In this work, near-lossless compression yielding strictly bounded reconstruction error is proposed for high-quality compression of remote sensing images. A classified causal DPCM scheme is presented for optical data, either multi/hyperspectral three-dimensional (3-D) or panchromatic two-dimensional (2-D) observations. It is based on a classified linear-regression prediction, followed by context-based arithmetic coding of the outcome prediction errors and provides excellent performances, both for reversible and for irreversible (near-lossless) compression. Coding times are affordable thanks to fast convergence of training. Decoding is always real time. If the reconstruction errors fall within the boundaries of the noise distributions, the decoded images will be virtually lossless even though encoding was not strictly reversible.