In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method
for obtaining stable approximate solutions to ill-posed operator equations modeled by linear
operators acting between Hilbert spaces. Geometrical properties of the problem are used
to derive a new strategy for choosing the sequence of regularization parameters (Lagrange
multipliers) for the NIT iteration. Convergence analysis for this new method is provided.
Numerical experiments are presented for two distinct applications: I) A 2D elliptic param-
eter identification problem (Inverse Potential Problem); II) An image deblurring problem.
The results obtained validate the efficiency of our method compared with standard im-
plementations of the NIT method (where a geometrical choice is typically used for the
sequence of Lagrange multipliers).