Learning Tomography: TOC

 

Table of Contents of this series dedicated to tomography and to the various algorithms used to compute a reconstruction from a series of projections.

Table of Contents

1. Introduction
• Playing with shadows [TODO] 
• Data Collection [Link]
• Projection [TODO]
• 2D reconstruction and sinogram [TODO]
  
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2. 2D reconstruction
• Simple Back-projection [Link]
• Weighted (Filtered) Back-projection [Link]
• Weighted (Filtered) Back-projection in action [Link] 
• Improving backProj.js script [Link] 
• Artifacts and other problems
• Noise [TODO]
• Missing data [TODO]
• Centered projections
1. Introduction [Link]
2. A script[Link]
3. Playing with dots [Link]


3. Input data
   
• How to compute a Radon Transform or Sinogram? [Link]
• Managing borders in sinogram computation [Link]
• How many projections do we need? [Link]
• What about the angular coverage ? [Link] and [Link]
• Where are the sinograms in 2D projections ?  [Link]
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4. Iterative Techniques
• Algebraic Reconstruction Technique (ART)
• ART-Kaczmarz: Principle [Link]
• ART-Kaczmarz: Simple implementation [Link]
• ART: Adding Constraints [Link]
• MART: Multiplicative ART [Link]
• Simultaneous Iterative Reconstruction Technique (SIRT)
• SIRT implementation [TODO]
• SART: a SIRT variant [TODO]
•  




5. Direct Fourier Reconstruction 
• Introduction [Link]
• Implementation
• Part I: Computing the Fourier Transform of the sinogram [Link]
• Part II: Filling 2D Fourier space and ... final reconstruction [Link]
• Another (usual) implementation  [Link] 
• Improvement
• Zero padding [Link]
• Better interpolation scheme [Link]
• 
  
• Using Fourier transform rather than Hartley Transform
• Part I: Computing FT(sinogram) [Link]
• Part II: Computing 2D reconstruction [Link]
•  Movie [Link]
• Blurry back-projection vs Direct Fourier Reconstruction [Link]
• 
  




6. Calculating a 3D reconstruction
• Slice by slice [Link]
• From various viewpoints [TODO]


7. Conclusion
• And now?... it's time to visualize your 3D reconstruction [TOC]
• 
  



References

• Books 
  • Joachim F, Chapter 5: Three-dimensional Reconstruction in  "Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State", Academic Press.
  •  
•  Radon Transform and Reconstruction algorithms
  • Toft P, The Radon Transform - Theory and Implementation, PhD thesis, 1996, [Link].
  •  
• Iterative Reconstruction Techniques
  • Kak AC, Slaney M, Chapter 7 - Algebraic Reconstruction Algorithms in "Principles of Computerized Tomographic Imaging", Society of Industrial and Applied Mathematics, 2001, [Link].
  •  
•  Direct Fourier Reconstruction
• centralslice : CT scan Reconstruction by Direct Fourier Reconstruction,  [Link].
• Zosso D, Bach Cuadra M,Thiran JP, Direct Fourier Tomographic Reconstruction Image-to-Image Filter, 2007, [PDF].