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We demonstrate that there are many direct inversion formulae for the two-dimensional (2D) Radon transform that are not equivalent to Radon's original inversion formula. Our explicit formulae have a form similar to classical filtered backprojection but do require some information about the support of the object function. We present some numerical results to illustrate significant differences in reconstructions as alternate formulae are applied to noisy data.
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Clackdoyle et al. (2004) studied this question.
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