On the earth mover's distance as a performance metric for sparse support recovery

Abstract

Compressed Sensing (CS) is a recently emerged framework for simultaneous sampling and compression of signals that are sparse or compressible in some representation. Besides signal reconstruction, the CS framework is often adopted for compressive parameter estimation. Performance metrics commonly used in CS are well suited for performance evaluation in terms of recovery rates but provide little insight into the estimation accuracy in a parameter estimation setting. In this contribution, we study an alternative metric based on the Earth Mover's Distance (EMD). We define the EMD in the context of support recovery and derive exact formulas for its calculation for supports with equal as well as arbitrary cardinalities. Our simulation results suggest that the EMD provides a better alternative to common CS metrics in that it reflects the distance between the individual estimates in case of the imperfect support recovery.