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Modified Radon transform inversion using moments. (English) Zbl 1451.44002

The paper basically is a study of the Radon transform and the related theory. A modified version of the Radon transform is defined by the authors using the convolution theory, various properties related to it are derived and further its inversion formula is given. Moreover, a connection is shown between the moments of the Radon and the modified Radon transform. Reconstruction or recovery of the input function from the moments of the modified Radon transform is also shown, which is a useful aspect of the paper. Further, to demonstrate the convergence of the reconstruction algorithm based on the moments of the modified Radon transform a flow chart is given that elaborates the algorithm and some numerical examples related to it. The rate of convergence is given which describes the efficiency of the algorithm. The paper is written in an organized manner. The proofs of theorems and various results are correct. A numerical example to demonstrate the convergence is given and a graphical representation of the solution is shown which is well represented. It opens an area of research like generalization of this modified Radon transform and various applications related to it.

MSC:

44A12 Radon transform
44A60 Moment problems
47A57 Linear operator methods in interpolation, moment and extension problems
28A25 Integration with respect to measures and other set functions
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References:

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