Adaptive truncated total least square on distorted born iterative method in ultrasound inverse scattering problem

2019 ◽  
Author(s):  
Anita Carević ◽  
Xingzhao Yun ◽  
Mohamed Almekkawy
Keyword(s):  
Iterative Method ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Least Square ◽  
Total Least Square

scholarly journals Nonlinear Electromagnetic Inverse Scattering Imaging Based on IN-LSQR

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Huilin Zhou ◽  
Youwen Liu ◽  
Yuhao Wang ◽  
Liangbing Chen ◽  
Rongxing Duan
Keyword(s):  
Inverse Scattering ◽  
Large Scale ◽  
Linear Equations ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Least Square ◽  
Qr Factorization ◽  
Inexact Newton Method ◽  
Nonlinear Inversion ◽  
Electromagnetic Inverse Scattering

A nonlinear inversion scheme is proposed for electromagnetic inverse scattering imaging. It exploits inexact Newton (IN) and least square QR factorization (LSQR) methods to tackle the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem. A nonlinear model of the inverse scattering in functional form is developed. At every IN iteration, the sparse storage method is adopted to solve the storage and computational bottleneck of Fréchet derivative matrix, a large-scale sparse Jacobian matrix. Moreover, to address the slow convergence problem encountered in the inexact Newton solution via Landweber iterations, an LSQR algorithm is proposed for obtaining a better solution of the internal large-scale sparse linear equations in the IN step. Numerical results demonstrate the applicability of the proposed IN-LSQR method to quantitative inversion of scatterer electric performance parameters. Moreover, compared with the inexact Newton method based on Landweber iterations, the proposed method significantly improves the convergence rate with less computational and storage cost.

scholarly journals Microwave Bone Imaging: A Preliminary Investigation on Numerical Bone Phantoms for Bone Health Monitoring

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6320
Author(s):  
Bilal Amin ◽  
Atif Shahzad ◽  
Martin O’Halloran ◽  
Muhammad Adnan Elahi
Keyword(s):  
Dielectric Properties ◽  
Compressed Sensing ◽  
Iterative Method ◽  
Inverse Scattering ◽  
Bone Health ◽  
Preliminary Investigation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Linear Inversion ◽  
Trabecular Bones

Microwave tomography (MWT) can be used as an alternative modality for monitoring human bone health. Studies have found a significant dielectric contrast between healthy and diseased human trabecular bones. A set of diverse bone phantoms were developed based on single-pole Debye parameters of osteoporotic and osteoarthritis human trabecular bones. The bone phantoms were designed as a two-layered circular structure, where the outer layer mimics the dielectric properties of the cortical bone and the inner layer mimics the dielectric properties of the trabecular bone. The electromagnetic (EM) inverse scattering problem was solved using a distorted Born iterative method (DBIM). A compressed sensing-based linear inversion approach referred to as iterative method with adaptive thresholding for compressed sensing (IMATCS) has been employed for solving the underdetermined set of linear equations at each DBIM iteration. To overcome the challenges posed by the ill-posedness of the EM inverse scattering problem, the L2-based regularization approach was adopted in the amalgamation of the IMATCS approach. The simulation results showed that osteoporotic and osteoarthritis bones can be differentiated based on the reconstructed dielectric properties even for low values of the signal-to-noise ratio. These results show that the adopted approach can be used to monitor bone health based on the reconstructed dielectric properties.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Sign in / Sign up

Export Citation Format

Share Document