Image compression plays a crucial role in medical imaging, allowing efficient manipulation, storage, and transmission of binary, grey-scale, or colour images. Nevertheless, in medical applications the need to conserve the diagnostic validity of the image requires the use of lossless compression methods, producing low compression factors. In this paper, a novel near-lossless compression algorithm from projections, which almost eliminates both redundant information and noise from a greyscale image while retaining all relevant structures and producing high compression factors, is proposed. The algorithm is tested on experimental medical greyscale images from different modalities and different body districts and results are reported.