Ultrasonic Doppler measurement of flows with continuous ultrasound gives rise to velocity spectras along lines. These measurements can be used to find tomographic data about the region in which reflecting particles are present, the support of the flow. The flow can e.g. be a blood flow inside a human body, then the reflecting particles are the blood corpuscles. Here we give a new algorithm, that uses the fact that the characteristic function of the support is binary, for reconstruction. We prove that the algorithm converges in an ideal case and simulations suggests that an adjusted version works fine with noisy data. Keywords: Radon transform, Doppler tomography, flow tomography. 1 Introduction It is well known that a scalar function can be reconstructed from all its line integrals, the X-ray transform, see e.g. [6]. This topic was first addressed in [10] by Radon, where an explicit reconstruction formula was given. There exist several different numerical approaches, when only a fini...