In this paper we present an iterative method for the minimization of
the Tikhonov regularization functional in the absence of information
about noise. Each algorithm iteration updates both the estimate of
the regularization parameter and the Tikhonov solution. In order to
reduce the number of iterations, an inexact version of the algorithm
is also proposed. In this case the inner Conjugate Gradient (CG)
iterations are truncated before convergence. In the numerical
experiments the methods are tested on inverse ill posed problems
arising both in signal and image processing
