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Enhancing Image Quality: Restoration Techniques and Noise Reduction Methods

Learn about image restoration techniques, noise models, adaptive filters, and more to improve image quality effectively. Explore spatial filtering, adaptive median filtering, periodic noise reduction, and advanced deconvolution methods.

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Enhancing Image Quality: Restoration Techniques and Noise Reduction Methods

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  1. Chapter 5 Image Restoration

  2. Preview • Goal: improve an image in some predefined sense. • Image enhancement: subjective process • Image restoration: objective process • Restoration attempts to reconstruct an image that has been degraded by using a priori knowledge of the degradation process. • Modeling the degradation and applying the inverse process to recover the original image. • When degradation model is unknown  blind deconvolution (ICA)

  3. A Model of Degradation • or • Given g(x,y), some knowledge about H, and some knowledge about the noise term, obtain an estimate of the original image.

  4. Noise Models • Gaussian noise: electronic circuit sensor noise • Rayleigh noise: range imaging • Erlang (Gamma noise): laser imaging • Exponential noise: laser imaging • Uniform noise • Impulse (salt-and-pepper noise): faulty switching • Periodic noise

  5. Gaussian Noise • The PDF of a Gaussian random variable, z, is given by:

  6. Rayleigh Noise • The PDF of Rayleigh noise is given by: • Mean and variance are given by: • Useful for approximating skewed histograms.

  7. Erlang (Gamma) Noise • The PDF of Erlang noise is given by: • Mean and variance:

  8. Exponential Noise • The PDF of exponential noise is given by: where a >0 • Mean and variance:

  9. Uniform Noise • The PDF of uniform noise is given by: • Mean and variance:

  10. Impulse (Salt-and-Pepper) Noise • The PDF of (bipolar) impulse noise is given by:

  11. Periodic Noise • Arises typically from electrical or electromechanical interference during image acquisition. • The only type of spatially dependent noise considered in this chapter.

  12. Illustration (I)

  13. Illustration (II)

  14. Estimation of Noise Parameters • Periodic noises: from Fourier spectrum • Others: try to compute the mean and variance of a subimage S (containing only constant gray levels).

  15. Restoration in the Presence of Noise Only – Spatial Filtering • Mean filters: • Arithmetic mean filters • Geometric mean filter • Harmonic mean filter: • Contraharmonic mean filter:Q: the order of the filter. Q>0 eliminates pepper noise, Q <0 eliminates salt noise.

  16. Illustration (I)

  17. Illustration (II)

  18. Illustration (III)

  19. Order-Statistics Filters • Median filters • Max and min filters • Midpoint filter: • Alpha-trimmed mean filter: delete the d/2 lowest and d/2 highest gray-level values of g(s,t) in the neighborhood of Sxy , the average

  20. Illustration (I)

  21. Illustration (II)

  22. Illustration (III)

  23. Adaptive Filters • Filter’s behavior changes based on statistical characteristics of the image inside the filter region defined by the mxn window. • Adaptive, local noise reduction filter • Adaptive median filter

  24. Adaptive, local noise reduction filter • (a) g(x,y): the value of the noisy image at (x,y) • (b) The variance of the noise • (c) The mean of the pixels in Sxy • (d) Local variance of the pixels in Sxy • If (b) is zero, return g(x,y) • If (d) is high relative to (b), the filter should return a value close to g(x,y) • If the two variances are equal, return the arithmetic mean of the pixels in Sxy

  25. Illustration

  26. Adaptive Median Filter • Notation: • zmin: minimum gray level value in Sxy • zmax: maximum gray level value in Sxy • zmed: median of gray levels in Sxy • zxy: gray level value at (x,y) • Smax: maximum allowed size of Sxy • Level A: A1= zmed– zmin, A2= zmed– zmaxif A1> 0 and A2 <0, go to level BElse increase the window sizeIf window size <= Smax repeat level Aelse output zxy • Level B: B1= zxy– zmin, B2= zxy– zmaxif B1> 0 and B2 <0, output zxyElse output zmed

  27. Illustration

  28. Periodic Noise Reduction • By Fourier domain filtering: • Bandreject filters • Bandpass filters • Notch filters

  29. Illustration

  30. Ideal Notch Reject Filter • Ideal notch reject filter: where

  31. Butterworth Notch Reject Filter

  32. Gaussian Notch Reject Filter

  33. Notch Filters

  34. Linear, Position-Invariant Degradations • Estimating the degradation function • By image observation • By experimentation • By modeling

  35. Estimation by Image Observation • In the strong signal area, using sample gray levels of the object and background to construct an unblurred image • Then, • Use Hs(u,v) to estimate H(u,v)

  36. Estimation by Experimentation • Simulate an impulse by a (very) bright dot of light, the response G(u,v) is related to H(u,v) by:

  37. Figure 5.24

  38. Estimation by Modeling • Modeling atmospheric turbulence

  39. Atmospheric Turbulence

  40. Estimation by Modeling (cont’d) • Modeling effect of planar motion x0(t),y0(t): • If T is the duration of the exposure, then • It can be shown that:

  41. Motion Blur • If x0(t)=at/T and y0(t)=0, then

  42. Motion Blur Example

  43. Deconvolution • Inverse filtering • Minimum mean square error (Wiener) filtering • Constrained least squares filtering • Geometric mean filter

  44. Results (Inverse Filter)

  45. Results (Inverse and Wiener)

  46. Results (Motion Blurs)

  47. Results (Constrained LS Filter)

  48. Recent Developments • Blind deconvolution • http://cs.unc.edu/~lazebnik/research/fall08/lec05_deblurring.pdf • Removing camera shake from a single photographhttp://cs.nyu.edu/~fergus/research/deblur.html

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