Medical Image Reconstruction A Conceptual Tutorial introduces the classical and modern image reconstruction technologies, such as two-dimensional (2D) parallel-beam and fan-beam imaging, three-dimensional (3D) parallel ray, parallel plane, and cone-beam imaging. This book presents both analytical and iterative methods of these technologies and their applications in X-ray CT (computed tomography), SPECT (single photon emission computed tomography), PET (positron emission tomography),and MRI (magnetic resonance imaging). Contemporary research results in exact region-of-interest (ROI) reconstruction with truncated projections,Katsevich's cone-beam filtered backprojection algorithm, and reconstruction with highly undersampled data with/o-minimization are also included.
This book is written for engineers and researchers in the field of biomedical engineering specializing in medical imaging and image processing with image reconstruction.
- 1 Basic Principles of Tomography
- 1.1 Tomography
- 1.2 Projection
- 1.3 Image Reconstruction
- 1.4 Backprojection
- 1.5 Mathematical Expressions
- 1.6 Worked Examples
- 1.7 Summary
- Problems
- References
- 2 Parallel-Beam Image Reconstruction
- 2.1 Fourier Transform
- 2.2 Central Slice Theorem
- 2.3 Reconstruction Algorithms
- 2.4 A Computer Simulation
- 2.5 ROI Reconstruction with Truncated Projections
- 2.6 Mathematical Expressions
- 2.7 Worked Examples
- 2.8 Summary
- Problems
- References
- 3 Fan-Beam Image Reconstruction
- 3.1 Fan-Beam Geometry and Point Spread Function
- 3.2 Parallel-Beam to Fan-Beam Algorithm Conversion
- 3.3 Short Scan
- 3.4 Mathematical Expressions
- 3.5 Worked Examples
- 3.6 Summary
- Problems
- References
- 4 Transmission and Emission Tomography
- 4.1 X-Ray Computed Tomography
- 4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography
- 4.3 Attenuation Correction for Emission Tomography
- 4.4 Mathematical Expressions
- 4.5 Worked Examples
- 4.6 Summary
- Problems
- References
- 5 3D Image Reconstruction
- 5.1 Parallel Line-Integral Data
- 5.2 Parallel Plane-Integral Data
- 5.3 Cone-Beam Data
- 5.4 Mathematical Expressions
- 5.5 Worked Examples
- 5.6 Summary
- Problems
- References
- 6 Iterative Reconstruction
- 6.1 Solving a System of Linear Equations
- 6.2 Algebraic Reconstruction Technique
- 6.3 Gradient Descent Algorithms
- 6.4 Maximum-Likelihood Expectation-Maximization Algorithms
- 6.5 Ordered-Subset Expectation-Maximization Algorithm
- 6.6 Noise Handling
- 6.7 Noise Modeling as a Likelihood Function
- 6.8 Including Prior Knowledge
- 6.9 Mathematical Expressions
- 6.10 Reconstruction Using Highly Undersampled Data with 10 Minimization
- 6.11 Worked Examples
- 6.12 Summary
- Problems
- References
- 7 MRI Reconstruction
- 7.1 The \"M\"
- 7.2 The \"R\"
- 7.3 The \"T\"
- 7.4 Mathematical Expressions
- 7.5 Worked Examples
- 7.6 Summary
- Problems
- References
