Properties of hybrid LSQR method for the solution discrete inverse problems in Single Particle Analysis
Abstrakt
In this contribution, we focus on properties of hybrid LSQR method applied to the solution of discrete inverse problems Ax TILDE OPERATOR+D91 b arising in single particle analysis. Hybrid LSQR represents a combination of iterative projection by Golub-Kahan bidiagonalization with Tikhonov regularization applied to the projected problem.
Such a combination has shown to be efficient in prevention of over-fitting of the computed approximation while maintaining the computational cost feasible. Properties of the algorithm are, however, highly dependent on the choice of regularization parameters.
Here, we describe suitable choices of regularization parameters for hybrid LSQR motivated by the underlying application. Further, we analyze the resulting properties of the projected problem, its solution and residual vectors, and compare them to the properties of standard LSQR.