In this article we study the fan-beam Radon transform Dm of
symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc
D as the operator, acting from the object space L2(D;Sm) to the data space L2([0,2π)×[0,2π)).
The orthogonal polynomial basis sn,k(±m) of solenoidal tensor
fields on the disc D was built with the help of Zernike polynomials
and then a singular value decomposition (SVD) for the operator Dm
was obtained. The inversion formula for the fan-beam tensor transform 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.Comment: LaTeX, 37 pages with 5 figure