The exponential radon transform and projection filtering in radiotherapy planning

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Abstract
The mathematical problem of generating a desired dose distribution in a patient who has to undergo external beam radiotherapy is closely related to the problem of reconstructing an image from its projections. Under some simplifying assumptions the theory of the exponential Radon transform as developed for SPECT image reconstruction can be successfully applied to the field of radiotherapy. This results in a projection‐filtering algorithm for the calculation of optimal beam profiles. The method yields analytical solutions for circular and triangular dose distributions, and combinations thereof. Practical solutions for arbitrary cases can be found numerically. The problem of unphysical negative values in the calculated beam profiles is solved by a method combining “cutting off” and “shifting”.

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