A compression-boosting transform for 2D data

In this paper, we present an invertible transform for 2D data which has the objective of reordering the matrix to improve its (lossless) compression at later stages. Given a binary matrix, the transform involves first searching for the largest uniform submatrix, that is, a submatrix solely composed by the same symbol (either 0 or 1) induced by a subset of rows and columns (which are not necessarily contiguous). Then, the rows and the columns are reordered such that the uniform submatrix is moved to the left-upper corner of the matrix. The transform is recursively applied on the rest of the matrix. The recursion is stopped when the partition produces a matrix which is smaller than a predetermined threshold. The inverse transform (decompression) is fast and can be implemented in linear time in the size of the matrix. The effects of the transform on the compressibility of 2D data is studied empirically by comparing the performance of gzip and bzip2 before and after the application of the transform on several inputs. The preliminary results show that the transform boosts compression.