Image compression is required for preview functionality in large image databases (e.g. Hubble Space Telescope archive); with interactive sky atlases, linking image and catalog information (e.g. Aladin, Strasbourg Observatory); and for image data transmission, where more global views are communicated to the user, followed by more detail if desired.

Subject to an appropriate noise model, much of what is discussed in this chapter relates to faithful reproducibility of faint and sharp features in images from any field (astronomical, medical, etc.)

Textual compression (e.g. Lempel-Ziv, available in the Unix compress command) differs from image compression. In astronomy, the following methods and implementations have wide currency:

1. hcompress (White, Postman and Lattanzi, 1992). This method is most similar in spirit to the approach described in this chapter, and some comparisons are shown below, hcompress uses a Haar wavelet transform approach, whereas we argue below for a nonwavelet (multiscale) approach.

2. FITSPRESS (Press, 1992; Press et al., 1992) is based on the non-isotropic Daubechies wavelet transform, and truncation of wavelet coefficients. The approach described below uses an isotropic multiresolution transform.

3. COMPFITS (Véran and Wright, 1994), relies on an image decomposition by bit-plane. Low-order, i.e. noisy, bit-planes may then be suppressed. Any effective lossless compression method can be used on the high-order bit-planes.

4. JPEG (Hung, 1993), although found to provide photometric and astrometric results of high quality (Dubaj, 1994), is not currently well-adapted for astronomical input images.