Abstrakt
Discrete inverse problems of the form Ax ALMOST EQUAL TO b arise in many practical applications. The ill-conditioning of the large-scale matrix A in combination with the presence of noise in the vector b make their solution a challenging task.
Hybrid methods represent a combination of iterative projection methods with direct regularization applied on the projected problem. Such a combination has shown to be efficient in prevention of semi-convergence and thus over-fitting of the solution while maintaining the computational cost feasible.
In this presentation we concentrate on iterative hybrid LSQR method with inner Tikhonov regularization. We describe the algorithm, its key properties and connections.
Further, we focus on the properties of the solution of the projected problem and its residual vector. Suitable stopping criteria and their dependence on the choice of the regularization parameter will be discussed.
Numerical experiments performed on problems arising in cryo-electron microscopy single particle analysis will be used for demonstration.