Laser-scanning methods are a means to observe streaming particles, such as the flow of red blood cells in a blood vessel. Typically, particle velocity is extracted from images formed from cyclically repeated line-scan data that is obtained along the center-line of the vessel; motion leads to streaks whose angle is a function of the velocity. Past methods made use of shearing or rotation of the images and a Singular Value Decomposition (SVD) to automatically estimate the average velocity in a temporal window of data. Here we present an alternative method that makes use of the Radon transform to calculate the velocity of streaming particles. We show that this method is over an order of magnitude faster than the SVD-based algorithm and is more robust to noise.