  Accurate determination of the regularization parameter in inverse problems
still represents an analytical challenge, owing mainly to the considerable
difficulty to separate the unknown noise from the signal. We present a new
approach for determining the parameter for the general-form Tikhonov
regularization of linear ill-posed problems. In our approach the parameter is
found by approximate minimization of the distance between the unknown noiseless
data and the data reconstructed from the regularized solution. We approximate
this distance by employing the Picard parameter to separate the noise from the
data in the coordinate system of the generalized SVD. A simple and reliable
algorithm for the estimation of the Picard parameter enables accurate
implementation of the above procedure. We demonstrate the effectiveness of our
method on several numerical examples. A MATLAB-based implementation of the
proposed algorithms can be found at
https://www.weizmann.ac.il/condmat/superc/software/
