Sparse recovery for Earth Mover Distance

We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m × 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 show, in some scenarios, its advantages over the “usual” recovery in the ℓ_p norms.