Full Reconstruction of a Vector Field from Its Attenuated Vectorial Radon Transform

A.A. Bukhgeim and S.G. Kazantsev (Russia)


Vectorial and emission tomography, SPECT, fan-beam geometry, transport equation, inverse problems.


We consider the problem of inverting the 2D attenuated vectorial Radon transform within the framework of a fan beam scanning geometry. In the case of a vector field sup ported on the unit disc an explicit formula for reconstructing this vector field is derived. In the unattenuated case it is known that only the solenoidal part of a vector field can be reconstructed and the full reconstruction requires additional information. In this paper we get full reconstruction of the vector field from its attenuated vectorial Radon trans form (which is a single scalar function of two variables). This invertion formula was obtained by analogy with the one for the scalar case, see [4]. Numerical results are presented.

Important Links:

Go Back