Exponential Function Singular Value Correction Regularization Method for MSBAS InSAR Deformation Inversion

Multidimensional small baseline subset interferometric synthetic aperture radar (MSBAS InSAR) is a multidimensional deformation time series inversion method that integrates multiorbit SAR data. Due to plenty of observations and the quite strong multicollinearity between the column vectors of the coefficient matrix, the MSBAS InSAR deformation observation model has serious ill-posed problems. Tikhonov regularization method is a common method for solving the ill-posed problem of geodetic measurement. Although the regularization matrix constructed by the existing methods can achieve selective correction of singular value, the nonnegative definite property of the matrix is often neglected. Therefore, an exponential function singular value correction regularization method is proposed to ensure the nonnegative definite characteristic of the regularization matrix. In addition, an exponential function regulatory factor is introduced to ensure that the value of the regularization matrix is within a reasonable range. The rationality of the exponential function regulatory factor is analyzed theoretically, and a method of determining the regulatory factor in the sense of minimum mean square error is proposed. The exponential function singular value correction regularization method is applied to the MSBAS InSAR deformation inversion in a mining area, and the effectiveness of the method is verified by the leveling results in the study area. The results show that the proposed method can not only effectively improve the ill-posed problems of the MSBAS InSAR deformation inversion but also reduce the visual ambiguity caused by the single line of sight and improve the accuracy of the results by 28% compared with the results of widely used truncated singular value decomposition method.