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Nonlinear inverse problems in imaging [[electronic resource] /] / Jin Keun Seo, Eung Je Woo
| Nonlinear inverse problems in imaging [[electronic resource] /] / Jin Keun Seo, Eung Je Woo |
| Autore | Seo Jin Keun |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Chichester, West Sussex, U.K., : John Wiley & Sons Inc., 2013 |
| Descrizione fisica | 1 online resource (375 p.) |
| Disciplina |
621.367
621.3670151 |
| Altri autori (Persone) | WooE. J (Eung Je) |
| Soggetto topico |
Image processing - Mathematics
Cross-sectional imaging - Mathematics Inverse problems (Differential equations) Nonlinear theories |
| ISBN |
1-118-47814-2
1-283-99384-8 1-118-47817-7 1-118-47815-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Preface List of Abbreviations 1 Introduction 1.1 Forward Problem 1.2 Inverse Problem 1.3 Issues in Inverse Problem Solving 1.4 Linear, Nonlinear and Linearized Problems 2 Signal and System as Vectors 2.1 Vector Space 2.1.1 Vector Space and Subspace 2.1.2 Basis, Norm and Inner Product 2.1.3 Hilbert Space 2.2 Vector Calculus 2.2.1 Gradient 2.2.2 Divergence 2.2.3 Curl 2.2.4 Curve 2.2.5 Curvature 2.3 Taylor's Expansion 2.4 Linear System of Equations 2.4.1 Linear System and Transform 2.4.2 Vector Space of Matrix 2.4.3 Least Square Solution 2.4.4 Singular Value Decomposition (SVD) 2.4.5 Pseudo-inverse 2.5 Fourier Transform 2.5.1 Series Expansion 2.5.2 Fourier Transform 2.5.3 Discrete Fourier Transform (DFT) 2.5.4 Fast Fourier Transform (FFT) 2.5.5 Two-dimensional Fourier Transform References 3 Basics for Forward Problem 3.1 Understanding PDE using Images as Examples 3.2 Heat Equation 3.2.1 Formulation of Heat Equation 3.2.2 One-dimensional Heat Equation 3.2.3 Two-dimensional Heat Equation and Isotropic Diffusion 3.2.4 Boundary Conditions 3.3 Wave Equation 3.4 Laplace and Poisson Equations 3.4.1 Boundary Value Problem 3.4.2 Laplace Equation in a Circle 3.4.3 Laplace Equation in Three-dimensional Domain 3.4.4 Representation Formula for Poisson Equation References 4 Analysis for Inverse Problem 4.1 Examples of Inverse Problems in Medical Imaging 4.1.1 Electrical Property Imaging 4.1.2 Mechanical Property Imaging 4.1.3 Image Restoration 4.2 Basic Analysis 4.2.1 Sobolev Space 4.2.2 Some Important Estimates 4.2.3 Helmholtz Decomposition 4.3 Variational Problems 4.3.1 Lax-Milgram Theorem 4.3.2 Ritz Approach 4.3.3 Euler-Lagrange Equations 4.3.4 Regularity Theory and Asymptotic Analysis 4.4 Tikhonov Regularization and Spectral Analysis 4.4.1 Overview of Tikhonov Regularization 4.4.2 Bounded Linear Operators in Banach Space 4.4.3 Regularization in Hilbert Space or Banach Space 4.5 Basics of Real Analysis 4.5.1 Riemann Integrable 4.5.2 Measure Space 4.5.3 Lebesgue Measurable Function 4.5.4 Pointwise, Uniform, Norm Convergence and Convergence in Measure 4.5.5 Differentiation Theory References 5 Numerical Methods 5.1 Iterative Method for Nonlinear Problem 5.2 Numerical Computation of One-dimensional Heat equation 5.2.1 Explicit Scheme 5.2.2 Implicit Scheme 5.2.3 Crank-Nicolson Method 5.3 Numerical Solution of Linear System of Equations 5.3.1 Direct Method using LU Factorization 5.3.2 Iterative Method using Matrix Splitting 5.3.3 Iterative Method using Steepest Descent Minimization 5.3.4 Conjugate Gradient (CG) Method 5.4 Finite Difference Method (FDM) 5.4.1 Poisson Equation 5.4.2 Elliptic Equation 5.5 Finite Element Method (FEM) 5.5.1 One-dimensional Model 5.5.2 Two-dimensional Model 5.5.3 Numerical Examples References 6 CT, MRI and Image Processing Problems 6.1 X-ray CT 6.1.1 Inverse Problem 6.1.2 Basic Principle and Nonlinear Effects 6.1.3 Inverse Radon Transform 6.1.4 Artifacts in CT 6.2 MRI 6.2.1 Basic Principle 6.2.2 K-space Data 6.2.3 Image Reconstruction 6.3 Image Restoration 6.3.1 Role of p in (6.35) 6.3.2 Total Variation Restoration 6.3.3 Anisotropic Edge-preserving Diffusion 6.3.4 Sparse Sensing 6.4 Segmentation 6.4.1 Active Contour Method 6.4.2 Level Set Method 6.4.3 Motion Tracking for Echocardiography References 7 Electrical Impedance Tomography 7.1 Introduction 7.2 Measurement Method and Data 7.2.1 Conductivity and Resistance 7.2.2 Permittivity and Capacitance 7.2.3 Phasor and Impedance 7.2.4 Admittivity and Trans-impedance 7.2.5 Electrode Contact Impedance 7.2.6 EIT System 7.2.7 Data Collection Protocol and Data Set 7.2.8 Linearity between Current and Voltage 7.3 Representation of Physical Phenomena 7.3.1 Derivation of Elliptic PDE 7.3.2 Elliptic PDE for Four-electrode Method 7.3.3 Elliptic PDE for Two-electrode Method 7.3.4 Min-max Property of Complex Potential 7.4 Forward Problem and Model 7.4.1 Continuous Neumann-to-Dirichlet Data 7.4.2 Discrete Neumann-to-Dirichlet Data 7.4.3 Nonlinearity between Admittivity and Voltage 7.5 Uniqueness Theory and Direct Reconstruction Method 7.5.1 Calder´on's Approach 7.5.2 Uniqueness and Three-dimensional Reconstruction: Infinite Measurements 7.5.3 Nachmann's D-bar Method in Two Dimension 7.6 Backprojection Algorithm 7.7 Sensitivity and Sensitivity Matrix 7.7.1 Perturbation and Sensitivity 7.7.2 Sensitivity Matrix 7.7.3 Linearization 7.7.4 Quality of Sensitivity Matrix 7.8 Inverse Problem of EIT 7.8.1 Inverse Problem of RC Circuit 7.8.2 Formulation of EIT Inverse Problem 7.8.3 Ill-posedness of EIT Inverse Problem 7.9 Static Imaging 7.9.1 Iterative Data Fitting Method 7.9.2 Static Imaging using 4-channel EIT System 7.9.3 Regularization 7.9.4 Technical Difficulty of Static Imaging 7.10 Time-difference Imaging 7.10.1 Data Sets for Time-difference Imaging 7.10.2 Equivalent Homogeneous Admittivity 7.10.3 Linear Time-difference Algorithm using Sensitivity Matrix 7.10.4 Interpretation of Time-difference Image 7.11 Frequency-difference Imaging 7.11.1 Data Sets for Frequency-difference Imaging 7.11.2 Simple Difference Ft,ω2− Ft,ω1 7.11.3 Weighted Difference Ft,ω2− [alpha] Ft,ω1 7.11.4 Linear Frequency-difference Algorithm using Sensitivity Matrix 7.11.5 Interpretation of Frequency-difference Image References 8 Anomaly Estimation and Layer Potential Techniques 8.1 Harmonic Analysis and Potential Theory 8.1.1 Layer Potentials and Boundary Value Problems for Laplace Equation 8.1.2 Regularity for Solution of Elliptic Equation along Boundary of Inhomogeneity 8.2 Anomaly Estimation using EIT 8.2.1 Size Estimation Method 8.2.2 Location Search Method 8.3 Anomaly Estimation using Planar Probe 8.3.1 Mathematical Formulation 8.3.2 Representation Formula References 9 Magnetic Resonance Electrical Impedance Tomography 9.1 Data Collection using MRI 9.1.1 Measurement of Bz 9.1.2 Noise in Measured Bz Data 9.1.3 Measurement of B = (Bx,By,Bz) 9.2 Forward Problem and Model Construction 9.2.1 Relation between J , Bz and σ 9.2.2 Three Key Observations 9.2.3 Data Bz Traces σ∇u × e z-directional Change of σ 9.2.4 Mathematical Analysis toward MREIT Model 9.3 Inverse Problem Formulation using B or J 9.4 Inverse Problem Formulation using Bz 9.4.1 Model with Two Linearly Independent Currents 9.4.2 Uniqueness 9.4.3 Defected Bz Data in a Local Region 9.5 Image Reconstruction Algorithm 9.5.1 J-substitution Algorithm 9.5.2 Harmonic Bz Algorithm 9.5.3 Gradient Bz Decomposition and Variational Bz Algorithm 9.5.4 Local Harmonic Bz Algorithm 9.5.5 Sensitivity Matrix Based Algorithm 9.5.6 Anisotropic Conductivity Reconstruction Algorithm 9.5.7 Other Algorithms 9.6 Validation and Interpretation 9.6.1 Image Reconstruction Procedure using Harmonic Bz Algorithm 9.6.2 Conductivity Phantom Imaging 9.6.3 Animal Imaging 9.6.4 Human Imaging 9.7 Applications References 10 Magnetic Resonance Elastography 10.1 Representation of Physical Phenomena 10.1.1 Overview of Hooke's Law 10.1.2 Strain Tensor in Lagrangian Coordinates 10.2 Forward Problem and Model 10.3 Inverse Problem in MRE 10.4 Reconstruction Algorithms 10.4.1 Reconstruction of [mu] with the Assumption of Local Homogeneity 10.4.2 Reconstruction of [mu] without the Assumption of Local Homogeneity 10.4.3 Anisotropic Elastic Moduli Reconstruction 10.5 Technical Issues in MRE References. |
| Record Nr. | UNINA-9910141514703321 |
Seo Jin Keun
|
||
| Chichester, West Sussex, U.K., : John Wiley & Sons Inc., 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear inverse problems in imaging [[electronic resource] /] / Jin Keun Seo, Eung Je Woo
| Nonlinear inverse problems in imaging [[electronic resource] /] / Jin Keun Seo, Eung Je Woo |
| Autore | Seo Jin Keun |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Chichester, West Sussex, U.K., : John Wiley & Sons Inc., 2013 |
| Descrizione fisica | 1 online resource (375 p.) |
| Disciplina |
621.367
621.3670151 |
| Altri autori (Persone) | WooE. J (Eung Je) |
| Soggetto topico |
Image processing - Mathematics
Cross-sectional imaging - Mathematics Inverse problems (Differential equations) Nonlinear theories |
| ISBN |
1-118-47814-2
1-283-99384-8 1-118-47817-7 1-118-47815-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Preface List of Abbreviations 1 Introduction 1.1 Forward Problem 1.2 Inverse Problem 1.3 Issues in Inverse Problem Solving 1.4 Linear, Nonlinear and Linearized Problems 2 Signal and System as Vectors 2.1 Vector Space 2.1.1 Vector Space and Subspace 2.1.2 Basis, Norm and Inner Product 2.1.3 Hilbert Space 2.2 Vector Calculus 2.2.1 Gradient 2.2.2 Divergence 2.2.3 Curl 2.2.4 Curve 2.2.5 Curvature 2.3 Taylor's Expansion 2.4 Linear System of Equations 2.4.1 Linear System and Transform 2.4.2 Vector Space of Matrix 2.4.3 Least Square Solution 2.4.4 Singular Value Decomposition (SVD) 2.4.5 Pseudo-inverse 2.5 Fourier Transform 2.5.1 Series Expansion 2.5.2 Fourier Transform 2.5.3 Discrete Fourier Transform (DFT) 2.5.4 Fast Fourier Transform (FFT) 2.5.5 Two-dimensional Fourier Transform References 3 Basics for Forward Problem 3.1 Understanding PDE using Images as Examples 3.2 Heat Equation 3.2.1 Formulation of Heat Equation 3.2.2 One-dimensional Heat Equation 3.2.3 Two-dimensional Heat Equation and Isotropic Diffusion 3.2.4 Boundary Conditions 3.3 Wave Equation 3.4 Laplace and Poisson Equations 3.4.1 Boundary Value Problem 3.4.2 Laplace Equation in a Circle 3.4.3 Laplace Equation in Three-dimensional Domain 3.4.4 Representation Formula for Poisson Equation References 4 Analysis for Inverse Problem 4.1 Examples of Inverse Problems in Medical Imaging 4.1.1 Electrical Property Imaging 4.1.2 Mechanical Property Imaging 4.1.3 Image Restoration 4.2 Basic Analysis 4.2.1 Sobolev Space 4.2.2 Some Important Estimates 4.2.3 Helmholtz Decomposition 4.3 Variational Problems 4.3.1 Lax-Milgram Theorem 4.3.2 Ritz Approach 4.3.3 Euler-Lagrange Equations 4.3.4 Regularity Theory and Asymptotic Analysis 4.4 Tikhonov Regularization and Spectral Analysis 4.4.1 Overview of Tikhonov Regularization 4.4.2 Bounded Linear Operators in Banach Space 4.4.3 Regularization in Hilbert Space or Banach Space 4.5 Basics of Real Analysis 4.5.1 Riemann Integrable 4.5.2 Measure Space 4.5.3 Lebesgue Measurable Function 4.5.4 Pointwise, Uniform, Norm Convergence and Convergence in Measure 4.5.5 Differentiation Theory References 5 Numerical Methods 5.1 Iterative Method for Nonlinear Problem 5.2 Numerical Computation of One-dimensional Heat equation 5.2.1 Explicit Scheme 5.2.2 Implicit Scheme 5.2.3 Crank-Nicolson Method 5.3 Numerical Solution of Linear System of Equations 5.3.1 Direct Method using LU Factorization 5.3.2 Iterative Method using Matrix Splitting 5.3.3 Iterative Method using Steepest Descent Minimization 5.3.4 Conjugate Gradient (CG) Method 5.4 Finite Difference Method (FDM) 5.4.1 Poisson Equation 5.4.2 Elliptic Equation 5.5 Finite Element Method (FEM) 5.5.1 One-dimensional Model 5.5.2 Two-dimensional Model 5.5.3 Numerical Examples References 6 CT, MRI and Image Processing Problems 6.1 X-ray CT 6.1.1 Inverse Problem 6.1.2 Basic Principle and Nonlinear Effects 6.1.3 Inverse Radon Transform 6.1.4 Artifacts in CT 6.2 MRI 6.2.1 Basic Principle 6.2.2 K-space Data 6.2.3 Image Reconstruction 6.3 Image Restoration 6.3.1 Role of p in (6.35) 6.3.2 Total Variation Restoration 6.3.3 Anisotropic Edge-preserving Diffusion 6.3.4 Sparse Sensing 6.4 Segmentation 6.4.1 Active Contour Method 6.4.2 Level Set Method 6.4.3 Motion Tracking for Echocardiography References 7 Electrical Impedance Tomography 7.1 Introduction 7.2 Measurement Method and Data 7.2.1 Conductivity and Resistance 7.2.2 Permittivity and Capacitance 7.2.3 Phasor and Impedance 7.2.4 Admittivity and Trans-impedance 7.2.5 Electrode Contact Impedance 7.2.6 EIT System 7.2.7 Data Collection Protocol and Data Set 7.2.8 Linearity between Current and Voltage 7.3 Representation of Physical Phenomena 7.3.1 Derivation of Elliptic PDE 7.3.2 Elliptic PDE for Four-electrode Method 7.3.3 Elliptic PDE for Two-electrode Method 7.3.4 Min-max Property of Complex Potential 7.4 Forward Problem and Model 7.4.1 Continuous Neumann-to-Dirichlet Data 7.4.2 Discrete Neumann-to-Dirichlet Data 7.4.3 Nonlinearity between Admittivity and Voltage 7.5 Uniqueness Theory and Direct Reconstruction Method 7.5.1 Calder´on's Approach 7.5.2 Uniqueness and Three-dimensional Reconstruction: Infinite Measurements 7.5.3 Nachmann's D-bar Method in Two Dimension 7.6 Backprojection Algorithm 7.7 Sensitivity and Sensitivity Matrix 7.7.1 Perturbation and Sensitivity 7.7.2 Sensitivity Matrix 7.7.3 Linearization 7.7.4 Quality of Sensitivity Matrix 7.8 Inverse Problem of EIT 7.8.1 Inverse Problem of RC Circuit 7.8.2 Formulation of EIT Inverse Problem 7.8.3 Ill-posedness of EIT Inverse Problem 7.9 Static Imaging 7.9.1 Iterative Data Fitting Method 7.9.2 Static Imaging using 4-channel EIT System 7.9.3 Regularization 7.9.4 Technical Difficulty of Static Imaging 7.10 Time-difference Imaging 7.10.1 Data Sets for Time-difference Imaging 7.10.2 Equivalent Homogeneous Admittivity 7.10.3 Linear Time-difference Algorithm using Sensitivity Matrix 7.10.4 Interpretation of Time-difference Image 7.11 Frequency-difference Imaging 7.11.1 Data Sets for Frequency-difference Imaging 7.11.2 Simple Difference Ft,ω2− Ft,ω1 7.11.3 Weighted Difference Ft,ω2− [alpha] Ft,ω1 7.11.4 Linear Frequency-difference Algorithm using Sensitivity Matrix 7.11.5 Interpretation of Frequency-difference Image References 8 Anomaly Estimation and Layer Potential Techniques 8.1 Harmonic Analysis and Potential Theory 8.1.1 Layer Potentials and Boundary Value Problems for Laplace Equation 8.1.2 Regularity for Solution of Elliptic Equation along Boundary of Inhomogeneity 8.2 Anomaly Estimation using EIT 8.2.1 Size Estimation Method 8.2.2 Location Search Method 8.3 Anomaly Estimation using Planar Probe 8.3.1 Mathematical Formulation 8.3.2 Representation Formula References 9 Magnetic Resonance Electrical Impedance Tomography 9.1 Data Collection using MRI 9.1.1 Measurement of Bz 9.1.2 Noise in Measured Bz Data 9.1.3 Measurement of B = (Bx,By,Bz) 9.2 Forward Problem and Model Construction 9.2.1 Relation between J , Bz and σ 9.2.2 Three Key Observations 9.2.3 Data Bz Traces σ∇u × e z-directional Change of σ 9.2.4 Mathematical Analysis toward MREIT Model 9.3 Inverse Problem Formulation using B or J 9.4 Inverse Problem Formulation using Bz 9.4.1 Model with Two Linearly Independent Currents 9.4.2 Uniqueness 9.4.3 Defected Bz Data in a Local Region 9.5 Image Reconstruction Algorithm 9.5.1 J-substitution Algorithm 9.5.2 Harmonic Bz Algorithm 9.5.3 Gradient Bz Decomposition and Variational Bz Algorithm 9.5.4 Local Harmonic Bz Algorithm 9.5.5 Sensitivity Matrix Based Algorithm 9.5.6 Anisotropic Conductivity Reconstruction Algorithm 9.5.7 Other Algorithms 9.6 Validation and Interpretation 9.6.1 Image Reconstruction Procedure using Harmonic Bz Algorithm 9.6.2 Conductivity Phantom Imaging 9.6.3 Animal Imaging 9.6.4 Human Imaging 9.7 Applications References 10 Magnetic Resonance Elastography 10.1 Representation of Physical Phenomena 10.1.1 Overview of Hooke's Law 10.1.2 Strain Tensor in Lagrangian Coordinates 10.2 Forward Problem and Model 10.3 Inverse Problem in MRE 10.4 Reconstruction Algorithms 10.4.1 Reconstruction of [mu] with the Assumption of Local Homogeneity 10.4.2 Reconstruction of [mu] without the Assumption of Local Homogeneity 10.4.3 Anisotropic Elastic Moduli Reconstruction 10.5 Technical Issues in MRE References. |
| Record Nr. | UNINA-9910830155303321 |
|
Seo Jin Keun
|
||
| Chichester, West Sussex, U.K., : John Wiley & Sons Inc., 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear inverse problems in imaging [[electronic resource] /] / Jin Keun Seo, Eung Je Woo
| Nonlinear inverse problems in imaging [[electronic resource] /] / Jin Keun Seo, Eung Je Woo |
| Autore | Seo Jin Keun |
| Edizione | [1st edition] |
| Pubbl/distr/stampa | Chichester, West Sussex, U.K., : John Wiley & Sons Inc., 2013 |
| Descrizione fisica | 1 online resource (375 p.) |
| Disciplina |
621.367
621.3670151 |
| Altri autori (Persone) | WooE. J (Eung Je) |
| Soggetto topico |
Image processing - Mathematics
Cross-sectional imaging - Mathematics Inverse problems (Differential equations) Nonlinear theories |
| ISBN |
1-118-47814-2
1-283-99384-8 1-118-47817-7 1-118-47815-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Preface List of Abbreviations 1 Introduction 1.1 Forward Problem 1.2 Inverse Problem 1.3 Issues in Inverse Problem Solving 1.4 Linear, Nonlinear and Linearized Problems 2 Signal and System as Vectors 2.1 Vector Space 2.1.1 Vector Space and Subspace 2.1.2 Basis, Norm and Inner Product 2.1.3 Hilbert Space 2.2 Vector Calculus 2.2.1 Gradient 2.2.2 Divergence 2.2.3 Curl 2.2.4 Curve 2.2.5 Curvature 2.3 Taylor's Expansion 2.4 Linear System of Equations 2.4.1 Linear System and Transform 2.4.2 Vector Space of Matrix 2.4.3 Least Square Solution 2.4.4 Singular Value Decomposition (SVD) 2.4.5 Pseudo-inverse 2.5 Fourier Transform 2.5.1 Series Expansion 2.5.2 Fourier Transform 2.5.3 Discrete Fourier Transform (DFT) 2.5.4 Fast Fourier Transform (FFT) 2.5.5 Two-dimensional Fourier Transform References 3 Basics for Forward Problem 3.1 Understanding PDE using Images as Examples 3.2 Heat Equation 3.2.1 Formulation of Heat Equation 3.2.2 One-dimensional Heat Equation 3.2.3 Two-dimensional Heat Equation and Isotropic Diffusion 3.2.4 Boundary Conditions 3.3 Wave Equation 3.4 Laplace and Poisson Equations 3.4.1 Boundary Value Problem 3.4.2 Laplace Equation in a Circle 3.4.3 Laplace Equation in Three-dimensional Domain 3.4.4 Representation Formula for Poisson Equation References 4 Analysis for Inverse Problem 4.1 Examples of Inverse Problems in Medical Imaging 4.1.1 Electrical Property Imaging 4.1.2 Mechanical Property Imaging 4.1.3 Image Restoration 4.2 Basic Analysis 4.2.1 Sobolev Space 4.2.2 Some Important Estimates 4.2.3 Helmholtz Decomposition 4.3 Variational Problems 4.3.1 Lax-Milgram Theorem 4.3.2 Ritz Approach 4.3.3 Euler-Lagrange Equations 4.3.4 Regularity Theory and Asymptotic Analysis 4.4 Tikhonov Regularization and Spectral Analysis 4.4.1 Overview of Tikhonov Regularization 4.4.2 Bounded Linear Operators in Banach Space 4.4.3 Regularization in Hilbert Space or Banach Space 4.5 Basics of Real Analysis 4.5.1 Riemann Integrable 4.5.2 Measure Space 4.5.3 Lebesgue Measurable Function 4.5.4 Pointwise, Uniform, Norm Convergence and Convergence in Measure 4.5.5 Differentiation Theory References 5 Numerical Methods 5.1 Iterative Method for Nonlinear Problem 5.2 Numerical Computation of One-dimensional Heat equation 5.2.1 Explicit Scheme 5.2.2 Implicit Scheme 5.2.3 Crank-Nicolson Method 5.3 Numerical Solution of Linear System of Equations 5.3.1 Direct Method using LU Factorization 5.3.2 Iterative Method using Matrix Splitting 5.3.3 Iterative Method using Steepest Descent Minimization 5.3.4 Conjugate Gradient (CG) Method 5.4 Finite Difference Method (FDM) 5.4.1 Poisson Equation 5.4.2 Elliptic Equation 5.5 Finite Element Method (FEM) 5.5.1 One-dimensional Model 5.5.2 Two-dimensional Model 5.5.3 Numerical Examples References 6 CT, MRI and Image Processing Problems 6.1 X-ray CT 6.1.1 Inverse Problem 6.1.2 Basic Principle and Nonlinear Effects 6.1.3 Inverse Radon Transform 6.1.4 Artifacts in CT 6.2 MRI 6.2.1 Basic Principle 6.2.2 K-space Data 6.2.3 Image Reconstruction 6.3 Image Restoration 6.3.1 Role of p in (6.35) 6.3.2 Total Variation Restoration 6.3.3 Anisotropic Edge-preserving Diffusion 6.3.4 Sparse Sensing 6.4 Segmentation 6.4.1 Active Contour Method 6.4.2 Level Set Method 6.4.3 Motion Tracking for Echocardiography References 7 Electrical Impedance Tomography 7.1 Introduction 7.2 Measurement Method and Data 7.2.1 Conductivity and Resistance 7.2.2 Permittivity and Capacitance 7.2.3 Phasor and Impedance 7.2.4 Admittivity and Trans-impedance 7.2.5 Electrode Contact Impedance 7.2.6 EIT System 7.2.7 Data Collection Protocol and Data Set 7.2.8 Linearity between Current and Voltage 7.3 Representation of Physical Phenomena 7.3.1 Derivation of Elliptic PDE 7.3.2 Elliptic PDE for Four-electrode Method 7.3.3 Elliptic PDE for Two-electrode Method 7.3.4 Min-max Property of Complex Potential 7.4 Forward Problem and Model 7.4.1 Continuous Neumann-to-Dirichlet Data 7.4.2 Discrete Neumann-to-Dirichlet Data 7.4.3 Nonlinearity between Admittivity and Voltage 7.5 Uniqueness Theory and Direct Reconstruction Method 7.5.1 Calder´on's Approach 7.5.2 Uniqueness and Three-dimensional Reconstruction: Infinite Measurements 7.5.3 Nachmann's D-bar Method in Two Dimension 7.6 Backprojection Algorithm 7.7 Sensitivity and Sensitivity Matrix 7.7.1 Perturbation and Sensitivity 7.7.2 Sensitivity Matrix 7.7.3 Linearization 7.7.4 Quality of Sensitivity Matrix 7.8 Inverse Problem of EIT 7.8.1 Inverse Problem of RC Circuit 7.8.2 Formulation of EIT Inverse Problem 7.8.3 Ill-posedness of EIT Inverse Problem 7.9 Static Imaging 7.9.1 Iterative Data Fitting Method 7.9.2 Static Imaging using 4-channel EIT System 7.9.3 Regularization 7.9.4 Technical Difficulty of Static Imaging 7.10 Time-difference Imaging 7.10.1 Data Sets for Time-difference Imaging 7.10.2 Equivalent Homogeneous Admittivity 7.10.3 Linear Time-difference Algorithm using Sensitivity Matrix 7.10.4 Interpretation of Time-difference Image 7.11 Frequency-difference Imaging 7.11.1 Data Sets for Frequency-difference Imaging 7.11.2 Simple Difference Ft,ω2− Ft,ω1 7.11.3 Weighted Difference Ft,ω2− [alpha] Ft,ω1 7.11.4 Linear Frequency-difference Algorithm using Sensitivity Matrix 7.11.5 Interpretation of Frequency-difference Image References 8 Anomaly Estimation and Layer Potential Techniques 8.1 Harmonic Analysis and Potential Theory 8.1.1 Layer Potentials and Boundary Value Problems for Laplace Equation 8.1.2 Regularity for Solution of Elliptic Equation along Boundary of Inhomogeneity 8.2 Anomaly Estimation using EIT 8.2.1 Size Estimation Method 8.2.2 Location Search Method 8.3 Anomaly Estimation using Planar Probe 8.3.1 Mathematical Formulation 8.3.2 Representation Formula References 9 Magnetic Resonance Electrical Impedance Tomography 9.1 Data Collection using MRI 9.1.1 Measurement of Bz 9.1.2 Noise in Measured Bz Data 9.1.3 Measurement of B = (Bx,By,Bz) 9.2 Forward Problem and Model Construction 9.2.1 Relation between J , Bz and σ 9.2.2 Three Key Observations 9.2.3 Data Bz Traces σ∇u × e z-directional Change of σ 9.2.4 Mathematical Analysis toward MREIT Model 9.3 Inverse Problem Formulation using B or J 9.4 Inverse Problem Formulation using Bz 9.4.1 Model with Two Linearly Independent Currents 9.4.2 Uniqueness 9.4.3 Defected Bz Data in a Local Region 9.5 Image Reconstruction Algorithm 9.5.1 J-substitution Algorithm 9.5.2 Harmonic Bz Algorithm 9.5.3 Gradient Bz Decomposition and Variational Bz Algorithm 9.5.4 Local Harmonic Bz Algorithm 9.5.5 Sensitivity Matrix Based Algorithm 9.5.6 Anisotropic Conductivity Reconstruction Algorithm 9.5.7 Other Algorithms 9.6 Validation and Interpretation 9.6.1 Image Reconstruction Procedure using Harmonic Bz Algorithm 9.6.2 Conductivity Phantom Imaging 9.6.3 Animal Imaging 9.6.4 Human Imaging 9.7 Applications References 10 Magnetic Resonance Elastography 10.1 Representation of Physical Phenomena 10.1.1 Overview of Hooke's Law 10.1.2 Strain Tensor in Lagrangian Coordinates 10.2 Forward Problem and Model 10.3 Inverse Problem in MRE 10.4 Reconstruction Algorithms 10.4.1 Reconstruction of [mu] with the Assumption of Local Homogeneity 10.4.2 Reconstruction of [mu] without the Assumption of Local Homogeneity 10.4.3 Anisotropic Elastic Moduli Reconstruction 10.5 Technical Issues in MRE References. |
| Record Nr. | UNINA-9910841901203321 |
|
Seo Jin Keun
|
||
| Chichester, West Sussex, U.K., : John Wiley & Sons Inc., 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
OIPE 2012 / / guest editors, Professor Luc Dupré and Dr. Guillaume Crevecoeur
| OIPE 2012 / / guest editors, Professor Luc Dupré and Dr. Guillaume Crevecoeur |
| Pubbl/distr/stampa | [Bradford, England] : , : Emerald, , 2014 |
| Descrizione fisica | 1 online resource (360 p.) |
| Disciplina | 537.0151 |
| Collana | COMPEL : The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Soggetto topico |
Electromagnetism - Mathematics
Inverse problems (Differential equations) Mathematical optimization |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-78441-187-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Editorial advisory board; Guest editorial; Topology optimization of rotor poles in a permanent-magnet machine using level set method and continuum design sensitivity analysis; Bi-objective optimization of induction machine using interval-based interactive algorithms; Framework for the optimization of online computable models; A modified lambda algorithm for optimization in electromagnetics; Simple sensitivity calculation for inverse design problems in electrical engineering; Optimal household energy management using V2H flexibilities
Optimization of EMI filters for electrical drives in aircraftAdaptive level set method for accurate boundary shape in optimization of electromagnetic systems; Amodified immune algorithm with spatial filtering for multiobjective topology optimisation of electromagnetic devices; Use of compensation theorem for the robustness assessment of electromagnetic devices optimal design; Multi-physics optimisation of an energy harvester device for automotive application; Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model n-level output space mapping for electromagnetic design optimizationHigh-speed functionality optimization of five-phase PM machine using third harmonic current; Topology optimization of magnetostatic shielding using multistep evolutionary algorithms with additional searches in a restricted design space ; Adaptive unscented transform for uncertainty quantification in EMC large-scale systems; Ant colony optimization for the topological design of interior permanent magnet (IPM)machines; Multiobjective approach developed for optimizing the dynamic behavior of incremental linear actuators Radial output space mapping for electromechanical systems designMinimum energy control of descriptor positive discrete-time linear systems; Current spectrum estimation using Prony's estimator and coherent resampling; Optimal shape design of flux barriers in IPM synchronous motors using the phase field method; Conformal antennas arrays radiation synthesis using immunity tactic; Multi-level design of an isolation transformer using collaborative optimization; Model-free discrete control for robot manipulators using a fuzzy estimator |
| Record Nr. | UNINA-9910465369103321 |
| [Bradford, England] : , : Emerald, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
OIPE 2012 / / guest editors, Professor Luc Dupré and Dr. Guillaume Crevecoeur
| OIPE 2012 / / guest editors, Professor Luc Dupré and Dr. Guillaume Crevecoeur |
| Pubbl/distr/stampa | [Bradford, England] : , : Emerald, , 2014 |
| Descrizione fisica | 1 online resource (360 p.) |
| Disciplina | 537.0151 |
| Collana | COMPEL : The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Soggetto topico |
Electromagnetism - Mathematics
Inverse problems (Differential equations) Mathematical optimization |
| ISBN | 1-78441-187-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Editorial advisory board; Guest editorial; Topology optimization of rotor poles in a permanent-magnet machine using level set method and continuum design sensitivity analysis; Bi-objective optimization of induction machine using interval-based interactive algorithms; Framework for the optimization of online computable models; A modified lambda algorithm for optimization in electromagnetics; Simple sensitivity calculation for inverse design problems in electrical engineering; Optimal household energy management using V2H flexibilities
Optimization of EMI filters for electrical drives in aircraftAdaptive level set method for accurate boundary shape in optimization of electromagnetic systems; Amodified immune algorithm with spatial filtering for multiobjective topology optimisation of electromagnetic devices; Use of compensation theorem for the robustness assessment of electromagnetic devices optimal design; Multi-physics optimisation of an energy harvester device for automotive application; Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model n-level output space mapping for electromagnetic design optimizationHigh-speed functionality optimization of five-phase PM machine using third harmonic current; Topology optimization of magnetostatic shielding using multistep evolutionary algorithms with additional searches in a restricted design space ; Adaptive unscented transform for uncertainty quantification in EMC large-scale systems; Ant colony optimization for the topological design of interior permanent magnet (IPM)machines; Multiobjective approach developed for optimizing the dynamic behavior of incremental linear actuators Radial output space mapping for electromechanical systems designMinimum energy control of descriptor positive discrete-time linear systems; Current spectrum estimation using Prony's estimator and coherent resampling; Optimal shape design of flux barriers in IPM synchronous motors using the phase field method; Conformal antennas arrays radiation synthesis using immunity tactic; Multi-level design of an isolation transformer using collaborative optimization; Model-free discrete control for robot manipulators using a fuzzy estimator |
| Record Nr. | UNINA-9910786521803321 |
| [Bradford, England] : , : Emerald, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
OIPE 2012 / / guest editors, Professor Luc Dupré and Dr. Guillaume Crevecoeur
| OIPE 2012 / / guest editors, Professor Luc Dupré and Dr. Guillaume Crevecoeur |
| Pubbl/distr/stampa | [Bradford, England] : , : Emerald, , 2014 |
| Descrizione fisica | 1 online resource (360 p.) |
| Disciplina | 537.0151 |
| Collana | COMPEL : The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Soggetto topico |
Electromagnetism - Mathematics
Inverse problems (Differential equations) Mathematical optimization |
| ISBN | 1-78441-187-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Editorial advisory board; Guest editorial; Topology optimization of rotor poles in a permanent-magnet machine using level set method and continuum design sensitivity analysis; Bi-objective optimization of induction machine using interval-based interactive algorithms; Framework for the optimization of online computable models; A modified lambda algorithm for optimization in electromagnetics; Simple sensitivity calculation for inverse design problems in electrical engineering; Optimal household energy management using V2H flexibilities
Optimization of EMI filters for electrical drives in aircraftAdaptive level set method for accurate boundary shape in optimization of electromagnetic systems; Amodified immune algorithm with spatial filtering for multiobjective topology optimisation of electromagnetic devices; Use of compensation theorem for the robustness assessment of electromagnetic devices optimal design; Multi-physics optimisation of an energy harvester device for automotive application; Stochastic modeling error reduction using Bayesian approach coupled with an adaptive Kriging-based model n-level output space mapping for electromagnetic design optimizationHigh-speed functionality optimization of five-phase PM machine using third harmonic current; Topology optimization of magnetostatic shielding using multistep evolutionary algorithms with additional searches in a restricted design space ; Adaptive unscented transform for uncertainty quantification in EMC large-scale systems; Ant colony optimization for the topological design of interior permanent magnet (IPM)machines; Multiobjective approach developed for optimizing the dynamic behavior of incremental linear actuators Radial output space mapping for electromechanical systems designMinimum energy control of descriptor positive discrete-time linear systems; Current spectrum estimation using Prony's estimator and coherent resampling; Optimal shape design of flux barriers in IPM synchronous motors using the phase field method; Conformal antennas arrays radiation synthesis using immunity tactic; Multi-level design of an isolation transformer using collaborative optimization; Model-free discrete control for robot manipulators using a fuzzy estimator |
| Record Nr. | UNINA-9910813966503321 |
| [Bradford, England] : , : Emerald, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Optimization and inverse Problems in electromagnetism / / guest editor, Alessandro Salvini
| Optimization and inverse Problems in electromagnetism / / guest editor, Alessandro Salvini |
| Pubbl/distr/stampa | [Place of publication not identified] : , : Emerald Publishing, , 2018 |
| Descrizione fisica | 1 online resource (465 pages) |
| Disciplina | 537.0151 |
| Collana | Compel: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Soggetto topico |
Electromagnetism - Mathematics
Mathematical optimization Inverse problems (Differential equations) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-78756-134-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910466918003321 |
| [Place of publication not identified] : , : Emerald Publishing, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Optimization and inverse Problems in electromagnetism / / guest editor, Alessandro Salvini
| Optimization and inverse Problems in electromagnetism / / guest editor, Alessandro Salvini |
| Pubbl/distr/stampa | [Place of publication not identified] : , : Emerald Publishing, , 2018 |
| Descrizione fisica | 1 online resource (465 pages) |
| Disciplina | 537.0151 |
| Collana | Compel: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Soggetto topico |
Electromagnetism - Mathematics
Mathematical optimization Inverse problems (Differential equations) |
| ISBN | 1-78756-134-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910796859203321 |
| [Place of publication not identified] : , : Emerald Publishing, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Optimization and inverse Problems in electromagnetism / / guest editor, Alessandro Salvini
| Optimization and inverse Problems in electromagnetism / / guest editor, Alessandro Salvini |
| Pubbl/distr/stampa | [Place of publication not identified] : , : Emerald Publishing, , 2018 |
| Descrizione fisica | 1 online resource (465 pages) |
| Disciplina | 537.0151 |
| Collana | Compel: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |
| Soggetto topico |
Electromagnetism - Mathematics
Mathematical optimization Inverse problems (Differential equations) |
| ISBN | 1-78756-134-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910817501203321 |
| [Place of publication not identified] : , : Emerald Publishing, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Parameter estimation and inverse problems / Richard C. Aster, Clifford H. Thurber
| Parameter estimation and inverse problems / Richard C. Aster, Clifford H. Thurber |
| Autore | Aster, Richard C. |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Waltham, MA : Academic Press, 2013 |
| Descrizione fisica | x, 360 p. : ill. ; 24 cm |
| Disciplina | 515.357 |
| Altri autori (Persone) | Thurber, Clifford H |
| Soggetto topico |
Parameter estimation
Inverse problems (Differential equations) Inversion (Geophysics) Mathematical models |
| ISBN | 9780123850485 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002944609707536 |
|
Aster, Richard C.
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| Waltham, MA : Academic Press, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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