1. SIAM Annual Meeting 20051 An Iterative, Projection-Based Algorithm for General Form Tikhonov Regularization Misha Kilmer, Tufts University Per Christian Hansen, Technical University of Denmark Malena Español, Tufts University

2. SIAM Annual Meeting 20052 Outline Problem Background Algorithm Numerical Examples Conclusion and future work

3. SIAM Annual Meeting 20053 Discrete Ill-Posed problem

4. SIAM Annual Meeting 20054 Need for regularization

5. SIAM Annual Meeting 20055 Tikhonov Regularization

6. SIAM Annual Meeting 20056 Tikhonov Method: choosing L-curve (Lawson-Hansen)

7. SIAM Annual Meeting 20057 Tikhonov Regularization

8. SIAM Annual Meeting 20058 Bidiagonalization

9. SIAM Annual Meeting 20059 Relating A,L

10. SIAM Annual Meeting 200510 Projected Problem

11. SIAM Annual Meeting 200511 Choosing

12. SIAM Annual Meeting 200512 Iterative Method

13. SIAM Annual Meeting 200513 Regularizing algorithm

14. SIAM Annual Meeting 200514 TGSVD of the Projected Problem

15. SIAM Annual Meeting 200515 Numerical Examples

16. SIAM Annual Meeting 200516 Original and blurred images OriginalBlurred + Error

17. SIAM Annual Meeting 200517 Restoration L =derivative operator Original Restored

18. SIAM Annual Meeting 200518 Restoration L= Laplacian OriginalRestored

19. SIAM Annual Meeting 200519 Comparing with L=I and L=Laplacian OriginalBlurred + Error L=Derivative Op.L=Laplacian Op.L=Identity

20. SIAM Annual Meeting 200520 Conclusion and Future work