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Robust Super-Resolution

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  1. Robust Super-Resolution Presented By: Sina Farsiu

  2. Project Goals • Understanding & simulation of Dr. Assaf Zomet, et.al. paper : “Robust Super-Resolution” [1] • Comparing the results obtained by this method to other methods • Enhancing the method introduced in: [1]

  3. Super-Resolution Objective • Generation of a high-resolution image from multiple low-resolution moving frames of a scene.

  4. Super-Resolution Formulation

  5. Solutions for S-R Problem • No Noise: • With Noise

  6. Problem with These Solutions • In the presence of outliers (error in motion estimation, inaccurate blur model, pepper & salt noise, …), these methods do not work accurately. • Robust S-R methods can help in these situations.

  7. Robust S-R Formulation

  8. Robust S-R Formulation • Robustness

  9. Why Median? • Median is an estimate of mean. • Unlike regularization method only one of low resolution frames contributes to reconstruct each pixel in the high-resolution frame. So outliers in other frames are discarded in the reconstruction process. • Claim: In the absence of additive noise to all frames median method works better than regularization method.

  10. What if noise is added to all frames? • Claim: If considerable amount of additive noise is present in all frames regularization method works as good or even better than median method.

  11. Median-Average Reconstruction • Instead of using We can combine average and median operators to get better results.

  12. Bias Detection Procedure • It is useful to detect the outliers in the low resolution frames. • We can omit those outlier pixels in our procedures. • The difficulty is to differentiate between aliasing and outlier effects.

  13. Bias Detection • Formulation • After thresholding non zero values are due to aliasing or outliers.

  14. Due to outlier Due to aliasing Bias Detection Result

  15. Bias detection Procedure • 1: compute • 2: Threshold • 3: Filter the result with a LPF • 4: Threshold • 5: Omit corresponding pixels from super-resolution procedure

  16. Bias Detection • B-D method works only for uniform gray level outliers. • In many situations median operation in robust super-resolution eliminates the bias of the estimator.

  17. Original L-R Frame

  18. Robust S-R Reconstructed H-R Frame mse=0.0017

  19. Median Reconstruction after adding noise 0.0131

  20. Regularized S-R Reconstructed H-R Frame mse=0.0131`

  21. Regularized Reconstruction after adding noise mse=.0125

  22. Error Due to Outlier

  23. Error Due to Aliasing

  24. Conclusion • Robust super-resolution method is quite effective in the presence of outliers, and produces better results in comparison with regularization method. • In the presence of additive noise in all low –resolution frames this method loses its superiority to the regularization method.

  25. Conclusion & Results • Combination of mean and median operators can help us in this situation. • Proposed bias detection algorithm is an effective method to detect outliers. • If outliers are the only source of error in the L-R frames(no additive noise), more iterations we use smaller mse we will achieve.

  26. Suggestions for Future Research • Combining regularization and robust super-resolution methods. • Using bias detection results in regularization method. • Using robust super-resolution method in frequency domain.

  27. Acknowledgment • Thanks to Dr.Assaf Zomet, Dr.Michael Elad, Dirk Robinson and Dr. Peyman Milanfar for their valuable advices & suggestions.

  28. references • "Robust Super Resolution",  A. Zomet, A. Rav-Acha and S. Peleg Proceedings of the International Conference on Computer Vision and Pattern Recognition (CVPR), Hawaii, December 2001. • "Efficient Super-Resolution and Applications to Mosaics", A. Zomet and S. Peleg, Proceedings of the International Conference on Pattern Recognition (ICPR), Barcelona, September 2000.

  29. “A Computationally effective Image super-resolution Algorithm”, Nguyen, N., P. Milanfar, G.H. Golub, IEEE Transactions on Image Processing, vol. 10, no. 4, pp. 573-583, April 2001 • “A Fast Super-Resolution Reconstruction Algorithm for Pure Transnational Motion and Common Space Invariant Blur”, M. Elad and Y. Hel-Or, the IEEE Trans. on Image Processing, Vol.10, no.8, pp.1187-93, August 2001.

  30. Thank You All

  31. Additional Simulatins

  32. Original H-R Frame

  33. Blured median

  34. Projected L-R frame

  35. L-R Frame

  36. Regularization with high noisemse=.0481

  37. Median with high noisemse=.0693

  38. Composite Median & AverageMSE=0.0592

  39. Original H.R. Frame

  40. L.R. Frame Before Adding Noise

  41. L.R. Frame After Adding Noise

  42. Regularized ReconstructionMSE=.0216

  43. Median ReconstructionMSE=.0077