Abstract
In this contribution, we concentrate on approaches for the choice of regularization parameters in inner-outer regularization methods. We specically focus on discrete inverse problems of the form Ax ~b arising in cryo-electron microscopy single particle analysis.
These problems have very specic properties such as an extremely large level of noise in the input data or an atypical form of the point spread function that represents eects of the optics of an electron microscope. We describe a variant of an inner-outer regularization method combining Golub-Kahan iterative bidiagonalization with inner Tikhonov regularization and discuss how the non-standard properties of the studied problem aect its behavior.
Namely, we analyze two approaches for the choice of regularization parameter for the inner Tikhonov regularization and study its inuence on stopping criteria and the quality of the obtained solution.