DOPPLER TOMOGRAPHY FOR VECTOR-FIELDS

The problem considered is to reconstruct a vector field in the case wh en, for each line, the distribution of the vector field components alo ng the line is known. Such data are obtained from spectral analysis of signals, affected by Doppler shifts, caused by reflections on moving particles ('velocity spectra'). In the general setting, the problem is unsolved. Using only integrated data along lies, one encounters the s ame problem as when reconstructing vector fields by means of time-of-f light measurements. Reconstruction formulae are given in this case, es tablishing the known fact that only the curl of the vector field can b e reconstructed without additional information. Inspired by the applic ation to which the paper is most devoted, i.e. ultrasound Doppler meas urements on blood flow, the case where the flow takes place in narrow channels is investigated in simulations and experiments.