1. Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-image Raw-data Alessandro Foi, Mejdi Trimeche, Vladimir Katkovnik, and Karen Egiazarian Department of Signal Processing, Tampere University of Technology

2. Noise Modeling for General Cases Noisy Images Variant Acquisition Devices Image Processing Output Images Noise Model It is hard to construct a general noise model!

3. Noise Modeling for Specific Case Noisy Images Image Processing Output Images Noise Model Foi, A., M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw- data”, IEEE Trans. Image Process., vol. 17, no. 10, pp. 1737-1754, October 2008.

4. An Example of Application: Sharpness Enhancement Noisy Image Sharpness Enhancement Output Image Noise Model Original Image Enhanced Image with Noise Suppression

5. Application with Noise Model Spatial Index Intensity

6. Application with Noise Model Scene Radiance Image Sensor Camera Processing Output Image Camera System Denoising, Demosaicing, Deblurring, Compression Raw-Data Noise Modeling

7. Noise Model Scene Light Photon Sensor Electrical Devices Image Raw-data Poisson Noise Gaussian Noise Signal-dependentSignal-independent Camera Sensor

8. Noise Model

9. Poissonian-Gaussian Noise Poisson: Gaussian: Overall Variance of z: Overall Standard-deviation of z:

10. Noise Level Function Intensity Standard-deviation Intensity Standard-deviation a = 0.02 2, 0.06 2, 0.10 2, b = 0.04 2 a = 0.4 2, b = 0.02 2, 0.06 2, 0.10 2

11. Poissonian-Gaussian Noise

12. Raw-data Modeling Overall Standard-deviation of z: 1.Quantum Efficiency 2.Pedestal Parameter 3.Analog Gain Efficiency ↑  a↓ The percentage of photons hitting the photoreactive surface that will produce an electron

13. Noise Model Sensor Model Noise Model

14. Sensor Parameter and Noise Parameter Sensor Parameter: ISO-number  Gain Temperature Shutter Time

15. Sensor Parameter and Noise Parameter

16. Two Stages of Noise Estimation Local estimation of multiple expectation/standard-deviation pairs. Global parametric model fitting. Intensity Standard-deviation

17. Two Stages of Noise Estimation Local Estimation Intensity Standard-deviation Global Parametric Model Fitting

18. Local Estimation Local Expectation/ Standard-deviation Pair Locally Smoothed Value Locally Detail Value

19. Wavelet Analysis Local Expectation/ Standard-deviation Pair Locally Smoothed Value Locally Detail Value Noise Component

20. Wavelet Analysis Noise Component For Smooth Region

21. Wavelet Analysis Noise Component For Smooth Region

22. Smooth Region Segmentation Smooth Region Segmentation Edge Detection Smoothing

23. Level Sets Segmentation Smooth Region Segmentation Smooth Region … Level Segmentation Intensity 01 …

24. Local Estimation of y i … Estimation

25. Local Estimation of σ i … This factor, which comes from the mean of the chi-distribution with n − 1 degrees of freedom, makes the estimate unbiased for normally and identically independently distributed (i.i.d.)

26. Global Fitting Intensity Standard-deviation

27. Clipping Effect Intensity Spatial Index 1 0 Intensity Spatial Index 1 0 Clipping from above Clipping from below

28. Clipping Effect Intensity Standard-deviation

29. Clipping Model Original Signal Clipped Signal

30. Clipping Model Original Signal Clipped Signal

31. Clipping Effect Original Signal Clipped Signal

32. Clipping Model For Image Noise Original Signal Clipped Signal

33. Clipping Correction Ideal EstimationEstimation under Clipping Direct Transformation Inverse Transformation

34. Direct Transformation Clipped from Ideal

35. Direct Transformation Clipped from Ideal

36. Clipping Correction Ideal EstimationEstimation under Clipping Direct Transformation Inverse Transformation

38. Ideal EstimationEstimation under Clipping Direct Transformation Inverse Transformation

39. Clipping from above and below Intensity Spatial Index 1 0 Clipping from above Clipping from below

40. Correction Results Intensity Standard-deviation

41. Algorithm Overview Wavelet Analysis Input Image Smooth Region Segmentation Smooth Region Segmentation Level Sets Segmentation Level Sets Segmentation Local Estimation Clipping Correction Clipping Correction Global Fitting Global Fitting

42. Experiments Original y Observation z degraded by Poissonian and Gaussian noise with parameters χ = 100 (a = 0.01) and b = 0.042

43. Results Intensity Standard-deviation Reduce the influence of fine textures and edges Standard-deviation Intensity

44. Test Image Intensity

45. Test Image Intensity

46. Test Image Intensity

47. Test Image Intensity Test Image

48. Denoising Clipped Signals Foi, A.,.Practical denoising of clipped or overexposed noisy images., Proc. 16th European Signal Process. Conf., EUSIPCO 2008, Lausanne, Switzerland, August 2008. Original Signal Clipped Estimated Signal Spatial Index

49. Denoising Clipped Signals Noisy Image

50. Denoising Clipped Signals (FujiÞlm FinePix S9600 Camera), Denoised Result

51. Denoising Clipped Signals Denoised and Debiased Result