A novel approach for regularization matrix construction and its application in SBAS deformation model inversion. Issue 10 (18th May 2020) - Zhai, Min; Liu, Guolin; Tao, Qiuxiang; Jiang, Zhaoying; Xin, Mingzhen
ABSTRACT: The Tikhonov regularization reduces the ill-conditioned nature of an equation by introducing a regularization parameter and a regularization matrix to correct an ill-conditioned matrix. Therefore, the appropriate determination of the regularization matrix can increase the reliability of solutions. In this paper, a regularization matrix construction approach based on the minimum mean square error is proposed. The approach constructs the regularization matrix using the small singular value vectors. The boundary of small singular values that satisfies the minimum mean square error is determined by comparing the reduced variance and introduced bias. The boundary value is utilized to construct the regularization matrix to obtain a more reliable parameter estimation. The proposed approach is applied to the small baseline subset interferometric synthetic aperture radar deformation inversion model experiment, and the feasibility and effectiveness of the approach are verified. Compared with the original approach of determining small singular values, the proposed approach is more stable and reliable, and it improves the accuracy of the Tikhonov regularization.