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 log 2 K 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.
Highlights
Today, lossless compression can be found everywhere
Golomb-Rice coding [23] was used to code the integer coefficients decomposed from the reversible ITI transforms
The compression results from using the state-of-the-art algorithms JPEG2000 lossless mode and JPEG-LS are shown in the Table
Summary
Lossless compression can be found everywhere. In certain applications, such as military and medical applications, lossless compression is indispensable. A lot of research work on reversible ITI filters has been focused on how to realize the lifting scheme for exact-reconstruction filters/filterbanks and on the associated. If the coding results from using the conventional 5/3-filter decomposition are compared with those from using the nonseparable 9/7-filter decomposition, i.e., both decompositions use the same number of 8 rounding operations for a 2D decomposition, the 5/3 filters still consistently achieve higher compression ratio This shows that other than the coding gain and the accumulated rounding errors, there are still some important mechanisms that need to be considered in evaluating the compression performance for reversible ITI filters on lossless compression. We only focus on 2-channel biorthogonal exact-reconstruction filters in this paper
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