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Image Restoration - Focus on Noise

Image Restoration - Focus on Noise. References. Gonzales and Wood second edition Jain. Enhancement - Restoration. Overview. Measured. From [1]. Unknown Approximation. Noise sources. Device noise (often thermal) Digitization process Sampling and quantization Transmission Environment.

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Image Restoration - Focus on Noise

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  1. Image Restoration - Focus on Noise

  2. References • Gonzales and Wood second edition • Jain

  3. Enhancement - Restoration

  4. Overview Measured From [1] Unknown Approximation

  5. Noise sources • Device noise (often thermal) • Digitization process • Sampling and quantization • Transmission • Environment

  6. Noise models • White noise: autocorrelation is an impulse • Colored noise • Usually assume that noise is uncorrelated with the image • Gaussian: circuit noise, illumination, environment (thermal) • Rayleigh: range imaging • Uniform: easy to model • Others: exponential, impulse (salt and pepper)

  7. Sample pdfs From [1]

  8. Test image 3 distinct gray levels From [1]

  9. Additive Noise Noise is added to the respective gray levels. Hence the multiple lobe histograms From [1]

  10. Additive Noise From [1]

  11. Estimation of Noise Parameters – Periodic Noise • Periodic noise – filter in frequency domain. Appears as pair of impulses. The removal can be automated when the impulses are more pronounced. From [1]

  12. Noise Parameter Estimation – Known Model • Noise parameters can be computed by focusing on small sub-image (patch). From [1]

  13. Mean and S.D. estimation

  14. Image Restoration – Noise Only Degradation Use Filters: Spatial Filter n(x,y) is unknown. For periodic noise, N(u,v) can be estimated from G(u,v) – spikes at predominant noise frequencies.

  15. Noise Reduction Filters Noise Reduction Filters

  16. Applying Arithmetic and Geometric Filters From [1]

  17. More Noise Reduction Filters

  18. Comparisons of Filters • Arithmetic: Smoothing reduces noise. Blurring. • Geometric: Smoothing. Less loss of image detail than Arithmetic. • Harmonic: Reduces salt noise. No impact on pepper noise. • Contraharmonic: Reduces salt and pepper noise. Q>0 reduces pepper noise. Q<0 reduces salt noise. Cannot reduce salt and pepper noise in the same pass. Q = 0 yields Arithmetic Q = -1 yields Harmonic

  19. Order Statistics Filters

  20. Multiple applications of the Median Filter From [1]

  21. Order Statistics Filters - 2

  22. Adaptive Filter – Reduce Local Noise

  23. Arithmetic, Geometric and Adaptive Filters From [1]

  24. Adaptive Median Filter • Preserve detail. • Smooth non-impulse noise {different from tradition median filter}. • Like Adaptive Filter use a window Sxy. • The center of the window is replaced by the result • Unlike Adaptive Filter, the size of the window is increased. • Notation zmin = min gray level in Sxy. zmax = max gray level in Sxy. zmed = median gray level in Sxy. zxy = gray level at coordinate (x,y). Smax = max allowed size of Sxy.

  25. Adaptive Median Filter Level A: { is zmed an impulse?} while window size is less than Smax do if zmed > zmin AND zmed < zmax, then Go To Level B else increase the window size end while output zxy Level B: { is zxy an impulse?} if zxy > zmin AND zxy < zmax, then output zxy else output zmed • Algorithm objectives • Remove salt and pepper noise • Smooth other noise • Reduce distortions, e.g. excessive thinning or thickening of boundaries

  26. Adaptive Median Filter From [1]

  27. Periodic Noise • Band reject filters • Band pass filters • Notch filters

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