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An Iterative, Projection-Based Algorithm for General Form Tikhonov Regularization

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. Outline. Problem Background Algorithm Numerical Examples Conclusion and future work.

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An Iterative, Projection-Based Algorithm for General Form Tikhonov Regularization

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  1. 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 SIAM Annual Meeting 2005

  2. Outline • Problem • Background • Algorithm • Numerical Examples • Conclusion and future work SIAM Annual Meeting 2005

  3. Discrete Ill-Posed problem SIAM Annual Meeting 2005

  4. Need for regularization SIAM Annual Meeting 2005

  5. Tikhonov Regularization SIAM Annual Meeting 2005

  6. Tikhonov Method: choosing l L-curve (Lawson-Hansen) SIAM Annual Meeting 2005

  7. Tikhonov Regularization SIAM Annual Meeting 2005

  8. Bidiagonalization SIAM Annual Meeting 2005

  9. Relating A,L SIAM Annual Meeting 2005

  10. Projected Problem SIAM Annual Meeting 2005

  11. Choosing l SIAM Annual Meeting 2005

  12. Iterative Method SIAM Annual Meeting 2005

  13. Regularizing algorithm SIAM Annual Meeting 2005

  14. TGSVD of the Projected Problem SIAM Annual Meeting 2005

  15. Numerical Examples SIAM Annual Meeting 2005

  16. Original and blurred images Original Blurred + Error SIAM Annual Meeting 2005

  17. Restoration L =derivative operator Original Restored SIAM Annual Meeting 2005

  18. Restoration L= Laplacian Original Restored SIAM Annual Meeting 2005

  19. Comparing with L=I and L=Laplacian Original Blurred + Error L=Derivative Op. L=Laplacian Op. L=Identity SIAM Annual Meeting 2005

  20. Conclusion and Future work SIAM Annual Meeting 2005

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