Exponential vector field tomography
In the exponential Radon transform in R2, the integrals of a scalar function f over lines, with exponential weight functions, are determined. In this paper we demonstrate how to define two different kinds of exponential Radon transforms for vector fields in R2 in a natural way. It is shown that having data from these transforms it is possible to reconstruct the vector field uniquely.
The motivation to study this problem is ultrasound measurements of flows, from which velocity spectra along lines can be determined. The first moment of these can be interpreted by means of one of the exponential vectorial Radon transforms.
KeywordsVector Field Filter Back Projection Tomographic Reconstruction Velocity Spectrum Straight Pipe
- 3.P. Juhlin. Principles of Doppler tomography. Technical report, Dept. of Mathematics, Lund Institute of Technology, 1992.Google Scholar
- 4.F. Natterer. The Mathematics of Computerized Tomography. John Wiley & Sons, Chichester, Mew York, Brisbane, Toronto, Singapore, 1986.Google Scholar
- 8.K. Stråhlén. Reconstructions from Doppler Radon transforms. In Proceedings of ICIP'96. IEEE, 1996.Google Scholar
- 9.K. Stråhlén, G. Sparr, M. Almqvist, and H. W. Persson. Ultrasound Doppler measurements of blood flows using tomographic methods. In Proceedings: BIOSIGNAL'96, 1996.Google Scholar
- 10.K. Stråhlén. Some Integral Transforms of Vector Fields. Licentiate thesis, Dept. of Mathematics, Lund Institute of Technology, Lund University, 1996.Google Scholar