A new framework for multi-parameter regularization (Q329016)

The authors investigate a new approach to determine the regularization vector \(\Lambda\) of multi-parameter regularization methods based on the discrepancy principle. The new method first determines a set of regularization vectors \(\{ \Lambda_j \}, j=1, \dots, q\) that satisfy the discrepancy principle. Then, it chooses from this set a vector that maximizes \(\Phi(x_{\Lambda_j})\) for some functional \(\Phi\), including the well-known cases: \(\| x_{\Lambda_j}\|\), \(\| L x_{\Lambda_j}\|\) and \(\| x_{\Lambda_j}\|^2 +\| L x_{\Lambda_j}\|^2\), with \(L\) a regularization matrix.