Abstract : Compression of biomedical images, especially for imaging modalities such as computed tomography (CT), magnetic resonance imaging (MRI) and virtual microscopy in anatomopathology (VM), is an important economic issue, especially for archival and transmission. This thesis provides an overview of the medical needs and of the existing compression solutions. It also aims, in this context, at providing new digital compression algorithms that are efficient in comparison with the state of the art standards. For CT and MRI, legal and medical constraints require a really good quality archival. Therefore this work has focused on lossless and near-lossless compression. It is proporsed to i) combine the hierarchical interpolation predictive model with the adaptive DPCM predictive one to provide a resolution scalable compression that is effective for lossless compression and especially for near-lossless compression, ii) rely on an optimization for lossless compression of a wavelet packet decomposition structure, that is specific to the image content. The results of both contributions shows that there is still a room for the improvement of the compression on most regular/smooth and less noisy images. The physical slides of the VM can be stored, so the issue more concerns the transfer for remote access than the archival. By the nature of their content, the learning of the properties of these images seems to be interesting. So, this third contribution aims to optimize offline K orthonormal transforms that are optimal for the decorrelation of training data (K-KLT}). This method is applied to learn in particular post-transforms for a wavelet decomposition. Their application in a quality scalable compression scheme shows that the approach can yield rather interesting quality gains in terms of PSNR.