A universal multi-dimensional lossy compression algorithm

A universal algorithm to compress multi-dimensional data is presented. Besides being able to explore multidimensional correlations of the data, it incorporates two other fundamental innovations when compared to its predecessors, the Lossy Lempel-Ziv (LLZ) and Hierarchical String Matching algorithms: first, instead of building a dictionary of strings to match the data, it builds a dictionary of basis functions in which the data will be decomposed in the spirit of Mallat's matching pursuits; second, any basis function in the dictionary can be dilated or contracted when used to match the data. Simulation results show that it has good coding performance for a large class of image data. With Gaussian sources it has shown good performance, outperforming LLZ algorithms for low data rates, being close to the R(D). With real image data, when LLZ fails at all rates, it has performed even better, showing a great improvement over LLZ.