  A computational method is introduced for choosing the regularization
parameter for total variation (TV) regularization. The approach is based on
computing reconstructions at a few different resolutions and various values of
regularization parameter. The chosen parameter is the smallest one resulting in
approximately discretization-invariant TV norms of the reconstructions. The
method is tested with X-ray tomography data measured from a walnut and compared
to the S-curve method. The proposed method seems to automatically adapt to the
desired resolution and noise level, and it yields useful results in the tests.
The results are comparable to those of the S-curve method; however, the S-curve
method needs a priori information about the sparsity of the unknown, while the
proposed method does not need any a priori information (apart from the choice
of a desired resolution). Mathematical analysis is presented for (partial)
understanding of the properties of the proposed parameter choice method. It is
rigorously proven that the TV norms of the reconstructions converge with any
choice of regularization parameter.
