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The problem considered is to reconstruct a vector eld in the case when for each line the distribution of the vector eld components along the line is known. Such data are obtained from spectral analysis of signals, a ected by Doppler shifts, caused by re ections on moving particles (\velocity spectra"). In the general setting, the problem is unsolved. Using only integrated data along lines, one encounters the same problem as when reconstructing vector elds by means of time-of-ight measurements. Reconstruction formulas are given in this case, establishing the known fact that only the curl of the vector eld can be reconstructed without additional information. Inspired by the application to which the paper is most devoted, ultrasound Doppler measurements on blood ows, the case where the ow takes place in narrow channels is investigated in simulations and experiments.

Interpolation of Normed Abelian Groups(% J. ][)~ET~E and G. SPA~ (a Lurid, Svezi~) Smmnary-. -A theory o/ interpolation o/ normed AbeIian groups is developed, which notably generalizes and extends the theory o/ K. and J.spaces i~ the Banaeh space ease. Various applications to approximation theory and other branches o] analysis are given.

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Purpose: To develop a fast and highly automated method for calculating two-dimensional myocardial motion and deformation using velocity encoded magnetic resonance imaging. Materials and Methods:Two-dimensional phase contrast magnetic resonance imaging was used to acquire time resolved velocity maps of the myocardium. Cardiac motion was calculated by an iterative integration-regularization scheme of low computational cost. Image segmentation was performed using active appearance models.Results: Validation of motion tracking was performed in N ϭ 47 subjects using saturation grid-tagging and closely followed "tag-lines." Image segmentation was validated vs. manual delineation. Conclusion:The speed and limited user interaction gives the method good potential for use in clinical practice.

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