Lossless Astronomical Image Compression and the Effects of Noise

ABSTRACT.We compare a variety of lossless image compression methods on a large sample of astronomical images and show how the compression ratios and speeds of the algorithms are affected by the amount of noise (that is, entropy) in the images. In the ideal case where the image pixel values have a random Gaussian distribution, the equivalent number of uncompressible noise bits per pixel is given by Nbits=log2(σ12) and the lossless compression ratio is given by R=BITPIX/(Nbits+K) where BITPIX is the bit length of the pixel values (typically 16 or 32), and KK is a measure of the efficiency of the compression algorithm. We show that real astronomical CCD images also closely follow these same relations, by using a robust algorithm for measuring the equivalent number of noise bits from the dispersion of the pixel values in background regions of the image. We perform image compression tests on a large sample of 16-bit integer astronomical CCD images using the GZIP compression program and using a newer FITS tiled...