DeepAI AI Chat
Log In Sign Up

Least-Squares Method for Inverse Medium Problems

01/02/2022
by   Kazufumi Ito, et al.
Purdue University
NC State University
The Chinese University of Hong Kong
0

We present a two-stage least-squares method to 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 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 great tolerance of noise.

READ FULL TEXT

page 14

page 15

page 16

page 17

page 18

05/01/2022

Quantum-inspired algorithm for truncated total least squares solution

Total least squares (TLS) methods have been widely used in data fitting....
10/29/2021

MINRES for second-order PDEs with singular data

Minimum residual methods such as the least-squares finite element method...
04/29/2023

A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems

In this work, we focus on the inverse medium scattering problem (IMSP), ...
06/18/2018

Gradient Descent-based D-optimal Design for the Least-Squares Polynomial Approximation

In this work, we propose a novel sampling method for Design of Experimen...
03/29/2023

A data-assisted two-stage method for the inverse random source problem

We propose a data-assisted two-stage method for solving an inverse rando...
03/25/2019

Active Learning of Spin Network Models

Complex networks can be modeled as a probabilistic graphical model, wher...