Characterizing compressibility with Lorenz curves

This paper revisits earlier work on rate distortion behavior of sparse sources, namely it highlights the fact that a graphical sparsity characterization proposed in [1] is a Lorenz curve, a tool for summarizing income inequality that has been used by economists for over a century. The Lorenz curve associated to a memoryless source can be used to obtain upper bounds on the distortion rate function, thus characterizing source compressibility. It is shown that an order relation on Lorenz curves induces an analogous relation on distortion rate upper bounds. This can be used to characterize the compressibility of certain parametric families of source distributions, for which an order on the parameters induces an order on Lorenz curves.