Pub Date : 2021-11-16DOI: 10.1080/17415977.2021.2000977
S. Kassabek, S. Kharin, D. Suragan
In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application of the heat polynomials method (HPM) for solving one- and two-dimensional inverse Stefan problems, where the boundary data is reconstructed on a fixed boundary. We present numerical results illustrating an application of the heat polynomials method for several benchmark examples. We study the effects of accuracy and measurement error for different degree of heat polynomials. Due to ill-conditioning of the matrix generated by HPM, optimization techniques are used to obtain regularized solution. Therefore, the sensitivity of the method to the data disturbance is discussed. Theoretical properties of the proposed method, as well as numerical experiments, demonstrate that to reach accurate results it is quite sufficient to consider only a few of the polynomials. The heat flux for two-dimensional inverse Stefan problem is reconstructed and coefficients of a solution function are found approximately.
{"title":"A heat polynomial method for inverse cylindrical one-phase Stefan problems","authors":"S. Kassabek, S. Kharin, D. Suragan","doi":"10.1080/17415977.2021.2000977","DOIUrl":"https://doi.org/10.1080/17415977.2021.2000977","url":null,"abstract":"In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application of the heat polynomials method (HPM) for solving one- and two-dimensional inverse Stefan problems, where the boundary data is reconstructed on a fixed boundary. We present numerical results illustrating an application of the heat polynomials method for several benchmark examples. We study the effects of accuracy and measurement error for different degree of heat polynomials. Due to ill-conditioning of the matrix generated by HPM, optimization techniques are used to obtain regularized solution. Therefore, the sensitivity of the method to the data disturbance is discussed. Theoretical properties of the proposed method, as well as numerical experiments, demonstrate that to reach accurate results it is quite sufficient to consider only a few of the polynomials. The heat flux for two-dimensional inverse Stefan problem is reconstructed and coefficients of a solution function are found approximately.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3423 - 3450"},"PeriodicalIF":1.3,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47064441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-15DOI: 10.1080/17415977.2021.1997401
G. Dulikravich
One of the longest serving members of the Board of Scientific Advisors of the journal Inverse Problems in Science andEngineering (IPSE) passed away recently. Kyriacos D. Papailiou, Professor Emeritus at the National Technical University of Athens (NTUA) and founder of the Lab. of Thermal Turbomachines of NTUA, graduated from the School of Mechanical Engineering of NTUA and continued his education at the von Karman Institute for Fluid Dynamics (VKI Diploma in Experimental Aerodynamics, with Great Distinction). He completed his Doctorate in Applied Sciences at the University of Liege (with Great Distinction), and his Doctorate in Sciences Physiques at the University Claude Bernard, Lyon (Doctorat d’État with ‘mention très honorable’). While pursuing his PhD, he developed his first ‘inverse’ method, an innovative (then) method of designing blade geometry and inverse design of viscous boundary layers by selecting optimum velocity profiles. During the next years, Kyriacos held various research and professor positions at VKI, the Naval Postgraduate School in Monterey, CA (with Prof Vavra), and the École Centrale de Lyon, France where he formed a Research Group (10 engineers) and a Turbomachinery Lab within the Fluid Mechanics Lab. of the ECL. He also held engineering positions at SNECMA-Centre d’Essais Villaroche, Ste. Metraflu and served as a consultant to well-known companies. In 1978, Kyriacos joined the faculty at the School of Mechanical Engineering of NTUA and, until his retirement (2006), was Professor and Director of the Laboratory of Thermal Turbomachines of NTUA. In NTUA, he formed a similar Research Group (15 engineers), as well as the Turbomachinery Lab. in the Mechanical Engineering Department of the NTUA. In total, 15 mechanical engineers acquired their Ph.D. degree at NTUA and several others under his supervision in Europe. He also installed (in the end of the 1980s) the first parallel computer in Greece and, sometime later two of the 500 largest worldwide supercomputers foreseeing the need for computational and inverse design engineering problem solving. He designed several important turbomachinery elements (a 10 MW pump which cools the nuclear electricity production unit in southern France), compressors (axial and radial), ventilators (axial and radial) for various applications, turbines (axial and radial), as, for instance an axial turbine, which was used to power a Czech helicopter, as well as the water droplet separator (system patented by EDF) used to remove water from dry steam, in the case of the previously mentioned EDF nuclear power station. The successful two-phase flow design of the droplet separator resulted in a reduction of the nuclear power station volume by 40%. Throughout his career, Kyriacos received international recognition for his contributions to the aerospace and turbomachinery field. He was one of the early initiators of the International Society for Air-Breathing Engines (ISOABE), ERCOFTAC, vice-President (2001-
《科学与工程逆问题》(IPSE)期刊科学顾问委员会任职时间最长的成员之一最近去世。Kyriacos D. Papailiou是雅典国立技术大学(NTUA)的名誉教授，也是该实验室的创始人。毕业于南洋理工大学机械工程学院，并在von Karman流体动力学研究所继续深造(VKI实验空气动力学文凭，以优异成绩)。他在列日大学(University of Liege)获得了应用科学博士学位(以优异的成绩)，并在里昂克劳德伯纳德大学(University Claude Bernard)获得了物理科学博士学位(Doctorat d ' État with ' mention tr honorable ')。在攻读博士学位期间，他开发了他的第一个“逆”方法，这是一种通过选择最佳速度剖面来设计叶片几何形状和逆设计粘性边界层的创新方法。在接下来的几年里，Kyriacos在VKI、加利福尼亚州蒙特利海军研究生院(与Vavra教授一起)和法国École Centrale de Lyon(他在那里组建了一个研究小组(10名工程师)和流体力学实验室内的涡轮机械实验室)担任过各种研究和教授职位。ECL的成员。他还在SNECMA-Centre d 'Essais Villaroche, st .担任工程职位。并担任知名公司的顾问。1978年，Kyriacos加入了南洋理工大学机械工程学院，直到他退休(2006年)，一直担任南洋理工大学热涡轮机械实验室的教授和主任。在东大，他成立了一个类似的研究小组(15名工程师)，以及涡轮机械实验室。在南洋理工大学机械工程系工作。共有15位机械工程师在东大获得博士学位，另有几位在他的指导下在欧洲获得博士学位。他还(在20世纪80年代末)在希腊安装了第一台并行计算机，后来又在全球500台最大的超级计算机中安装了两台，预见到计算和逆向设计工程问题解决的需求。他设计了几个重要的涡轮机械元件(用于冷却法国南部核电生产装置的10兆瓦泵)，压缩机(轴向和径向)，用于各种应用的通风机(轴向和径向)，涡轮机(轴向和径向)，例如用于为捷克直升机提供动力的轴向涡轮机，以及用于从干蒸汽中除去水的水滴分离器(EDF专利系统)。以前面提到的法国电力公司核电站为例。液滴分离器的两相流设计成功，使核电站体积减少了40%。在他的职业生涯中，Kyriacos因其对航空航天和涡轮机械领域的贡献而获得国际认可。他是国际吸气式发动机学会(ISOABE)的早期发起人之一，ERCOFTAC，欧洲应用科学计算方法共同体(ECCOMAS)副主席(2001-2005)，欧洲委员会航空计划专家，顾问
{"title":"Eulogy: Kyriacos D. Papailiou (1939–2021)","authors":"G. Dulikravich","doi":"10.1080/17415977.2021.1997401","DOIUrl":"https://doi.org/10.1080/17415977.2021.1997401","url":null,"abstract":"One of the longest serving members of the Board of Scientific Advisors of the journal Inverse Problems in Science andEngineering (IPSE) passed away recently. Kyriacos D. Papailiou, Professor Emeritus at the National Technical University of Athens (NTUA) and founder of the Lab. of Thermal Turbomachines of NTUA, graduated from the School of Mechanical Engineering of NTUA and continued his education at the von Karman Institute for Fluid Dynamics (VKI Diploma in Experimental Aerodynamics, with Great Distinction). He completed his Doctorate in Applied Sciences at the University of Liege (with Great Distinction), and his Doctorate in Sciences Physiques at the University Claude Bernard, Lyon (Doctorat d’État with ‘mention très honorable’). While pursuing his PhD, he developed his first ‘inverse’ method, an innovative (then) method of designing blade geometry and inverse design of viscous boundary layers by selecting optimum velocity profiles. During the next years, Kyriacos held various research and professor positions at VKI, the Naval Postgraduate School in Monterey, CA (with Prof Vavra), and the École Centrale de Lyon, France where he formed a Research Group (10 engineers) and a Turbomachinery Lab within the Fluid Mechanics Lab. of the ECL. He also held engineering positions at SNECMA-Centre d’Essais Villaroche, Ste. Metraflu and served as a consultant to well-known companies. In 1978, Kyriacos joined the faculty at the School of Mechanical Engineering of NTUA and, until his retirement (2006), was Professor and Director of the Laboratory of Thermal Turbomachines of NTUA. In NTUA, he formed a similar Research Group (15 engineers), as well as the Turbomachinery Lab. in the Mechanical Engineering Department of the NTUA. In total, 15 mechanical engineers acquired their Ph.D. degree at NTUA and several others under his supervision in Europe. He also installed (in the end of the 1980s) the first parallel computer in Greece and, sometime later two of the 500 largest worldwide supercomputers foreseeing the need for computational and inverse design engineering problem solving. He designed several important turbomachinery elements (a 10 MW pump which cools the nuclear electricity production unit in southern France), compressors (axial and radial), ventilators (axial and radial) for various applications, turbines (axial and radial), as, for instance an axial turbine, which was used to power a Czech helicopter, as well as the water droplet separator (system patented by EDF) used to remove water from dry steam, in the case of the previously mentioned EDF nuclear power station. The successful two-phase flow design of the droplet separator resulted in a reduction of the nuclear power station volume by 40%. Throughout his career, Kyriacos received international recognition for his contributions to the aerospace and turbomachinery field. He was one of the early initiators of the International Society for Air-Breathing Engines (ISOABE), ERCOFTAC, vice-President (2001-","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1669 - 1670"},"PeriodicalIF":1.3,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41556722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-07DOI: 10.1080/17415977.2021.1998040
W. B. da Silva, J. Dutra, C. Kopperschimidt, D. Lesnic, R. Aykroyd
In many thermal engineering problems involving high temperatures/high pressures, the boundary conditions are not fully known since there are technical difficulties in obtaining such data in hostile conditions. To perform the task of estimating the desired parameters, inverse problem formulations are required, which entail to performing some extra measurements of certain accessible and relevant quantities. In this paper, justified also by uniqueness of solution conditions, this extra information is represented by either local or non-local boundary temperature measurements. Also, the development of numerical methods for the study of coefficient identification thermal problems is an important topic of research. In addition, in order to decrease the computational burden, meshless methods are becoming popular. In this article, we combine, for the first time, the method of fundamental solutions (MFS) with a particle filter sequential importance resampling (SIR) algorithm for estimating the time-dependent heat transfer coefficient in inverse heat conduction problems. Two different types of measurements are used. Numerical results indicate that the combination of MFS and SIR shows high performance on several test cases, which include both linear and nonlinear Robin boundary conditions, in comparison with other available methods.
{"title":"Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters","authors":"W. B. da Silva, J. Dutra, C. Kopperschimidt, D. Lesnic, R. Aykroyd","doi":"10.1080/17415977.2021.1998040","DOIUrl":"https://doi.org/10.1080/17415977.2021.1998040","url":null,"abstract":"In many thermal engineering problems involving high temperatures/high pressures, the boundary conditions are not fully known since there are technical difficulties in obtaining such data in hostile conditions. To perform the task of estimating the desired parameters, inverse problem formulations are required, which entail to performing some extra measurements of certain accessible and relevant quantities. In this paper, justified also by uniqueness of solution conditions, this extra information is represented by either local or non-local boundary temperature measurements. Also, the development of numerical methods for the study of coefficient identification thermal problems is an important topic of research. In addition, in order to decrease the computational burden, meshless methods are becoming popular. In this article, we combine, for the first time, the method of fundamental solutions (MFS) with a particle filter sequential importance resampling (SIR) algorithm for estimating the time-dependent heat transfer coefficient in inverse heat conduction problems. Two different types of measurements are used. Numerical results indicate that the combination of MFS and SIR shows high performance on several test cases, which include both linear and nonlinear Robin boundary conditions, in comparison with other available methods.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3322 - 3341"},"PeriodicalIF":1.3,"publicationDate":"2021-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45236723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1080/17415977.2021.1988589
Shuyong Duan, Lutong Shi, Li Wang, Guirong Liu
Due to structural complexity of robot arms, constraints of experiments, especially uncertainty of design parameters, numerical models for dynamics analysis of robot arms can produce erroneous results, which can seriously affect the performance of the designed robot arms. Reliable parameter uncertainty identification for robot arms becomes important. The current methods for uncertainty analysis have double-layered processes, in which the inner layer is for uncertainty propagation and the outer layer is an iterative optimization process. Such a nested double-layered approach limits computational efficiency. This work proposes a novel inverse method for parameter uncertainty identification using a two-way neural network. First, an element (FE) model of a robot arm is established and validated experimentally. Sensitivity analysis is then conducted using the FE model to determine a set of major parameters to be identified. A two-way neural network is next established, and the explicit formulae of direct weight inversion (DWI) use to inverse these parameters of the robot arm. Finally, the inverse result is validated by experiments. Our study show that the present inverse method can greatly improve the computational efficiency. It provides a new avenue to tackle complex inverse problems in engineering and sciences.
{"title":"An uncertainty inversion technique using two-way neural network for parameter identification of robot arms","authors":"Shuyong Duan, Lutong Shi, Li Wang, Guirong Liu","doi":"10.1080/17415977.2021.1988589","DOIUrl":"https://doi.org/10.1080/17415977.2021.1988589","url":null,"abstract":"Due to structural complexity of robot arms, constraints of experiments, especially uncertainty of design parameters, numerical models for dynamics analysis of robot arms can produce erroneous results, which can seriously affect the performance of the designed robot arms. Reliable parameter uncertainty identification for robot arms becomes important. The current methods for uncertainty analysis have double-layered processes, in which the inner layer is for uncertainty propagation and the outer layer is an iterative optimization process. Such a nested double-layered approach limits computational efficiency. This work proposes a novel inverse method for parameter uncertainty identification using a two-way neural network. First, an element (FE) model of a robot arm is established and validated experimentally. Sensitivity analysis is then conducted using the FE model to determine a set of major parameters to be identified. A two-way neural network is next established, and the explicit formulae of direct weight inversion (DWI) use to inverse these parameters of the robot arm. Finally, the inverse result is validated by experiments. Our study show that the present inverse method can greatly improve the computational efficiency. It provides a new avenue to tackle complex inverse problems in engineering and sciences.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3279 - 3304"},"PeriodicalIF":1.3,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42756368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-25DOI: 10.1080/17415977.2021.1988590
Shaowen Yan, Guoxi Ni, Jingjing Liu
Blind image deconvolution is one of the most challenging problems in image restoration. Inspired by the work on sparsity constraint and deblurring of blind motion, we propose a model with fractional-order regularization and sparsity constraint for blind restoration and construct split Bregman combining an iterative thresholding algorithm. Fractional-order penalty term in Besov space is expanded by wavelet basis and computed using iterative thresholding algorithm. The regularized terms of blur kernel under tight wavelet frame systems are solved by the split Bregman method. Numerical experiments show that our algorithm can effectively remove different kinds of blur without requiring any prior information of the blur kernels and obtain higher signal-to-noise ratios and lower relative errors. In addition, fractional-order derivative in Besov space can preserve both edges and smoothness better than the integer-order derivative.
{"title":"A fractional-order regularization with sparsity constraint for blind restoration of images","authors":"Shaowen Yan, Guoxi Ni, Jingjing Liu","doi":"10.1080/17415977.2021.1988590","DOIUrl":"https://doi.org/10.1080/17415977.2021.1988590","url":null,"abstract":"Blind image deconvolution is one of the most challenging problems in image restoration. Inspired by the work on sparsity constraint and deblurring of blind motion, we propose a model with fractional-order regularization and sparsity constraint for blind restoration and construct split Bregman combining an iterative thresholding algorithm. Fractional-order penalty term in Besov space is expanded by wavelet basis and computed using iterative thresholding algorithm. The regularized terms of blur kernel under tight wavelet frame systems are solved by the split Bregman method. Numerical experiments show that our algorithm can effectively remove different kinds of blur without requiring any prior information of the blur kernels and obtain higher signal-to-noise ratios and lower relative errors. In addition, fractional-order derivative in Besov space can preserve both edges and smoothness better than the integer-order derivative.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3305 - 3321"},"PeriodicalIF":1.3,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46355317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-12DOI: 10.1080/17415977.2021.1985489
L. Valtonen, S. Saari, S. Pursiainen
This study focuses on advancing the inversion of aerosol data measured by a cascade impactor. We aim to find and validate a comprehensive and robust mathematical model for reconstructing a particle mass distribution. In this paper, we propose a fixed-point iteration as a method for inverting cascade impactor measurements with relatively simple measurement hardware, which is not optimized for handling advanced linear algebraic operations such as large matrices. We validate this iteration numerically against an iterative L1 norm regularized iterative alternating sequential inversion algorithm. In the numerical experiments, we investigate and compare a point-wise (matrix-free) and integrated kernel-based approach in inverting five different aerosol mass concentration distributions based on simulated measurements and sensitivity kernel functions.
{"title":"A matrix-free fixed-point iteration for inverting cascade impactor measurements with instrument's sensitivity kernels and hardware","authors":"L. Valtonen, S. Saari, S. Pursiainen","doi":"10.1080/17415977.2021.1985489","DOIUrl":"https://doi.org/10.1080/17415977.2021.1985489","url":null,"abstract":"This study focuses on advancing the inversion of aerosol data measured by a cascade impactor. We aim to find and validate a comprehensive and robust mathematical model for reconstructing a particle mass distribution. In this paper, we propose a fixed-point iteration as a method for inverting cascade impactor measurements with relatively simple measurement hardware, which is not optimized for handling advanced linear algebraic operations such as large matrices. We validate this iteration numerically against an iterative L1 norm regularized iterative alternating sequential inversion algorithm. In the numerical experiments, we investigate and compare a point-wise (matrix-free) and integrated kernel-based approach in inverting five different aerosol mass concentration distributions based on simulated measurements and sensitivity kernel functions.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3261 - 3278"},"PeriodicalIF":1.3,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47042096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-06DOI: 10.1080/17415977.2021.1974019
N. Benmeghnia
We study the geometric inverse problem of cavities identification in linear elasticity equation with partially over-determined boundary data. This work proposes a way to compute the topological derivative based on the topological sensitivity analysis concepts, adopting the energy-gap and the -gap as cost functionals. Then, a comparison of both functionals is presented to determine the best choice for numerical studies. Further, several numerical experiences are shown to explore the efficiency of this method.
{"title":"Cavities identification in linear elasticity: energy-gap versus L2-gap cost functionals","authors":"N. Benmeghnia","doi":"10.1080/17415977.2021.1974019","DOIUrl":"https://doi.org/10.1080/17415977.2021.1974019","url":null,"abstract":"We study the geometric inverse problem of cavities identification in linear elasticity equation with partially over-determined boundary data. This work proposes a way to compute the topological derivative based on the topological sensitivity analysis concepts, adopting the energy-gap and the -gap as cost functionals. Then, a comparison of both functionals is presented to determine the best choice for numerical studies. Further, several numerical experiences are shown to explore the efficiency of this method.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3117 - 3147"},"PeriodicalIF":1.3,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48601380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-04DOI: 10.1080/17415977.2021.1982934
Omprakash Gottam, N. Naik, Prabodh Kumar Pandey, S. Gambhir
Pharmacokinetic fluorescence optical tomography (PK-FOT) and dynamic contrast enhancement (DCE) based multispectral optoacoustic tomography (DCE-MSOT) are non-ionizing alternatives to nuclear medicine and radiological modalities such as DCE-PET/CT/MRI for spatially-resolved quantitative imaging of PK parameters and fluorophore-concentrations. The present work introduces for the first time in literature, a fluorescence photoacoustic tomography (FPAT) based fully-nonlinear PK-FPAT reconstruction framework; in a 2-compartment PK-model and optical-fluorescence modelled frequency domain photoacoustic equation setting. From boundary pressure measurements, we solve the dynamic FPAT (compartment-concentration) state and (PK) parameter estimation problem with two shape-based RBF level-set reconstruction schemes in regularized trust region settings; a Jacobian-based Gauss–Newton filter and our newly proposed gradient-based gradient filter. The reconstruction algorithms are validated in two dimensional settings with synthetic cancer mimicking phantoms. Our PK-FPAT algorithms lead to more stable and superior reconstructions (observed in reconstructed normalized mean square errors having lesser-variation-between and reduced-values-across data-noise levels, respectively) than those obtained by PK-FOT for similar test cases, while, with respect to current DCE-MSOT schemes, incorporating more complete forward models including optical fluorescence and coupled-ODE compartment models with no simplifying assumptions (within the accuracy of the models considered) on the fluence, and reconstructing actual (rather than scaled) PK-parameters, in a fully-nonlinear framework.
{"title":"RBF level-set based fully-nonlinear fluorescence photoacoustic pharmacokinetic tomography","authors":"Omprakash Gottam, N. Naik, Prabodh Kumar Pandey, S. Gambhir","doi":"10.1080/17415977.2021.1982934","DOIUrl":"https://doi.org/10.1080/17415977.2021.1982934","url":null,"abstract":"Pharmacokinetic fluorescence optical tomography (PK-FOT) and dynamic contrast enhancement (DCE) based multispectral optoacoustic tomography (DCE-MSOT) are non-ionizing alternatives to nuclear medicine and radiological modalities such as DCE-PET/CT/MRI for spatially-resolved quantitative imaging of PK parameters and fluorophore-concentrations. The present work introduces for the first time in literature, a fluorescence photoacoustic tomography (FPAT) based fully-nonlinear PK-FPAT reconstruction framework; in a 2-compartment PK-model and optical-fluorescence modelled frequency domain photoacoustic equation setting. From boundary pressure measurements, we solve the dynamic FPAT (compartment-concentration) state and (PK) parameter estimation problem with two shape-based RBF level-set reconstruction schemes in regularized trust region settings; a Jacobian-based Gauss–Newton filter and our newly proposed gradient-based gradient filter. The reconstruction algorithms are validated in two dimensional settings with synthetic cancer mimicking phantoms. Our PK-FPAT algorithms lead to more stable and superior reconstructions (observed in reconstructed normalized mean square errors having lesser-variation-between and reduced-values-across data-noise levels, respectively) than those obtained by PK-FOT for similar test cases, while, with respect to current DCE-MSOT schemes, incorporating more complete forward models including optical fluorescence and coupled-ODE compartment models with no simplifying assumptions (within the accuracy of the models considered) on the fluence, and reconstructing actual (rather than scaled) PK-parameters, in a fully-nonlinear framework.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3227 - 3260"},"PeriodicalIF":1.3,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47277270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-30DOI: 10.1080/17415977.2021.1964496
M. J. Huntul
The scope of this paper is to determine the time-dependent potential term numerically in the fourth-order pseudo-hyperbolic equation with initial and boundary conditions from an additional measurement condition. From the literature, we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, we apply the Crank–Nicolson finite difference method combined with the Tikhonov regularization to find a stable and accurate numerical solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted. Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.
{"title":"Determination of a time-dependent potential in the higher-order pseudo-hyperbolic problem","authors":"M. J. Huntul","doi":"10.1080/17415977.2021.1964496","DOIUrl":"https://doi.org/10.1080/17415977.2021.1964496","url":null,"abstract":"The scope of this paper is to determine the time-dependent potential term numerically in the fourth-order pseudo-hyperbolic equation with initial and boundary conditions from an additional measurement condition. From the literature, we already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, we apply the Crank–Nicolson finite difference method combined with the Tikhonov regularization to find a stable and accurate numerical solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted. Numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3006 - 3023"},"PeriodicalIF":1.3,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48671524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-30DOI: 10.1080/17415977.2021.1977294
U. Iben, C. Wagner
In this paper, we discuss the so-called Taylor map approach to solve systems of ordinary differential equations. We demonstrate its capabilities of solving the corresponding inverse problems including parameter identification. The method applies even if the underlying ordinary differential equation is not explicitly known. This procedure is interpreted in terms of Polynomial Neural Networks. Physical knowledge is incorporated into the neural network since its architecture is designed directly on top of the Taylor map approach. This does not only improve the data efficiency but also reduce the effort of the included training procedure. We prove an asymptotic convergence result of polynomial neural networks. On this basis, we demonstrate validation examples to highlight the capabilities of this method in practice.
{"title":"Taylor mapping method for solving and learning of dynamic processes","authors":"U. Iben, C. Wagner","doi":"10.1080/17415977.2021.1977294","DOIUrl":"https://doi.org/10.1080/17415977.2021.1977294","url":null,"abstract":"In this paper, we discuss the so-called Taylor map approach to solve systems of ordinary differential equations. We demonstrate its capabilities of solving the corresponding inverse problems including parameter identification. The method applies even if the underlying ordinary differential equation is not explicitly known. This procedure is interpreted in terms of Polynomial Neural Networks. Physical knowledge is incorporated into the neural network since its architecture is designed directly on top of the Taylor map approach. This does not only improve the data efficiency but also reduce the effort of the included training procedure. We prove an asymptotic convergence result of polynomial neural networks. On this basis, we demonstrate validation examples to highlight the capabilities of this method in practice.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"3190 - 3213"},"PeriodicalIF":1.3,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47936773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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