Given the side-scanned image of a scene characterized by a random, time-varying reflectivity density, evolving in accordance with a dispersion relation, the linear, minimum mean-square error estimator of the scene at a given time is found. The data are corrupted by additive, ‘white’ noise. The minimum mean-square error does not depend on whether the real or the synthetic aperture technique is used or whether in the synthetic case, the ‘signal film’ or ‘complex’ image is the data. The effect of finite scanning velocity υ is to replace the white noise of spectral density ηo with a ‘colored’ noise of spectral density | - υgx(k)/υ|ηo where υgx(k) is the group velocity directed along υ it is assumed that υgx(k)/υ < 1. The anomalous behavior when υgx (k) exceeds υ is noted.