Digital image compression in astronomy morphology or wavelets

A wide-fleld astronomical image is often considered as a set of quasi point-like sources spread on a slow-varying backgound. With this model, the image is described as a set of connected flelds. We have to code the fleld positions, the fleld boundaries and their pixel values. It exists difierent methods for coding this information, they are mainly connected to the Mathematical Morphology. The flelds may be coded from their contours, their binary skeletons or the grey-tone ones. On difierent examples, we show that the morphological skeleton transformation in general gives us the best results. The H-transform is a two-dimensional generalization of the Haar transform, a typical wavelet transform. It is to-day often used for compressing astronomical images. Blocking efiects appear in the restored image. The quality of the restoration is improved by introducing in the inverse H-transform scheme an a priori knowledge on the solution which consists to choose the smoothest image at each scale. These two difierent approaches lead to high compression rates on classical astronomical images. In fact, the images are very difierently described. With the morphological methods, the highest compression rates are obtained if the images is composed only of small point-like sources, while the wavelet transform is well adapted to the compression of images with information at difierent scales. So the best compression technique is directly connected to the image modelling. The use of compression methods depends also of the further application. A perfect solution does not exist for image compression, we must take into account the image texture and the futur use.