Optimum update for motion-compensated lifting

In wavelet video coding with motion-compensated lifting, the update step typically reverses the motion vectors from the prediction step. Where motion compensation is not invertible, heuristic rules are used for the update step. This paper derives a closed-form expression for the optimal update step for a given general linear prediction step and applies the result to motion-compensated wavelet coding. The analysis justifies using reversed motion vectors, where possible, and yields new results on proper inversion of subpixel motion compensation and optimal treatment of motion discontinuities. A new sparse matrix technique is presented that allows the practical implementation of the optimal update step for motion-compensated wavelet video coding. Experimental results confirm that optimizing the update step improves the rate-distortion performance for a motion-compensated wavelet video coder and provide justification for heuristics used in conventional techniques.