Noncausal directional intra prediction: Theoretical analysis and simulation

This paper presents the theoretical analysis and simulation of noncausal directional intra prediction for image and video coding, where noncausal pixels, that is, pixels inside, below, or to the right of the target block, are used to predict the block, at the cost of extra bits to code those noncausal reference pixels. The proposed method generalizes the conventional causal intra prediction. The optimal number and locations of noncausal reference pixels are determined by minimizing the total differential entropies of the prediction residuals and the noncausal pixels. In order to obtain the differential entropy, a statistical image model is used to derive the autocorrelation of the residuals. In addition, the optimal sinusoidal approximations to transform the residuals are obtained by maximizing the coding gain. In the simulation, the optimal noncausal reference pixels and transforms of 4 × 4 and 8 × 8 blocks are identified for up to 33 directions. The results could provide insights for the design of more advanced directional intra prediction for the High Efficiency Video Coding (HEVC).