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This letter presents a novel backward adaptive pixel-based fast predictive motion estimation (BAPME) scheme for lossless video compression. Unlike the widely used block-matching motion estimation techniques, this method predicts the motion on a pixel-by-pixel basis by comparing a group of past observed pixels in two adjacent frames, eliminating the need of transmitting side information. Combined with prediction and a fast search technique, the proposed algorithm achieves better entropy results and significant reduction in computation than pixel-based full search for a set of standard test sequences. Experimental results also suggest that BAPME is superior to block-based full search in terms of speed and zero-order entropy.