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Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
In this article we study the fan-beam Radon transform of
symmetrical solenoidal 2D tensor fields of arbitrary rank in a unit disc
as the operator, acting from the object space to the data space
The orthogonal polynomial basis of solenoidal tensor
fields on the disc was built with the help of Zernike polynomials
and then a singular value decomposition (SVD) for the operator
was obtained. The inversion formula for the fan-beam tensor transform 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