Problems in Hierarchical Data Compression

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The research objective is to enable one to systematically design hierarchical algorithms for data compression that outperform sequential data compression algorithms. The methodology first involves finding hierarchical algorithms that yield good theoretical performance in compressing sufficiently large data sets. Then, computer experiments shall be performed in which hierarchical algorithms selected on the basis of theory are tested versus sequential algorithms in compressing archival test and image files. Hierarchical data compression algorithms based on string rewriting systems, wavelets, and iterated function systems shall be principally considered. This development of hierarchical data compression theory and practice may have significant impact on the development of personal communication technology.