Characterizing compressibility with Lorenz curves

Claudio Weidmann (1)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes

This paper revisits earlier work on rate distortion behavior of sparse sources, namely it highlights the fact that a graphical sparsity characterization proposed in \cite{Weidmann:00b} is a \emph{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.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Claudio Weidmann. Characterizing compressibility with Lorenz curves. IEEE International Symposium on Information Theory (ISIT 2011), Jul 2011, Saint-Petersburg, Russia. pp.2228-2232. ⟨hal-00688917⟩