Convexity results for a predictive video coder

The problem of bit allocation among frames in a predictively encoded video sequence is fundamental to video compression. This paper examines the convexity of multivariate distortion-rate data generated by predictive encoding of video. The underlying convex structure of the distortion-rate data is used to motivate an efficient near-optimal steepest-descent (SD) algorithm for the bit allocation problem. Faster variations on the SD method are also constructed and evaluated. Both the convex data model and the SD algorithm are experimentally validated using an MPEG-2 encoder.