On nondecreasing sequences of regularization parameters for nonstationary iterated Tikhonov

Nonstationary iterated Tikhonov is an iterative regularization
method that requires a strategy for defining the Tikhonov regularization
parameter at each iteration and an early termination of the iterative process.
A classical choice for the regularization parameters is a decreasing geometric
sequence which leads to a linear convergence rate. The early iterations
compute quickly a good approximation of the true solution, but the main
drawback of this choice is a rapid growth of the error for later iterations.
This implies that a stopping criteria, e.g. the discrepancy principle, could
fail in computing a good approximation. In this paper we show by a filter
factor analysis that a nondecreasing sequence of regularization parameters can
provide a rapid and stable convergence. Hence, a reliable stopping criteria is
no longer necessary. A geometric nondecreasing sequence of the Tikhonov
regularization parameters into a fixed interval is proposed and numerically
validated for deblurring problems.