Image noise restoration and predictive image coding are combined by implementing a maximum-a-posteriori (MAP) estimator on the differential signal in a differential pulse code modulation (DPCM) image compression scheme. For a Laplacian differential-signal probability density function (pdf) and a Gaussian noise pdf, the MAP estimator is an adaptive coring operator which is linear in the uncored region with a bias toward zero and a null operator in the cored region. The bias and the width of the coring region are functions of the noise and differential-signal variance, which are estimated from local image statistics over variable-length line segments. Independent segments are isolated by using a generalized-likelihood-ratio-test (GLRT) for Laplacian signals to determine whether or not adjacent segments have statistically equivalent differential variances. Because the MAP operator is an additive bias, it can be inserted in the transmitter of a DPCM encoder without error build-up or overhead information, and since it lowers the variance of the signal to be quantized by reducing the noise it can simplify the encoder by decreasing the number of levels that are required.