Theoretical Considerations Concerning Pixelwise Temporal Filtering

Temporal in loop filters present one possible way to reduce noise introduced in compressed video sequences at low bit rates. Some of these filtering approaches make use of the quantized and generally noisy motion information conveyed in the bit stream generated by the encoder. One key feature of such filters is an adaptive filter length depending on the image content and the quality of the motion field. This paper derives mathematical equations to model the behaviour of one such filter in the presence of noisy motion vectors. The predicted optimal filter lengths are demonstrated to have a global optimum. They also show strong correlation with a real-world implementation of the previously introduced Temporal Trajectory Filter based on the HEVC main profile.