1. A New SURE Approach to Image Denoising : Interscale Orthonormal Wavelet Thresholding Florian Luisier, Thierry Blu, Senior Member, IEEE, and Michael Unser, Fellow, IEEE IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 16, NO. 3, MARCH 2007 1

2. Outline Introduction SURE Approach to Image Denoising PSNR Comparisons and Visual Quality Computation Time CONCLUSION 2

3. Introduction A nonredundant transform may match the performance of redundant ones. Do not make any explicit hypotheses on the clean image. Near-optimal performance—both regarding quality and CPU requirement 3

4. SURE Approach to Image Denoising(1/5) 4 Our goal is to find a function that minimizes By Stein’s Lemma and leads to

5. SURE Approach to Image Denoising(2/5) 5 The sensitivity of the soft-thresholding function with respect to the value of T is high.

6. SURE Approach to Image Denoising(3/5) 6 Build a linearly parameterized denoising function of the form This linear system is solved for a by

7. SURE Approach to Image Denoising(4/5) 7

8. SURE Approach to Image Denoising(5/5) 8 The number of terms K and the parameter T can be fixed independently of the image.

9. Interscale Predictor 9

10. 10

11. PSNR Comparisons and Visual Quality 11

12. PSNR Comparisons and Visual Quality 12

13. PSNR Comparisons and Visual Quality 2 important criteria of judging visual quality are widely used ： – The visibility of processing artifacts can be reduced by taking into account intrascale dependencies – The conservation of image edges can be reduced by a careful consideration of interscale dependencies in the denoising function 13

14. Computation Time 14

15. CONCLUSION Demonstrate the efficiency of our SURE-based approach (best output PSNRs for most of the images). The visual quality of our denoised images is moreover characterized by fewer artifacts than the other methods. 15