Lossless Astronomical Image Compression and the Effects of Noise

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 randomGaussian distribution, the equivalent number of uncompressible noise bits per pixel is given byNbits = log2(σ √ 12) 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 K 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-image compression method that currently supports 4 compression algorithms: Rice, Hcompress, PLIO, and the same Lempel-Ziv algorithm that is used by GZIP. Overall, the Rice compression algorithm strikes the best balance of compression and computational efficiency; it is 2–3 times faster and produces about 1.4 times greater compression than GZIP (the uncompression speeds are about the same). The Rice algorithm has a measured K value of 1.2 bits per pixel, and thus produces 75%–90% (depending on the amount of noise in the image) as much compression as an ideal algorithm with K = 0. Hcompress produces slightly better compression but at the expense of 3 times more CPU time than Rice. Compression tests on a sample of 32-bit integer images show similar results, but the relative speed and compression ratio advantage of Rice over GZIP is even greater. We also briefly discuss a technique for compressing floating point images that converts the pixel values to scaled integers. The image compression and uncompression utility programs used in this study (called fpack and funpack) are publicly available from the HEASARC web site. A simple command-line interface may be used to compress or uncompress any FITS image file. Subject headings: image compression, FITS