Compression Using Lossless Decimation: Analysis and Application

A crude but commonly used technique for compressing ordered scientific data consists of simply retaining every sth datum (with a value of s = 10 generally the default) and discarding the remainder. Should the value of a discarded datum be required afterwards, an approximation is generated by linear interpolation of the two nearest retained values. Despite the widespread use of this and similar techniques, there is little by way of theoretical analysis of their expected performance. First, we quantify the accuracy achieved by linear interpolation when approximating values discarded by decimation, obtaining both deterministic bounds in terms of appropriate smoothness measures of the data and probabilistic bounds in terms of statistics of the data. Second, we investigate the efficiency of the lossless compression scheme consisting of decimation coupled with encoding of the interpolation errors. In particular, we bound the expected compression ratio in terms of the appropriate measures of the data. Finally, we provide numerical illustrations of the practical performance of the algorithm on some real datasets.