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T. J. Asaki, R. Chartrand, K. R. Vixie and B. Wohlberg, "Abel inversion using total-variation regularization", *Inverse Problems*, vol. 21, no. 6, pp. 1895--1903, 2005

In the case of radiography of a cylindrically symmetric
object, the Abel transform is useful for describing the
tomographic measurement operator. The inverse of this operator
is unbounded, so regularization is required for the computation
of satisfactory inversions. We introduce the use of the total
variation seminorm for this purpose, and prove existence and
uniqueness of solutions of the corresponding variational
problem. We illustrate the effectiveness of the total variation
regularization with an example and comparison with the
unregularized inverse and the
*H ^{1}* regularized
inverse.

@article{asaki-2005-abel,

author = {T. J. Asaki and R. Chartrand and K. R. Vixie and B. Wohlberg},

title = {Abel inversion using total-variation regularization},

year = {2005},

urlpdf = {http://brendt.wohlberg.net/publications/pdf/asaki-2005-abel.pdf},

journal = {Inverse Problems},

volume = {21},

number = {6},

pages = {1895--1903}

}