Index

B_z image

B_z-based MREIT

J-substitution algorithm

k-space

k-space data

Absolute continuity

Active contour method

Additivity

Admittivity

Algebraic inversion method

Ampère's law

Animal imaging

Anisotropic conductivity reconstruction algorithm

Anisotropic conductivity tensor

Anisotropic diffusion model

Anisotropic elastic moduli reconstruction

Asymptotic analysis

Attenuation coefficient

Back-projection

Back-projection algorithm

Baire category

Banach space

Basis

Beam hardening

Beer–Lambert law

Bichromatic

Bilinear map

Biot–Savart law

Bipolar method

Bloch equation

Block matching

Boundary conditions in EIT

Boundary geometry error

Boundary voltage data

Bregman distance

Calderón's approach

Cantor function

Caratheodory

Cauchy's infinitesimal strain tensor

Chan–Vese model

Characteristic coordinates

Characteristic function

Classical derivative

Compact operator

Complete electrode model

Complex MR image

Complex potential

Compression

Condition number

Conductivity

Conductivity phantom

Conductivity reconstructor using harmonic algorithms (CoReHA)

Conjugate gradient method

Conservation of mass

Consistency

Contact impedance

Continuity

Continuity equation

Contraction mapping

Convergence

Convergence behavior

Convolution

Coulomb's law

Crank–Nicolson method

Crank–Nicolson scheme

Cross-correlation

Curl

Current density

Current density streamline

Current injection MRI

Current injection time

Current source

Curvature

Curve

D-bar algorithm

Damped Jacobi method

Data subtraction method

Defected data in MREIT

Delta function

Denoising

Direct reconstruction technique

Dirichlet boundary condition

Dirichlet functional

Discrete Fourier transform (DFT)

Discrete Fourier transformation

Discretization

Displacement

Divergence

Divergence theorem

Double-layer potential

Echocardiography

Egorov's theorem

EIT

EIT inverse problem

EIT system

Elastic deformation

Elasticity

Elastography

Electrical impedance tomography

Electrode positioning error

Equation of motion

Equipotential line

Equivalent homogeneous admittivity

Error amplification

Euler's equation

Euler–Lagrange equation

Eulerian description

Existence

Explicit scheme

External measurement

Faraday's law

Fast Fourier transform (FFT)

Fatou's lemma

Filtered back-projection

Finite difference method

Finite element method

Forward problem

Forward problem in MRE

Forward problem in MREIT

Forward problem of EIT

Four-electrode method

Fourier inversion formula

Fourier slice theorem

Fourier transform

Fréchet derivative

Frequency-difference EIT (fdEIT)

Frequency-difference image

Frequency-difference imaging in EIT

Frequency-difference TAS

G-norm

G-space

Galerkin's method

Gauss's law

Gauss-Seidel method

Gaussian filter

Gaussian function

Gaussian kernel

Generalized derivative

Generalized system

Gradient

Gradient B_z decomposition algorithm

Gradient descent

Gradient vector flow

Gram–Schmidt process

Green's function

Gyromagnetic ratio

Hahn-Banach

Hardy-Littlewood-Sobolev inequality

Harmonic B_z algorithm

Harmonic function

Harmonic inpainting

Heat equation

Heat kernel

Helmholtz decomposition

Helmholtz–Hodge decomposition

Hilbert space

Hilbert transform

Homogeneity

Hooke's law

Hopf's lemma

Human imaging

Ill-posedness

Ill-posedness of EIT

Image restoration

Impedance

Implicit scheme

Injection current

Injection current nonlinear encoding (ICNE)

Inner product

Input identification

Internal measurement

Inverse problem

Inverse problem in MRE

Inverse problem in MREIT

Inverse problem of RC circuit

Inverse Radon transform

Inversion process

Isotropic diffusion

Iterative data fitting method

Iterative method in MRE

Jacobi method

Lagrangian coordinate

Lamé coefficients

Laplace equation

Lax equivalence theorem

Lax–Milgram theorem

Least-squares solution

Lebesgue dominated convergence theorem (LDCT)

Lebesgue integral

Lebesgue measure

Level set method

Linear frequency-difference algorithm

Linear momentum

Linear system

Linear system of equations

Linear time-difference algorithm

Linear transform

Linearity

Linearity between current and voltage

Linearization

Linearization in EIT

Linearized EIT problem

Linearly independent

Local harmonic B_z algorithm

Local homogeneity assumption

Location search method

Lucas–Kanade method

Magnetic flux density

Magnetic permeability

Magnetic resonance elastography (MRE)

Magnetic resonance electrical impedance tomography (MREIT)

Mathematical model of MREIT

Maximum principle

Maxwell's equations

Mean value property

Measurable

Measure space

Mechanical vibration

Minimal surface problem

Minimization problem

Minimization problem in static EIT imaging

Minimum-norm solution

Mixed boundary condition

Mixed boundary value problem

Mixing process

Modeling error

Monochromatic

Monotone convergence theorem

MR magnitude image

MR phase image

MRI

MRI scanner

Multi-frequency time-difference EIT (mftdEIT)

Negative Sobolev space

Neighboring data collection protocol

Neumann boundary condition

Neumann data

Neumann function

Neumann-to-Dirichlet (NtD) data

Newton's second law

Newton–Raphson algorithm

Newton–Raphson method

Noise in B_z

Noise standard deviation

Nonlinear system

Nonlinearity between admittivity and voltage

Norm

Normal equation

Normed linear space

Normed vector space

Nuclear magnetic resonance

Null space

Nyquist criterion

Orthogonal complement

Orthogonal term in fdEIT

Orthonormal basis

Oscillating magnetic field gradients

Outer measure

Outer product

Parallel MRI

Pattern matching

Permittivity

Perona–Malik model

Phase accumulation

Phase change

Phase encoding

Phase wrapping

Phasor

Poincaré inequality

Poisson equation

Poisson kernel

Poisson summation formula

Poisson's equation

Poisson's ratio

Preconditioned conjugate gradient algorithm

Preconditioner

Projection map

Projection matrix

Projection term in fdEIT

Projection theorem

Pseudo-inverse

Pseudo-inverse matrix

Pulse sequence

Radon transform

Radon–Nikodym

Radon–Nikodym derivative

Range space

Rank

Rayleigh distribution

Reciprocity error

Reciprocity property

Reciprocity theorem

Regularity theory

Regularization in EIT

Restricted isometry property

Riemann integral

Riesz representation theorem

Robin boundary condition

ROF model

Sampling theorem

Scaling uncertainty

Segmentation

Sensitivity analysis

Sensitivity in EIT

Sensitivity matrix

Sensitivity matrix based algorithm

Sensitivity problem

Series expansion

Shear modulus

Shear modulus image reconstruction

Shear stress

Signal-to-noise ratio (SNR)

Simple function

Simple voltage difference

Single-layer potential

Single-step local harmonic B_z algorithm

Singular value

Singular value decomposition (SVD)

Smoothness assumption of σ

Snake

Sobolev space

Sobolev's inequality

Span

Spark

Sparse sensing

Spatial resolution in EIT

Stability

Static imaging in EIT

Steepest descent minimization

Stiffness

Stiffness tensor

Stokes's theorem

Strain

Strain tensor

Stress

Stress tensor

Strong maximum principle

Subspace

Successive over-relaxation (SOR) method

System identification

System input

System output

System parameter

Systematic phase artifact

Taylor's approximation

Taylor's expansion

Tension

Tetrapolar method

Tikhonov regularization

Time-difference EIT (tdEIT)

Time-difference image

Time-difference imaging in EIT

Time-harmonic displacement

Time-harmonic voltage

Total variation

Total variation minimization problem

Trace formula

Trace inequality

Trace operator

Trans-admittance scanner

Trans-impedance

Transversely isotropic model

Truncated singular value decomposition (TSVD)

Truncation error

Two linearly independent currents

Two-electrode method

Ultrasound

Under-determined linear problem

Uniform boundedness principle

Uniqueness

Uniqueness in EIT

Uniqueness in MREIT

Variational B_z algorithm

Vector space

Vector space of matrix

Voigt notation

Von Neumann stability criterion

Wave equation

Weighted admittivity difference

Weighted voltage difference

Well-posedness

X-ray computed tomography

Young's modulus