1. Multilevel approaches for the total least squares method in deblurring problems Malena Español, Tufts University Misha Kilmer, Tufts University Dianne O’Leary, University of Maryland, College Park

2. ICIAM 2007 - Zurich, Switzerland2 Outline Problem Multilevel Method Algorithm Numerical Example Conclusion and Future Work

3. ICIAM 2007 - Zurich, Switzerland3 Problem

4. ICIAM 2007 - Zurich, Switzerland4 Total Least-Squares Method Regularization by Truncated TLS by Fierro, Golub, Hansen and O’Leary (1997)

5. ICIAM 2007 - Zurich, Switzerland5 Classical Two-Level Method Pre-Smoothing Post-Smoothing Coarse-Grid Correction Restriction Prolongation

6. ICIAM 2007 - Zurich, Switzerland6 Classical Multilevel Method

7. ICIAM 2007 - Zurich, Switzerland7 Two-level TLS Method “Post-Smoothing” Pre-Smoothing

8. ICIAM 2007 - Zurich, Switzerland8 Restriction and Prolongation Operators Haar wavelet transform V W1W1 V1V1

9. ICIAM 2007 - Zurich, Switzerland9 Changing basis Optical Tomography: Zhu, Wang and Zhang (1998)

10. ICIAM 2007 - Zurich, Switzerland10 Properties

11. ICIAM 2007 - Zurich, Switzerland11 Bandwidth reduction

12. ICIAM 2007 - Zurich, Switzerland12 Pre-Smoothing

13. ICIAM 2007 - Zurich, Switzerland13 Post-Smoothing

14. ICIAM 2007 - Zurich, Switzerland14 Two-Level Method V V1V1 W1W1

15. ICIAM 2007 - Zurich, Switzerland15 Multilevel Method V V1V1 V2V2 V3V3 W3W3 W2W2 W1W1

16. ICIAM 2007 - Zurich, Switzerland16 Numerical Example

17. ICIAM 2007 - Zurich, Switzerland17 Numerical Example

18. ICIAM 2007 - Zurich, Switzerland18 Numerical Example

19. ICIAM 2007 - Zurich, Switzerland19 Conclusions and Future work General Cases – Non Structured Matrices Extension to 2D, 3D Parameter Selection Additional Constraint on E