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Image Deblurring

Image Deblurring. Introduction Inverse filtering Suffer from noise amplification Wiener filtering Tradeoff between image recovery and noise suppression Iterative deblurring* Landweber algorithm. Introduction. Where does blur come from? Optical blur: camera is out-of-focus

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Image Deblurring

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  1. 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. Introduction • 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. 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. 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 Example FT Gaussian filter can be used to approximate out-of-focus blur EE465: Introduction to Digital Image Processing

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

  14. Image Example BSNR=10dB x(m,n) BSNR=40dB h(m,n): 1D horizontal motion blurring [1 1 1 1 1 1 1]/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. 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. ^ x(m,n) Inverse Filter x(m,n) h(m,n) y(m,n) hI(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) y(m,n) h(m,n) ^ hI(m,n) x(m,n) inverse filter Spatial: Frequency: amplified noise EE465: Introduction to Digital Image Processing

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

  22. 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. Norbert Wiener (1894-1964) 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. 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. Image Example motion blurred image at BSNR of 40dB deblurred image after wiener filtering (K=0.01) EE465: Introduction to Digital Image Processing

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

  29. 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. 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. 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. 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

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