Entropy-Constrained Linear Vector Predict ion for Motion-Compensated Video Coding

Theoretical and experimental results for motion-compensated linear prediction of video signals are presented. T h e rate distortion theory of motion-compensated prediction is extended to linear predictive models. For practical implementations, linear vector predictors are employed. The rate of the motion data is ccmtrolled by minimizing a Lagrangian cost function whore rate is weighted against distortion using a Lagrange multiplier. An adaptive algorithm for optimally selecting the number of input signals t o the linear vector predictor is given. I. THEORETICAL ANALYSIS Following the framework for the rate distortion analysis of motion-compensated prediction in [I], we derive a closed form expression, where the power spectrum of the prediction error is related to the displacement pdfs of an arbitrary number of scalar input signals to the linear predictor. Previous work of Girod on the subject can be found in [2]. Let s[z,y] be a scalar two-dimensional signal sampled on an orthogonal grid. We model motion-compensated prediction as the predicticin of the signal s by modified versions of itself it. The lit are modified from s in that they are shifted by arbitrary displacements and corrupted by additive noise 2,. Motion-compenFation is assumed to be the alignment of the 1, to s up to a certain accuracy producing the motioncompensated signals cl. The alignment data, i.e., the displacement vector field, can never be completely accurate since it has to be transmitted as side information to the video decoder. Fig. l shows the prediction gain as a function of the