A computational method is introduced for choosing the regularizationparameter for total variation (TV) regularization. The approach is based oncomputing reconstructions at a few different resolutions and various values ofregularization parameter. The chosen parameter is the smallest one resulting inapproximately discretization-invariant TV norms of the reconstructions. Themethod is tested with X-ray tomography data measured from a walnut and comparedto the S-curve method. The proposed method seems to automatically adapt to thedesired 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-curvemethod needs a priori information about the sparsity of the unknown, while theproposed method does not need any a priori information (apart from the choiceof a desired resolution). Mathematical analysis is presented for (partial)understanding of the properties of the proposed parameter choice method. It isrigorously proven that the TV norms of the reconstructions converge with anychoice of regularization parameter.
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