This paper addresses quality issues in Medical Image compression and proposes an approach to achieve near-lossless storage of digitized X-ray plates. An image is normalized to the standard deviation of its noise, which is estimated in an unsupervised fashion. The resulting bitmap is encoded without any further loss. The compression algorithm proposed is based on a two-stage recursive interpolation exploiting nonseparable median filtering a on a quincunx grid. The advantage is twofold: interpolation is performed from all error-free values and is unlikely to occur across edges, thereby reducing the coding cost of the outcome residuals. In addition, classification based on spatial context is employed to improve entropy coding. The scheme outperforms other established methods when applied to X-ray images.