Compressive parameter estimation via K-median

•We propose the use of earth mover’s distance (EMD), as applied to a pair of true and estimated sparse PD coefficient vectors, to measure the parameter estimation error.•We show that the EMD provides a better-suited metric for parameter estimation performance than the Euclidean distance.•We leverage the relationship between K-median clustering and EMD-optimal sparse approximation to develop improved PD-based parameter estimation algorithms.