Sparse Recovery for Earth Mover Distance

Abstract

We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specically, we design a distribution over m x n matrices A, for m << n, such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD distance. We also provide an empirical evaluation of the method that, in some scenarios, shows its advantages over the "usual" recovery in the lp norms.