Reversible Integer-to-Integer Wavelet Filter Design for Lossless Image Compression

Abstract

In this paper, factors that influence the lossless compression efficiency of reversible integer-tointeger (ITI) wavelet filters are presented. It is observed that there is a converged region for the bitrate of the compressed subbands. Reaching the converged region, the bitrate increment is equal to log₂K bps, where K is the increment in ratio of the coefficient magnitude mean. The advantages of the 5/3 filters for lossless compression are then clearly explained. Anew quantity, R_mn, which measures the efficiency of reversible ITI transforms on flat spectrum inputs, is defined and is used in the new reversible filter design. First, keeping the distinctive merits of the 5/3 filters for lossless compression, the half-band product filter series of the Daubechies wavelet series is selected as the analysis high-pass filters. Next, the analysis low-pass filter is found by experimentally minimizing the Rmn value. Finally, it is determined that the 17/11 filters, which employ the half-band product filter with 6 vanishing moments, have the highest compression efficiency. Coding results show that the new 17/11 filters lead to a bitrate reduction of 1.7% over the 5/3 filters for lossless image compression. With further enhancements on the transform part and combining the enhanced transform with more efficient entropy coding, bitrate reductions of about 3.1% and 4% respectively over the state-of-the-art lossless compression algorithms JPEG-LS and JPEG2000 lossless mode are achieved.