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Summary form only given. We show a parallel algorithm using a rectangle greedy matching technique which requires a linear number of processors and O(log(M)log(n)) time on the PRAM EREW model. The algorithm is suitable for practical parallel architectures as a mesh of trees, a pyramid or a multigrid. We implement a sequential procedure which simulates the compression performed by the parallel algorithm and it achieves 95 to 97 percent of the compression of a previous sequential heuristic. To achieve logarithmic time we partition an m×n image, I, in x×y rectangular areas where x and y are Θ(log12 / mn). In parallel for each area, one processor applies the sequential parsing algorithm, so that, in logarithmic time, each area is parsed in rectangles, some of which are monochromatic. Before encoding, we compute larger monochromatic rectangles by merging the ones adjacent on the horizontal boundaries and then on the vertical boundaries, doubling in this way the length and width of each area at each step.