An alphabet reduction algorithm for lossless compression of images with sparse histograms

In this paper, we propose a new adaptive arithmetic coding for lossless image compression applying an alphabet reduction algorithm. The algorithm is a reduction mechanism of the alphabet set within each block by assigning to each one an as small as possible symbol set including all the really present symbols called active symbols, instead of using the nominal alphabet set. The method can be considered as away to address the well-known zero-frequency problem which appears especially for images with sparse and locally sparse histograms. The analytical expression of the expected gain in terms of compression efficiency when using the block active symbol sets is derived. We show experimentally that the proposed method, in conjunction with adaptive arithmetic coding order-0 model applied for images with sparse and locally sparse histograms, provides promising compression ratios and outperforms several state-of-the-art lossless image compression standards such as JPEG2000, JPEG-LS and CALIC.