Compressive parameter estimation with earth mover's distance via K-median clustering

Abstract

In recent years, sparsity and compressive sensing have attracted significant attention in parameter estimation tasks, including frequency estimation, delay estimation, and localization. Parametric dictionaries collect observations for a sampling of the parameter space and can yield sparse representations for the signals of interest when the sampling is sufficiently dense. While this dense sampling can lead to high coherence in the dictionary, it is possible to leverage structured sparsity models to prevent highly coherent dictionary elements from appearing simultaneously in a signal representation, alleviating these coherence issues. However, the resulting approaches depend heavily on a careful setting of the maximum allowable coherence; furthermore, their guarantees apply to the coefficient vector recovery and do not translate in general to the parameter estimation task. We propose a new algorithm based on optimal sparse approximation measured by earth mover's distance (EMD). We show that EMD provides a better-suited metric for the performance of parametric dictionary-based parameter estimation. We leverage K-median clustering algorithms to solve the EMD-optimal sparse approximation problem, and show that the resulting compressive parameter estimation algorithms provide satisfactory performance without requiring control of dictionary coherence.