DUAL REGULARIZED TOTAL LEAST SQUARES SOLUTION FROM TWO-PARAMETER TRUST-REGION ALGORITHM
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초록
For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.
Abstract
For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.
참고문헌 (8)
- G. Arfken, "Mathematical Methods for Physicists" (1985), Academic Press
- P. C. Hansen, "Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems", Numerical Algorithms, 6, pp.1~35 (1998)
- G. Lee, "Fast high-resolution image reconstruction using Tikhonov regularization based total least squares", SIAM J. Sci. Comput, 35(1), pp.B275~B290 (2013)
- S. Lu, "Dual regularized total least squares and multi-parameter regularization", Comput. Methods Appl. Math, 8(3), pp.253~262 (2008)
- S. Lu, "Regularized total least squares: computational aspects and error bounds", SIAM J. Matrix Anal. Appl, 31(3) (2009)
- S. Lu, "A model function method in regularized total least squares", Appl. Anal, 89(11), pp.1693~1703 (2010)
- J. Nocedal, "Numerical Optimization" (2000), Springer-Verlag
- R. Renaut, "Efficient algorithms for solution of regularized total least squares", SIAM J. Matrix Anal. Appl, 26(2), pp.457~476 (2004)