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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, doi:10.1088/0266-5611/21/6/006, 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 H1 regularized inverse.

BibTeX Entry

author = {T. J. Asaki and R. Chartrand and K. R. Vixie and B. Wohlberg},
title = {Abel inversion using total-variation regularization},
year = {2005},
urlpdf = {},
journal = {Inverse Problems},
volume = {21},
number = {6},
doi = {10.1088/0266-5611/21/6/006},
pages = {1895--1903}