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Basic Principles of Computed Tomography: Understanding CT Algorithm

Learn about the mathematical transformation, Radon Transform, and the CT reconstruction process. Explore the history of CT imaging and the principles of back projection and filtered backprojection. Discover how 2-dimensional images are reconstructed from projection data.

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Basic Principles of Computed Tomography: Understanding CT Algorithm

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  1. Basic Principles of Computed Tomography Dr. Kazuhiko HAMAMOTO Dept. of Infor. Media Tech. Tokai University

  2. What is the CT? • Mathematical transform to the measured data. • Reconstruct n dimension function (image) => projection data of n – 1 dimension • Radon Transform (1917)“Two dimension and three dimension object can be reconstructed from the infinite set of projection data”. • The First CT: 1973 in the U.S.4 minutes scan, thickness of 10mm

  3. Concept of CT ・Getting the shape by back projection of the projection data. ・For example, outward view is the quadrangle => it is the cylinder CT Algorithm

  4. X Blur Basic principle of CT-Reconstruction of 2 dimensional image- Projection Data curvilinear integral of absorption coefficient regarding Y y y X-ray detector array Y X x x object X X-ray tube Reconstruction field Data Acquisition field Simple Backprojection

  5. y x X x ω or x Basic principle of CT -Reconstruction of 2 dimensional image- Projection Data x ＊ Filtered Projection data Reconstruction Filter Multidirectional Backprojection Filtered Backprojection

  6. Reconstruction process

  7. Reconstruction process Data acquisition at angle : 0 – 180 degree Obtain F(u,v) and then 2D IFFT -> reconstruction Radon Transform is equivalent to Filtered backprojection !

  8. Example of Simulation Model Image SimpleBackprojection Filtered Backprojection

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