This paper examines the role of the loop/interpolation filter in the motion compensation loop of hybrid coders. Using Wiener filtering concept and the statistical model developed by Chen and Pang [4], the optimum filter that minimises the prediction error has been found. The result is expressed in an explicit form in terms of a correlation parameter, rho and an inaccuracy parameter, alpha. It explains many current practices in MPEG and H.261 coders, as well as leakage predictor, 3-tap versus 8-tap filter and other related issues. The analysis shows that minimum bit rate can only be achieved if the loop filter matches the statistical characteristic of the motion compensated signal. Furthermore, since the motion noise characteristic could be very different in the horizontal and vertical direction for many sequences, decision to deploy the optimum filter should be made separately in the two directions. The paper also derives the scalar loop filter in DCT domain. The scalar filter is sub optimal, but it requires less computational load than the spatial domain filter (64 versus 484 multiplications per 8x8 block). Experiments show that it performs almost as efficiently as the optimum 3-tap spatial domain filter, thus ascertain that its performance has not been significantly compromised by the scalar requirement. Experimental simulations on test sequences confirm the theoretical optimum results, and indirectly show that the simple statistical model used in the derivation is adequate.
