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

SIAM Annual Meeting Discrete Ill-Posed problem

SIAM Annual Meeting Need for regularization

SIAM Annual Meeting Tikhonov Regularization

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

SIAM Annual Meeting Tikhonov Regularization

SIAM Annual Meeting Bidiagonalization

SIAM Annual Meeting Relating A,L

SIAM Annual Meeting Projected Problem

SIAM Annual Meeting Choosing

SIAM Annual Meeting Iterative Method

SIAM Annual Meeting Regularizing algorithm

SIAM Annual Meeting TGSVD of the Projected Problem

SIAM Annual Meeting Numerical Examples

SIAM Annual Meeting Original and blurred images OriginalBlurred + Error

SIAM Annual Meeting Restoration L =derivative operator Original Restored

SIAM Annual Meeting Restoration L= Laplacian OriginalRestored

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

SIAM Annual Meeting Conclusion and Future work