Wednesday, August 29, 2012

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]
    •  
  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]
    •  



  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

    • 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].

         

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