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Multilevel approaches for the total least squares method in deblurring problems

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. Outline. Problem Multilevel Method Algorithm Numerical Example Conclusion and Future Work.

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Multilevel approaches for the total least squares method in deblurring problems

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

  3. Problem ICIAM 2007 - Zurich, Switzerland

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

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

  6. Classical Multilevel Method ICIAM 2007 - Zurich, Switzerland

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

  8. Restriction and Prolongation Operators V Haar wavelet transform V1 W1 ICIAM 2007 - Zurich, Switzerland

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

  10. Properties ICIAM 2007 - Zurich, Switzerland

  11. Bandwidth reduction ICIAM 2007 - Zurich, Switzerland

  12. Pre-Smoothing ICIAM 2007 - Zurich, Switzerland

  13. Post-Smoothing ICIAM 2007 - Zurich, Switzerland

  14. Two-Level Method V V1 W1 ICIAM 2007 - Zurich, Switzerland

  15. Multilevel Method V V1 W1 V2 W2 V3 W3 ICIAM 2007 - Zurich, Switzerland

  16. Numerical Example ICIAM 2007 - Zurich, Switzerland

  17. Numerical Example ICIAM 2007 - Zurich, Switzerland

  18. Numerical Example ICIAM 2007 - Zurich, Switzerland

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

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