Data Compression Techniques in Image Processing for Astronomy

The classical way to digitally encode an image consists in sampling it on the nodes of a two dimensional grid and assigning to each pixel (picture element) a numerical value which expresses, to a desired accuracy, the luminance value on that node. A digital image can, therefore, be thought of as a matrix. Fig. 1 shows a plot of the luminance values of a bright star. Several effects are evident; na- mely saturation, irregular sampling and noise. Sampling irregulari- ties are the most complex problem indeed. They are clearly evident in highly structured image areas, but they are obviously present all over the image. They might not be as evident within the noisy (close to purely random, see fig. 2) background, but this could depend on aliasing noise, due to the small size of the spot of the scanner. In other words the exploring beam does not act as a prefilter of the data prior to sampling; thus it does not smooth completely the geome- trical irregularities of the scanner which show up in the digitized image. (Notice that deterministic irregularities of the scanning system can be corrected by a suitable program once they are precisely determined.) According to sampling theory, signal prefiltering is mandatory in order to avoid aliasing noise. The only way to two- dimensionally prefilter an image is through the use of an adeguately wide spot beam. As a consequence of the necessary filtering digital samples are correlated. This means that some redundance has to be present within the data and coding can be useful.