A new adaptive postprocessing algorithm to enhance the quality of a noisy video sequence is presented. The algorithm recognizes that the visibility of noise depends on local signal characteristics. It therefore classifies the video signal into different classes and uses separate nonlinear filters matched to each class. The most general version of the algorithm employs motion-compensated frame averaging to improve picture quality in a first stage. A classification algorithm subsequently divides subblocks of pixels in the averaged frame into four classes: edge, smooth, nonsmooth with motion and nonsmooth without motion. Spatial algorithms that perform multilevel median filtering, double median filtering, and median filtering are used for pixels belonging to edge, smooth, and nonsmooth with motion categories. Pixels in the nonsmooth, unmoving category are left unfiltered to preserve corresponding image texture. In a simpler version of this four-class system, the motion cues and motion-compensated frame averaging are eliminated, and the purely spatial filtering is based on a three-class algorithm. When used at the output of a 3-D subband coder at 384 kbps, the spatial postfilter was shown to provide a consistent gain in subjectively evaluated picture quality. Twenty-five viewers participated in an experiment involving three coded sequences. In a pairwise comparison of postfiltered and unfiltered sequences, the postfiltered version was judged to be better in 63 out of 75 instances.