Theoretical consideration of global motion temporal filtering

A widely used technique to reduce the noise variance of a signal is a temporal overlapping of several noisy versions of it. It will be shown that the same idea can be applied for video sequences. Several versions of the current frame can be aligned using motion compensation that adjacent frames represent a noisy version of the current frame. In a first theoretical calculation of this concept combining the temporal overlapping of several noisy versions of the same signal and a rate-distortion equation, it has been shown that a theoretical bit rate reduction of 1/2 log₂ (N) is possible. In this work, the concept will be advanced to be closer to practice by adding a model for the motion estimation error. It will be shown that the derived theoretical equation confirms the practice and models the behavior of a video encoding environment using parametric motion compensated temporal filtering very well.