This paper describes an image compression strategy potentially capable of preserving the scientific quality of astrophysical data, simultaneously allowing a consistent bandwidth reduction to be achieved. Unlike strictly lossless techniques, by which moderate compression ratios are attainable, and conventional lossy techniques, in which the mean squared error of the decoded data is globally controlled by user, near-lossless methods are capable to locally constrain the maximum absolute error, based on user's requirements. An advanced lossless/near-lossless differential pulse code modulation (DPCM) scheme, recently introduced by the authors and relying on a causal
spatial prediction, is adjusted to the specific characteristics of astrophysical image data (high radiometric resolution, generally low noise, etc.). The background noise is preliminarily estimated to drive the quantization stage for high quality, which is the primary concern in most of astrophysical applications. Extensive experimental results of lossless, near-lossless, and lossy compression of astrophysical images acquired by the Hubble Space Telescope show the advantages of the proposed method compared to standard techniques like JPEG-LS and JPEG2000. Eventually, the rationale of virtually-lossless compression, that is a noise-adjusted lossles/near-lossless compression, is highlighted and found to be in accordance with concepts well established for the astronomers' community.