The present invention presents fully noncausal predictive encoding and decoding methods for image, video and other signal coding. The presented noncausal predictive image coding methods largely reduce the prohibitive computational cost of the prior invention. The presented noncausal signal encoding method comprises: (1) splitting the source signal into a plurality of noncausal coding units; (2) extending each noncausal coding unit with the selected extension type; and (3) encoding each noncausal coding unit with the selected intra-unit noncausal predictor and intra-unit noncausal predictive encoding method.