scholarly journals Automated Regularization Parameters Method for the Inverse Problem in Ultrasound Tomography

2021 ◽  
Author(s):  
Anita Carević
Keyword(s):  
Inverse Problem ◽  
Ultrasound Tomography ◽  
Regularization Parameters

Ultrasound Tomography Imaging of Defects Using Neural Networks

1992 ◽  
Vol 4 (5) ◽  
pp. 758-771 ◽  
Author(s):  
Denis M. Anthony ◽  
Evor L. Hines ◽  
David A. Hutchins ◽  
J. T. Mottram
Keyword(s):  
Neural Networks ◽  
Inverse Problem ◽  
Artificial Neural Networks ◽  
Longitudinal Wave ◽  
Time Of Flight ◽  
Simplified Model ◽  
Gray Scale ◽  
Ultrasound Tomography ◽  
Tomography Imaging ◽  
Ultrasound Propagation

Simulations of ultrasound tomography demonstrated that artificial neural networks can solve the inverse problem in ultrasound tomography. A highly simplified model of ultrasound propagation was constructed, taking no account of refraction or diffraction, and using only longitudinal wave time of flight (TOF). TOF data were used as the network inputs, and the target outputs were the expected pixel maps, showing defects (gray scale coded) according to the velocity of the wave in the defect. The effects of varying resolution and defect velocity were explored. It was found that defects could be imaged using time of flight of ultrasonic rays.

A Reverse Solving Method of Regularization on the Calculation of Acoustic Field

2014 ◽  
Vol 488-489 ◽  
pp. 1006-1010
Author(s):  
Hai Hu ◽  
Xin Yue Wu ◽  
Long Ma
Keyword(s):  
Inverse Problem ◽  
Acoustic Field ◽  
Selection Method ◽  
Regularization Parameters ◽  
Method Of Regularization ◽  
Key Factor ◽  
Ill Posed

Based on the normalization of sample datas errors, a feasible reverse solving method of regularization is studied to avoid ill-posed problem in inverse problem. The analysis result shows that the high robustness in selection method of regularization parameters, rather than the strategy of regularization, is the key factor deciding the effectiveness of regularization.

scholarly journals A New Method for Optimal Regularization Parameter Determination in the Inverse Problem of Load Identification

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Gao ◽  
Kaiping Yu ◽  
Ying Wu
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Cross Validation ◽  
Regularization Parameter ◽  
New Method ◽  
Parameter Determination ◽  
Load Identification ◽  
Noise Levels ◽  
Regularization Parameters ◽  
Curve Method

According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF) is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM) is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV) method and theL-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.

scholarly journals A Lagrange-Newton Method for EIT/UT Dual-Modality Image Reconstruction

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 1966 ◽  
Author(s):  
Guanghui Liang ◽  
Shangjie Ren ◽  
Shu Zhao ◽  
Feng Dong
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Newton Method ◽  
Constraint Equation ◽  
Reconstruction Method ◽  
Ultrasound Tomography ◽  
Impedance Tomography ◽  
Dual Modality ◽  
Mesh Model ◽  
Image Reconstruction Method

An image reconstruction method is proposed based on Lagrange-Newton method for electrical impedance tomography (EIT) and ultrasound tomography (UT) dual-modality imaging. Since the change in conductivity distribution is usually accompanied with the change in acoustic impedance distribution, the reconstruction targets of EIT and UT are unified to the conductivity difference using the same mesh model. Some background medium distribution information obtained from ultrasound transmission and reflection measurements can be used to construct a hard constraint about the conductivity difference distribution. Then, the EIT/UT dual-modality inverse problem is constructed by an equality constraint equation, and the Lagrange multiplier method combining Newton-Raphson iteration is used to solve the EIT/UT dual-modality inverse problem. The numerical and experimental results show that the proposed dual-modality image reconstruction method has a better performance than the single-modality EIT method and is more robust to the measurement noise.

scholarly journals ON THE DISCRETE LINEAR ILL‐POSED PROBLEMS

1999 ◽  
Vol 4 (1) ◽  
pp. 147-152
Author(s):  
A. A. Stepanov
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Regularization Methods ◽  
Acoustic Spectroscopy ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Photo Acoustic Spectroscopy

An inverse problem of photo‐acoustic spectroscopy of semiconductors is investigated. The main problem is formulated as the integral equation of the first kind. Two different regularization methods are applied, the algorithms for defining regularization parameters are given.

scholarly journals Inverse problems of experimental data interpretation in 3D ultrasound tomography

2019 ◽  
pp. 254-269
Author(s):  
А.В. Гончарский ◽  
В.А. Кубышкин ◽  
С.Ю. Романов ◽  
С.Ю. Серёжников
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Inverse Problem ◽  
Acoustic Waves ◽  
Soft Tissues ◽  
Nonlinear Coefficient ◽  
3D Ultrasound ◽  
Acoustic Properties ◽  
Ultrasound Wave ◽  
Ultrasound Tomography

Обратная задача 3D ультразвуковой томографии рассматривается в статье как нелинейная коэффициентная обратная задача для уравнения гиперболического типа. Используемая математическая модель хорошо описывает как дифракционные эффекты, так и поглощение ультразвука в неоднородной среде. В рассматриваемой постановке реконструируется скорость распространения акустической волны как функция трех координат. Количество неизвестных в нелинейной обратной задаче составляет порядка 50 миллионов. Разработанные итерационные алгоритмы решения обратной задачи ориентированы на использование GPUкластеров. Основным результатом работы является апробация алгоритмов на экспериментальных данных. В эксперименте использовался стенд для 3D ультразвуковых томографических исследований, разработанный в МГУ имени М.В. Ломоносова. Акустические параметры фантомов близки к акустическим параметрам мягких тканей человека. Объем экспериментальных данных составляет порядка 3 ГБ. Интерпретация данных эксперимента позволила не только продемонстрировать эффективность разработанных алгоритмов, но и подтвердила адекватность математической модели реальности. Для реализации разработанных численных алгоритмов использовался графический кластер суперкомпьютера Ломоносов-2. The inverse problem of 3D ultrasound tomography is considered in this paper as a nonlinear coefficient inverse problem for a hyperbolic equation. The employed mathematical model accurately describes the effects of ultrasound wave diffraction and absorption in inhomogeneous media. The velocity of acoustic waves inside the test sample is reconstructed as an unknown function of three spatial coordinates. The number of unknowns in the nonlinear inverse problem reaches 50 million. The developed iterative algorithms for solving the inverse problem are designed for GPU clusters. The main result of this study is testing the developed algorithms on experimental data. The experiments were carried out using a 3D ultrasound tomographic setup developed at Lomonosov Moscow State University. Acoustic properties of the test samples were close to those of human soft tissues. The volume of data collected in experiments is up to 3 GB. Experimental results show the efficiency of the proposed algorithms and confirm that the mathematical model is adequate to reality. The proposed algorithms were tested on the GPU partition of Lomonosov2 supercomputer.

scholarly journals The problem of choosing initial approximations in inverse problems of ultrasound tomography

2017 ◽  
pp. 312-321
Author(s):  
А.В. Гончарский ◽  
С.Ю. Романов ◽  
С.Ю. Серёжников
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Soft Tissues ◽  
Iterative Algorithms ◽  
Initial Approximation ◽  
Explicit Representation ◽  
Nonlinear Inverse Problem ◽  
Ultrasound Tomography ◽  
Residual Functional ◽  
Wave Tomography

Статья посвящена разработке эффективных итерационных методов решения нелинейных обратных задач волновой томографии. Итерационные алгоритмы приближенного решения обратной задачи используют явное представление для градиента функционала невязки между экспериментально измеренным и расcчитанным волновым полем. Большое значение для сходимости итерационного процесса в нелинейной обратной задаче имеет выбор начального приближения. В статье исследована возможность использования в качестве начального приближения скоростного разреза, полученного из решения обратной задачи в лучевом приближении. Эффективность такого подхода проиллюстрирована решением модельных обратных задач на суперЭВМ. Модельные задачи ориентированы на томографическую ультразвуковую диагностику мягких тканей в медицине. This paper is devoted to developing efficient iterative methods to solve nonlinear inverse problems of wave tomography. The iterative algorithms used to obtain an approximate solution of the inverse problem are based on an explicit representation of the gradient of the residual functional between the measured and computed wave fields. The choice of the initial approximation is of great importance for the convergence of the iterative process in a nonlinear inverse problem. The possibility of using an initial approximation to the sound speed obtained via solving the inverse problem in the ray approximation is studied. The efficiency of this approach is illustrated by solving model problems using a supercomputer. These model problems are designed for the ultrasound tomographic imaging of soft tissues in medicine.

scholarly journals Simultaneous Determination of the Space-Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Shufang Qiu ◽  
Wen Zhang ◽  
Jianmei Peng
Keyword(s):  
Inverse Problem ◽  
Fourier Coefficients ◽  
Convergence Rates ◽  
Initial Distribution ◽  
Stability And Convergence ◽  
Convergence Results ◽  
Regularization Parameters ◽  
Regularization Problem ◽  
The Given

We consider an inverse problem for simultaneously determining the space-dependent source and the initial distribution in heat conduction equation. First, we study the ill-posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and obtain the regularization solutions with their stability and convergence results. Furthermore, convergence rates of the regularized solutions are presented under a prior and a posteriori strategies for selecting regularization parameters. Results of numerical examples show that the proposed regularization method is stable and effective for the considered inverse problem.

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