123 / 2023-06-19 20:46:07

MSBAS InSAR Regularization Method Based on Exponential Function Singular Value Modification

Tikhonov Regularization,ill-posed,MSBAS InSAR,ground surface deformation

MSBAS InSAR is a multidimensional deformation time series estimation that combines multi-track SAR data, which can effectively extract deformation information in the east-west and north-south directions of the study area. Compared to the SBAS InSAR, the number of observations in the MSBAS model remains the same, but the unknown parameters are doubled, so the ill-posed problem is serious.

Tikhonov regularization method is a common and effective method for solving geodetic ill-posed problems, the key factors affecting the solution effect of this method are regularization parameter and regularization matrix. Now, the existing research is mostly aimed at the determination of regularization parameter, while there is few research on regularization matrix, and the selection of regularization matrix will significantly affect the quality of the solution results. The construction of a regularization matrix with the targeted correction of singular values as the goal is a method for determining the singular values with a relatively sufficient theoretical basis, but it is difficult to clarify which singular values should be corrected and the degree of correction. In view of this, this paper studies the regularization matrix construction method based on the singular value modification of the exponential function. From the perspective of mean squared error, this matrix constructs a correction matrix based on exponential function based on the standard deviation component of each estimated parameter after correction of regularization parameter, and realizes the key correction of small singular values and reduces the degree of correction of larger singular values by selectively modifying singular values, so as to effectively estimate the accuracy and reliability of the estimation results.

Taking a mining area in Jiyang as an example, the effectiveness of the regularization method based on the correction of singular values of exponential function in the solution of MSBAS InSAR deformation model are studied, which the ridge estimation method, truncated singular value method, the regularization method with additional zero-order regularization matrix, and the regularization method based on the singular value modification of exponential function proposed in this paper are set up for comparative analysis. The results show that: (1) the ill-posed problem of the MSBAS InSAR deformation model is serious, and the ridge estimation method and the regularization method which additional zero-order regularization matrix are difficult to effectively improve the ill-posed of the model, resulting in small deformation values and unreliable results. (2) The truncated singular value decomposition method deletes too much effective information, resulting in low accuracy of the solution results; (3) The regularization matrix determination method proposed in this paper can effectively improve the ill-posed problem of the deformation model and have the best solution accuracy, which means that the method can effectively reduce the adverse impact of ill-posed on the estimation results through targeted correction of singular values, and at the same time avoid the problem that excessive effective information is deleted in the process of truncating singular values, thereby reducing the accuracy of the solution results.