2004/04/24 by Sergey G. Kazantsev, Alexandre A. Bukhgeim · 1 citation
Mathematics · Physics and Astronomy · #math.CV #math-ph #math.MP #msc:44A12 #msc:53A45 #msc:42C05
published as Journal of Inverse and Ill-Posed Problems, 2004, Vol. 12, No.3, pp. 245-278. · LaTeX, 37 pages with 5 figures
arxiv created 2004/04/24 · arxiv updated 2009/12/01
In this article we study the fan-beam Radon transform \cal Dm of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc \mathbb D as the operator, acting from the object space \mathbf L2(\mathbb D; \bf Sm) to the data space L2([0,2π)×[0,2π)). The orthogonal polynomial basis \bf s(± m)n,k of solenoidal tensor fields on the disc \mathbb D was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator \cal Dm was obtained. The inversion formula for the fan-beam tensor transform \cal Dm follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.