On the Fundamental Limit of Multipath Matching Pursuit

D Multipath matching pursuit (MMP) is a recent extension of the orthogonal matching pursuit algorithm that recovers sparse signals with a tree-searching strategy. In this paper, we present a new analysis for the MMP algorithm using the restricted isometry property. Our result shows that if the sampling matrix A is an element of R-mxn satisfies the RIP of order K + L with isometry constant delta(K+L) < root L/K+L then the MMP accurately recovers any K-sparse signal x is an element of R-n from the samples y = Ax, where L is the number of child paths for each candidate of the algorithm. Moreover, through a counterexample, we show that the proposed bound is optimal in that the MMP algorithm may fail under delta(K+L) = root L/K+ L.