Mathematical modeling of coding gain and rate-distortion function in multihypothesis motion compensation for video signals

This paper presents analytical model on motion-compensated predictive processing of the video signals. Multihypothesis prediction extends motion compensation with one prediction signal to the linear superposition of several motion-compensated prediction signals with the result of increased coding efficiency. The prediction error variances of the multihypothesis pictures are derived and minimized in this paper in order to find optimal bit allocations. Then, coding gains of the multihypothesis structures are calculated and compared, which is based on traditional prediction theories. Also, the corresponding rate-distortion functions are obtained in the closed form. Some experimental results show that more multihypotheses bring the smaller distortion of signals and hence improve the efficiency of video coding.