Abstract: The fact that a vascular tree occupies a very small portion of the surrounding space is profitably employed for reducing the number of reconstruction calculations and improving the quality of this reconstruction without thereby making restrictive geometrical hypotheses. A support region of the object is determined. An estimation of the object to be reconstructed is then carried out on the support region by means of an algebraic method. Determination of the object support involves a statistical evaluation of the detected observations and a comparison of this evaluation with a measurement of the intrinsic noise of the measurement chain. Noise problems are overcome by means of the statistical study. By utilizing a second estimation stage, and taking the support into account, one avoids a restrictive implicit assumption on a convex shape of the objects to be studied.