CODEWITHSUNDEEP
javascriptmatrixtomography-reconstruction
user3220072
user3220072

Reputation: 107

What is the general formula for radon back projection?

Trying to implement a simulation of computed tomography back projection in javascript/HTML5 canvas. Trying to figure the correct approach for dying a back projections and I have been studying this presentation.

On pp. 9-13 of the above presentation a step by step example of back projection is shown. This example involves a 2x2 matrix (with 4 projections and a total of 10 line integrals) and computes the line integrals of each projection where the value of each corresponding line integral is added to each matrix cell, respectively.

Subsequently the total number of line integrals is subtracted from the value of each matrix cell. Finally the resulting value in each matrix cell is divided by the number of projections minus one.

Does this approach hold in general for larger, say a 100x100 matrix with larger cell values, say around 100?

Upvotes: 0

Views: 197

Answers (1)

Nick X Tsui
Nick X Tsui

Reputation: 2912

Basically, yes the backprojection follows similar idea. However, in reality, the backprojection is also depending on the setup of the x-ray beam (parallel beam, fan beam). Therefore the best way is to draw some lines and figure out the complete geometry of each beam. Then you need to perform interpolation to convert the value of the beam to each image pixel.

Upvotes: 0

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