Computation of Regularization Parameters using the Fourier Coefficients.

In the solution of ill-posed problems by means of regularization methods, a crucial issue is the computation of the regularization parameter. In this work we focus on the Truncated Singular Value Decomposition (TSVD) and Tikhonov method and we define a method for computing the regularization parameter based on the behavior of Fourier coefficients. We compute a safe index for truncating the TSVD and consequently a value for the regularization parameter of the Tikhonov method. An extensive numerical experimentation is carried out on the Hansen's Regtool test problems and the results confirm the effectiveness and robustness of the method proposed.