We begin by explaining why transforms other than the wavelet transform are important for astronomical image compression. By definition, the wavelet coefficient mean is null. Every time we have a positive structure at a scale, we have negative values surrounding it. These negative values often create artifacts during the restoration process, or complicate the analysis. So at each scale, and at each point source, we will have the wavelet.
Cosmic rays can pollute all the scales of the wavelet transform.
This leads us to develop other multiresolution tools which we now present. The multiresolution median transform consists of a series of smoothings of the input image, with successively broader kernels. Each successive smoothing provides a new resolution scale. The multiresolution coefficient values constructed by differencing images at successive resolution scales are not necessarily of zero mean, and so the potential artifact-creation difficulties related to this aspect of wavelet transforms do not arise. For integer input image values, this transform can be carried out in integer arithmetic only, which may lead to computational savings.