Regularization of Large-scale Ill-conditioned Least Squares Problems Regularization of Large{scale Ill{conditioned Least Squares Problems

Ill{conditioned problems arise in important areas like geophysics, medical imaging and signal processing. The fact that the ill{cond-itioning is an intrinsic feature of these problems makes it necessary to develop special numerical methods to treat them. Regularization methods belong to this class. The lack of robust regularization methods for large{scale ill{cond-itioned problems motivated this project. Our goal is to develop a regularization method for the least squares problem as a large{scale discrete ill{posed problem arising in seismic inversion.