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

In this paper, factors that influence the lossless compression efficiency of reversible integer-to-integer (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 bps, where is the increment in ratio of the coefficient magnitude mean. The advantages of the 5/3 filters for lossless compression are then clearly explained. A new quantity, 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 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 & x0025; 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 & x0025; and 4 & x0025; respectively over the state-of-the-art lossless compression algorithms JPEG-LS and JPEG2000 lossless mode are achieved.