Blurring Filter Example (Con’t) FT
MATLAB code: h=FSPECIAL('motion',9,30);
Motion blurring can be approximated by 1D low-pass filter along the moving direction
EE465: Introduction to Digital Image Processing

13. EE465: Introduction to Digital Image Processing
The Curse of Noise
z(m,n)
y(m,n)
x(m,n)
h(m,n) +
Blurring SNR
EE465: Introduction to Digital Image Processing

14. Image Example BSNR=10dB BSNR=40dB
x(m,n)
BSNR=10dB
BSNR=40dB
h(m,n): 1D horizontal motion blurring [ ]/7
EE465: Introduction to Digital Image Processing

15. Blind vs. Nonblind Deblurring
Blind deblurring (deconvolution): blurring kernel h(m,n) is unknown
Nonblind deconvolution:
blurring kernel h(m,n) is known
In this course, we only cover the nonblind case (the easier case)
EE465: Introduction to Digital Image Processing

16. EE465: Introduction to Digital Image Processing
Image Deblurring
Introduction
Inverse filtering
Suffer from noise amplification
Wiener filtering
Tradeoff between image recovery and noise suppression
Iterative deblurring*
Landweber algorithm
EE465: Introduction to Digital Image Processing

17. EE465: Introduction to Digital Image Processing
Inverse Filter
x(m,n)
h(m,n)
y(m,n)
hI(m,n)
x(m,n) ^
blurring filter
inverse filter
hcombi (m,n)
To compensate the blurring, we require
EE465: Introduction to Digital Image Processing

18. Inverse Filtering (Con’t)
x(m,n)
h(m,n) +
y(m,n)
hI(m,n) ^
x(m,n)
inverse filter
Spatial:
Frequency:
amplified noise
EE465: Introduction to Digital Image Processing

19. EE465: Introduction to Digital Image Processing
Image Example
motion blurred image
at BSNR of 40dB
deblurred image after
inverse filtering
Q: Why does the amplified noise look so bad?
A: zeros in H(w1,w2) correspond to poles in HI (w1,w2)
EE465: Introduction to Digital Image Processing

20. Pseudo-inverse Filter
Basic idea:
To handle zeros in H(w1,w2), we treat them separately
when performing the inverse filtering
EE465: Introduction to Digital Image Processing

21. Image Example motion blurred image deblurred image after
at BSNR of 40dB
deblurred image after
Pseudo-inverse filtering
(=0.1)
EE465: Introduction to Digital Image Processing

22. EE465: Introduction to Digital Image Processing
Image Deblurring
Introduction
Inverse filtering
Suffer from noise amplification
Wiener filtering
Tradeoff between image recovery and noise suppression
Iterative deblurring*
Landweber algorithm
EE465: Introduction to Digital Image Processing

23. EE465: Introduction to Digital Image Processing
Norbert Wiener ( )
The renowned MIT professor Norbert Wiener
was famed for his absent-mindedness. While
crossing the MIT campus one day, he was
stopped by a student with a mathematical
problem. The perplexing question answered,
Norbert followed with one of his own: "In which
direction was I walking when you stopped me?"
he asked, prompting an answer from the
curious student. "Ah," Wiener declared,
"then I've had my lunch”
Anecdote of Norbert Wiener
EE465: Introduction to Digital Image Processing

24. EE465: Introduction to Digital Image Processing
Wiener Filtering
Also called Minimum Mean Square Error (MMSE) or Least-Square (LS) filtering
constant
noise energy
Example choice of K:
signal energy
K=0  inverse filtering
EE465: Introduction to Digital Image Processing

25. EE465: Introduction to Digital Image Processing
Image Example
motion blurred image
at BSNR of 40dB
deblurred image after
wiener filtering
(K=0.01)
EE465: Introduction to Digital Image Processing

26. EE465: Introduction to Digital Image Processing
Image Example (Con’t)
K=0.1
K=0.01
K=0.001
EE465: Introduction to Digital Image Processing

27. Constrained Least Square Filtering
Similar to Wiener but a different way of balancing the tradeoff between
Example choice of C:
Laplacian operator
=0  inverse filtering
EE465: Introduction to Digital Image Processing

28. EE465: Introduction to Digital Image Processing
Image Example
=0.1
 =0.01
 =0.001
EE465: Introduction to Digital Image Processing

29. EE465: Introduction to Digital Image Processing
Image Deblurring
Introduction
Inverse filtering
Suffer from noise amplification
Wiener filtering
Tradeoff between image recovery and noise suppression
Iterative deblurring*
Landweber algorithm
EE465: Introduction to Digital Image Processing

30. Method of Successive Substitution
A powerful technique for finding the roots of any function f(x)
Basic idea
Rewrite f(x)=0 into an equivalent equation x=g(x) (x is called fixed point of g(x))
Successive substitution: xi+1=g(xi)
Under certain condition, the iteration will converge to the desired solution
EE465: Introduction to Digital Image Processing

31. EE465: Introduction to Digital Image Processing
Numerical Example
Two roots:
successive substitution:
EE465: Introduction to Digital Image Processing

32. Numerical Example (Con’t)
Note that iteration quickly converges to x=1
EE465: Introduction to Digital Image Processing

33. EE465: Introduction to Digital Image Processing
Landweber Iteration
Linear blurring
We want to find the root of
relaxation parameter – controls convergence property
Successive substitution:
EE465: Introduction to Digital Image Processing

34. EE465: Introduction to Digital Image Processing
Asymptotic Analysis
Assume convergence condition:
we have
inverse filtering
EE465: Introduction to Digital Image Processing

35. Advantages of Landweber Iteration
No inverse operation (e.g., division) is involved
We can stop the iteration in the middle way to avoid noise amplification
It facilitates the incorporation of a priori knowledge about the signal (X) into solution algorithm
More detailed analysis is included in EE565: Advanced Image Processing
EE465: Introduction to Digital Image Processing