An introduction to mathematics of emerging biomedical imaging /

Saved in:

Bibliographic Details
Author / Creator:	Ammari, Habib.
Imprint:	Berlin ; New York : Springer, c2008.
Description:	1 online resource (x, 198 p.) : ill.
Language:	English
Series:	Mathématiques & applications, 1154-483x ; 62 Mathématiques & applications ; 62.
Subject:	Diagnostic imaging -- Mathematics. Biomedical engineering -- Mathematics. Diagnostic Imaging -- trends. Biomedical Engineering -- trends. Models, Theoretical. Biomedical engineering -- Mathematics. Diagnostic imaging -- Mathematics.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/8885585

Hidden Bibliographic Details
ISBN:	9783540795520 (alk. paper) 3540795529 (alk. paper) 9783540795537 (e-ISBN) 3540795537 (e-ISBN) 9786611493837 6611493832
Notes:	Includes bibliographical references (p. [189]-195) and index.
Summary:	Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.
Other form:	Print version: Ammari, Habib. Introduction to mathematics of emerging biomedical imaging. Berlin ; London : Springer, c2008 9783540795520 3540795529
Standard no.:	9786611493837

Table of Contents:

1. Biomedical Imaging Modalities
1.1. X-Ray Imaging and Computed Tomography
1.2. Magnetic Resonance Imaging
1.3. Electrical Impedance Tomography
1.4. T-Scan Electrical Impedance Imaging System for Anomaly Detection
1.5. Electrical and Magnetic Source Imaging
1.6. Magnetic Resonance Electrical Impedance Tomography
1.7. Impediography
1.8. Ultrasound Imaging
1.9. Microwave Imaging
1.10. Elastic Imaging
1.11. Magnetic Resonance Elastography
1.12. Optical Tomography
Part I. Mathematical Tools
2. Preliminaries
2.1. Special Functions
2.2. Sobolev Spaces
2.3. Fourier Analysis
2.3.1. Shannon's Sampling Theorem
2.3.2. Fast Fourier Transform
2.4. The Two-Dimensional Radon Transform
2.5. The Moore-Penrose Generalized Inverse
2.6. Singular Value Decomposition
2.7. Compact Operators
2.8. Regularization of Ill-Posed Problems
2.8.1. Stability
2.8.2. The Truncated SVD
2.8.3. Tikhonov-Phillips Regularization
2.8.4. Regularization by Truncated Iterative Methods
2.9. General Image Characteristics
2.9.1. Spatial Resolution
2.9.2. Signal-To-Noise Ratio
3. Layer Potential Techniques
3.1. The Laplace Equation
3.1.1. Fundamental Solution
3.1.2. Layer Potentials
3.1.3. Invertibility of [lambda]I-K*[subscript D]
3.1.4. Neumann Function
3.1.5. Transmission Problem
3.2. Helmholtz Equation
3.2.1. Fundamental Solution
3.2.2. Layer Potentials
3.2.3. Transmission Problem
3.3. Static Elasticity
3.3.1. Fundamental Solution
3.3.2. Layer Potentials
3.3.3. Transmission Problem
3.4. Dynamic Elasticity
3.4.1. Radiation Condition
3.4.2. Fundamental Solution
3.4.3. Layer Potentials
3.4.4. Transmission Problem
3.5. Modified Stokes System
3.5.1. Fundamental Solution
3.5.2. Layer Potentials
3.5.3. Transmission Problem
Part II. General Reconstruction Algorithms
4. Tomographic Imaging with Non-Diffracting Sources
4.1. Imaging Equations of CT and MRI
4.1.1. Imaging Equation of CT
4.1.2. Imaging Equation of MRI
4.2. General Issues of Image Reconstruction
4.3. Reconstruction from Fourier Transform Samples
4.3.1. Problem Formulation
4.3.2. Basic Theory
4.4. Reconstruction from Radon Transform Samples
4.4.1. The Inverse Radon Transform
4.4.2. Fourier Inversion Formula
4.4.3. Direct Backprojection Method
4.4.4. Filtered Backprojection Reconstruction
4.4.5. Noise in Filtered Backprojection Reconstruction
5. Tomographic Imaging with Diffracting Sources
5.1. Electrical Impedance Tomography
5.1.1. Mathematical Model
5.1.2. Ill-Conditioning
5.1.3. Static Imaging
5.1.4. Dynamic Imaging
5.1.5. Electrode Model
5.2. Ultrasound and Microwave Tomographies
5.2.1. Mathematical Model
5.2.2. Diffraction Tomography
6. Biomagnetic Source Imaging
6.1. Mathematical Models
6.1.1. The Electric Forward Problem
6.1.2. The Magnetic Forward Problem
6.2. The Inverse EEG Problem
6.3. The Spherical Model in MEG
Part III. Anomaly Detection Algorithms
7. Small Volume Expansions
7.1. Conductivity Problem
7.1.1. Formal Derivations
7.1.2. Polarization Tensor
7.2. Helmholtz Equation
7.2.1. Formal Derivations
7.3. Static Elasticity
7.3.1. Formal Derivations
7.3.2. Elastic Moment Tensor
7.4. Dynamic Elasticity
7.5. Modified Stokes System
7.6. Nearly Incompressible Bodies
7.6.1. Formal Derivations
7.6.2. Viscous Moment Tensor
7.7. Diffusion Equation
8. Imaging Techniques
8.1. Projection Type Algorithms
8.2. Multiple Signal Classification Type Algorithms
8.3. Time-Domain Imaging
8.3.1. Fourier- and MUSIC-Type Algorithms
8.3.2. Time-Reversal Imaging
Part IV. Hybrid Imaging Techniques
9. Magnetic Resonance Electrical Impedance Tomography
9.1. Mathematical Model
9.2. J-Substitution Algorithm
9.3. The Harmonic Algorithm
10. Impediography
10.1. Physical Model
10.2. Mathematical Model
10.3. E-Substitution Algorithm
11. Magnetic Resonance Elastography
11.1. Mathematical Model
11.2. Binary Level Set Algorithm
References
Index

An introduction to mathematics of emerging biomedical imaging /

Similar Items