Lossless Image Data Sequence Compression using Optimal Context Quantization

Context based entropy coding often faces the conflict of a desire for large templates and the problem of context dilution. We consider the problem of finding the quantizer $Q$ that quantizes the $K$-dimensional causal context $C_{i}$ = $(X_{i-{\rm t}_{1}}, X_{i-t_{2}}, \ldots, X_{i-{\rm t}_{K}})$ of a source symbol $X_{l}$ into one of $M$ conditioning states. A solution giving the minimum adaptive code length for a given data set is presented (when the cost of the context quantizer is neglected). The resulting context quantizers can be used for sequential coding of the sequence $x_{0}, x_{1}, x_{2}$,…. A coding scheme based on binary decomposition and context quantization for coding the binary decisions is presented and applied to digital maps and a-plane sequences. The optimal context quantization is also used to evaluate existing heuristic context quantizations.