Least-squares method for recovering multiple medium parameters. (1st December 2022)

• Record Type: Journal Article
• Authors: Ito, Kazufumi; Liang, Ying; Zou, Jun
• Is Part Of: Inverse problems. Volume 38:Number 12(2022)
• Publication Date: 2022-12-01
• Subjects: inverse medium problem -- multiple parameters -- least-squares method -- mixed regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac999a
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We present a two-stage least-squares method for inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the first stage, while a total least-squares method with a mixed regularization is used to recover the medium profile in the second stage. The total least-squares method is designed to minimize the residual of the model equation and the data fitting, along with an appropriate regularization, in an attempt to significantly improve the accuracy of the approximation obtained from the first stage. We shall also present an analysis on the well-posedness and convergence of this algorithm. Numerical experiments are carried out to verify the accuracies and robustness of this novel two-stage least-squares algorithm, with high tolerance of noise in the data.