Data compression is specified as part of the Transfer Syntax. DICOM used to support many different compression algorithms (eighteen in total). Prior to 2002, all compression schemes were JPEG based, except for run-length encoding (RLE).
There are two basic groups of JPEG compression schemes in use: lossless, which is used when the original image can be completely reconstructed from the compressed data, and lossy compression, causing some degree of information loss.
When compressing with more than a factor of about 3 to 1, lossless compression is not possible anymore, and the decompressed image will start to look different from the original image. As a matter of fact, when compressing more than about 10 to 1, using certain algorithms, visible artifacts will start to appear in images. Radiologists are very careful not to use too much compression because of the potential impact on the capability to perform a proper primary diagnosis.
The JPEG committee home page is http://www.jpeg.org/.