This note describes a fast algorithm for registering pairs of images from a time sequence of images. The algorithm solves a linear regression problem based on a linearization of the image matching equation, to obtain the registration coefficients. The problem of ill-posedness caused by differentiation of a noisy image sampled on a finite lattice is solved by means of a patch algorithm. The algorithm uses an integrated form of the linearized displacement equation. Registration is simultaneously carried out on a set of computationally fast prefilters providing three downsampled bandpass images for each input image. The filters are multilevel and permit an efficient and versatile hierarchical registration procedure. Downsampling the images before registration significantly reduces computation time. As a final step, registration is repeated using full-size images. Results for two-dimensional (2D) images using a six-parameter affine registration transformation and a 12-parameter second-order polynomial transformation indicate the method is 2.5 times faster (12.7 s/256 ฯซ 256 image pair) than a previous iterative method (28 s/pair) and, like the previous method, is robust to noise. The method may easily be generalized to 3D image registration and more general transformations, and is well-suited to parallel processing.