A data transformation is information preserving if the original data could, in principle, be recreated from the transformed data.  In audio processing Fourier transform are often used to transform a signal into frequency space, but a reverse transform can recreate the orginal sound.  Compression algorithms are often classified into lossless compression which is information preserving and lossy compression, for example in JPEG format, where some of the details of the image are irretrievably lost.
Used in Chap. 14: page 217
Used in glossary entries: Fourier transform, frequency domain