Summary form only given. Linear predictive schemes are some of the simplest techniques in lossless image compression. In spite of their simplicity they have proven to be surprisingly efficient. The current JPEG image coding standard uses linear predictive coders in its lossless mode. Predictive coding was originally used in lossy compression techniques such as differential pulse code modulation (DPCM). In these techniques the prediction error is quantized, and the quantized value transmitted to the receiver. In order to reduce the quantization error it was necessary to reduce the prediction error variance. Therefore techniques for generating "optimum" predictor coefficients generally attempt to minimize some measure of the prediction error variance. In lossless compression the objective is to minimize the entropy of the prediction error, therefore techniques geared to minimizing the variance of the prediction error may not be best suited for obtaining the predictor coefficients. We have attempted to obtain the predictor coefficient for lossless image compression by minimizing the first order entropy of the prediction error. We have used simulated annealing to perform the minimization. One way to improve the performance of linear predictive techniques is to first remap the pixel values such that a histogram of the remapped image contains no "holes" in it.