This paper presents a new systolic realization of the Fourier-based method for motion detection and velocity computation of multiple moving objects in images. In the architecture, the 2D discrete Fourier transform is computed via the 2D discrete Hartley transform (DHT) that involves only real valued arithmetic. The 2D DHT is realized based on the row-column decomposition without matrix transposition problems. The systolic system possesses the desirable features of regularity, modularity, and concurrency for VLSI implementation. It has a utilization efficiency of Min(N, M)/Max(N,M) X 100 percent and a throughput rate of one velocity estimation per T X Max(N,M) cycles, where N and M are the number of pixels of an image in the x- and y- directions, respectively, and T is the number of frames in the image sequence.