Computed Tomography Physics PDF 
E-Lectures

Preface - PDF File (456K Bytes)

 

1 Introduction - PDF File (304K Bytes)

 

References

2 Signal Processing Fundamentals - PDF File (4.6M Bytes)

 

2.1 One-Dimensional Signal Processing
Continuous and Discrete One-Dimensional Functions ° Linear Operations ° Fourier Representation ° Discrete Fourier Transform (DFT) ° Finite Fourier Transform ° Just How Much Data Is Needed? ° Interpretation of the FFT Output ° How to Increase the Display Resolution in the Frequency Domain ° How to Deal with Data Defined for Negative Time ° How to Increase Frequency Domain Display ° Resolution of Signals Defined for Negative Time ° Data Truncation Effects
2.2 Image Processing
Point Sources and Delta Functions ° Linear Shift Invariant Operations ° Fourier Analysis ° Properties of Fourier Transforms ° The Two-Dimensional Finite Fourier Transform ° Numerical Implementation of the Two-Dimensional FFT
2.3 References


3 Algorithms for Reconstruction with Nondiffracting Sources - PDF File (5.5M Bytes)

 

3.1 Line Integrals and Projections

3.2 The Fourier Slice Theorem

3.3 Reconstruction Algorithms for Parallel Projections
The Idea ° Theory ° Computer Implementation of the Algorithm

3.4 Reconstruction from Fan Projections
Equiangular Rays ° Equally Spaced Collinear Detectors ° A Re-sorting Algorithm

3.5 Fan Beam Reconstruction from a Limited Number of Views

3.6 Three-Dimensional Reconstructions
Three-Dimensional Projections ° Three-Dimensional Filtered Backprojection

3.7 Bibliographic Notes

3.8 References

4 Measurement of Projection Data - The Nondiffracting Case - PDF File (10.2M Bytes)

 

4.1 X-Ray Tomography
Monochromatic X-Ray Projections ° Measurement of Projection Data with Polychromatic Sources ° Polychromaticity Artifacts in X-Ray CT ° Scatter ° Different Methods for Scanning ° Applications

4.2 Emission Computed Tomography
Single Photon Emission Tomography ° Attenuation Compensation for Single Photon Emission CT ° Positron Emission Tomography ° Attenuation Compensation for Positron Tomography

4.3 Ultrasonic Computed Tomography
Fundamental Considerations ° Ultrasonic Refractive Index Tomography ° Ultrasonic Attenuation Tomography ° Applications

4.4 Magnetic Resonance Imaging

4.5 Bibliographic Notes

4.6 References

(Individual sections of this large chapter are also available: 4.1, 4.2, 4.3, 4.4, 4.5& 4.6)

5 Aliasing Artifacts and Noise in CT Images - PDF File (2.3M Bytes)

 

5.1 Aliasing Artifacts
What Does Aliasing Look Like? ° Sampling in a Real System

5.2 Noise in Reconstructed Images
The Continuous Case ° The Discrete Case

5.3 Bibliographic Notes

5.4 References

6 Tomographic Imaging with Diffracting Sources - PDF File (6.9M Bytes)

 

6.1 Diffracted Projections
Homogeneous Wave Equation ° Inhomogeneous Wave Equation

6.2 Approximations to the Wave Equation
The First Born Approximation ° The First Rytov Approximation

6.3 The Fourier Diffraction Theorem
Decomposing the Green's Function ° Fourier Transform Approach ° Short Wavelength Limit of the Fourier Diffraction Theorem ° The Data Collection Process

6.4 Interpolation and a Filtered Backpropagation Algorithm for Diffracting Sources
Frequency Domain Interpolation ° Backpropagation Algorithms

6.5 Limitations
Mathematical Limitations ° Evaluation of the Born Approximation ° Evaluation of the Rytov Approximation ° Comparison of the Born and Rytov Approximations

6.6 Evaluation of Reconstruction Algorithms

6.7 Experimental Limitations
Evanescent Waves ° Sampling the Received Wave ° The Effects of a Finite Receiver Length ° Evaluation of the Experimental Effects ° Optimization ° Limited Views

6.8 Bibliographic Notes

6.9 References

7 Algebraic Reconstruction Algorithms - PDF File (2.3M Bytes)

 

7.1 Image and Projection Representation

7.2 ART (Algebraic Reconstruction Techniques)

7.3 SIRT (Simultaneous Iterative Reconstructive Technique)

7.4 SART (Simultaneous Algebraic Reconstruction Technique)
Modeling the Forward Projection Process ° Implementation of the Reconstruction Algorithm

7.5 Bibliographic Notes

7.6 References

8 Reflection Tomography - PDF File (3.4M Bytes)

 

8.1 Introduction

8.2 B-Scan Imaging

8.3 Reflection Tomography
Plane Wave Reflection Transducers ° Reflection Tomography vs. Diffraction Tomography ° Reflection Tomography Limits

8.4 Reflection Tomography with Point Transmitter/Receivers
Reconstruction Algorithms ° Experimental Results

8.5 Bibliographic Notes

8.6 References

Index -  HTML File (with links) - PDF File (494K Bytes)

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