Author:

Keywords:

quadratic eigenvalue problem, regularization, total least squares, ill-posed problems, l-curve, tikhonov regularization, iterative methods, deconvolution, parameters, algorithm, SISTA, Science & Technology, Technology, Physical Sciences, Computer Science, Software Engineering, Mathematics, Applied, Computer Science, Mathematics, Total Least Squares, ILL-POSED PROBLEMS, L-CURVE, TIKHONOV REGULARIZATION, ITERATIVE METHODS, ALGORITHM, DECONVOLUTION, PARAMETERS, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4903 Numerical and computational mathematics

Abstract:

This paper presents a new computational approach for solving the Regularized Total Least Squares problem. The problem is formulated by adding a quadratic constraint to the Total Least Square minimization problem. Starting from the fact that a quadratically constrained Least Squares problem can be solved via a quadratic eigenvalue problem, an iterative procedure for solving the regularized Total Least Squares problem based on quadratic eigenvalue problems is presented. Discrete ill-posed problems are used as simulation examples in order to numerically validate the method.