R.M.: An analysis of the zero-crossing method for choosing regularization parameter

Abstract. Solving discrete ill-posed problems via Tikhonov regularization introduces the prob-lem of determining a regularization parameter. There are several methods available for choosing such a parameter, yet, in general, the uniqueness of this choice is an open question. Two empirical methods for determining a regularization parameter (which appear in the biomedical engineering literature) are the composite residual and smoothing operator and the zero-crossing method. An equivalence is established between the zero-crossing method and a minimum product criterion, which has previously been linked with the L-curve method. Finally, the uniqueness of a choice of regularization param-eter is established under certain restrictions on the Fourier coefficients of the data in the ill-posed problem