Lossless image compression has many applications, for example, in medical imaging, space photograph and film industry. In this thesis, we propose an efficient lossless image compression scheme for both binary images and gray-scale images. The scheme first decomposes images into a set of progressively refined binary sequences and then uses the context-based, adaptive arithmetic coding algorithm to encode these sequences. In order to deal with the context dilution problem in arithmetic coding, we propose a Lloyd-like iterative algorithm to quantize contexts. Fixing the set of input contexts and the number of quantized contexts, our context quantization algorithm iteratively finds the optimum context mapping in the sense of minimizing the compression rate. Experimental results show that by combining image decomposition and context quantization, our scheme can achieve competitive lossless compression performance compared to the JBIG algorithm for binary images, and the CALIC algorithm for gray-scale images. In contrast to CALIC, our scheme provides the additional feature of allowing progressive transmission of gray-scale images, which is very appealing in applications such as web browsing
