A model function method in regularized total least squares

In this article, we investigate the dual regularized total least squares (dual RTLS) from a computational aspect. More precisely, we propose a strategy for finding two regularization parameters in the resulting equation of dual RTLS. This strategy is based on an extension of the idea of model function originally proposed by Kunisch, Ito and Zou for a realization of the discrepancy principle in the standard one-parameter Tikhonov regularization. For dual RTLS we derive a model function of two variables and show its reliability using standard numerical tests.

[1]  Sabine Van Huffel,et al.  Total least squares problem - computational aspects and analysis , 1991, Frontiers in applied mathematics.

[2]  Claude Brezinski,et al.  Multi-parameter regularization techniques for ill-conditioned linear systems , 2003, Numerische Mathematik.

[3]  N. Hengartner,et al.  Adaptive estimation for inverse problems with noisy operators , 2005 .

[4]  Jun Zou,et al.  An improved model function method for choosing regularization parameters in linear inverse problems , 2002 .

[5]  V. Ivanov,et al.  The approximate solution of operator equations of the first kind , 1966 .

[6]  F. Bauer,et al.  The quasi-optimality criterion for classical inverse problems , 2008 .

[7]  E. Miller,et al.  Efficient determination of multiple regularization parameters in a generalized L-curve framework , 2002 .

[8]  Gene H. Golub,et al.  An analysis of the total least squares problem , 1980, Milestones in Matrix Computation.

[9]  Sergei V. Pereverzev,et al.  On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales , 2010 .

[10]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[11]  K. Kunisch,et al.  Iterative choices of regularization parameters in linear inverse problems , 1998 .

[12]  Sabine Van Huffel,et al.  The total least squares problem , 1993 .

[13]  Gene H. Golub,et al.  Tikhonov Regularization and Total Least Squares , 1999, SIAM J. Matrix Anal. Appl..

[14]  G. Golub,et al.  Regularized Total Least Squares Based on Quadratic Eigenvalue Problem Solvers , 2004 .

[15]  Shuai Lu,et al.  Regularized Total Least Squares: Computational Aspects and Error Bounds , 2009, SIAM J. Matrix Anal. Appl..

[16]  Kazufumi Ito,et al.  On the Choice of the Regularization Parameter in Nonlinear Inverse Problems , 1992, SIAM J. Optim..

[17]  Olha Ivanyshyn,et al.  Optimal regularization with two interdependent regularization parameters , 2007 .

[18]  Guanrong Chen,et al.  Approximate Solutions of Operator Equations , 1997 .