Improving the Correlation Lower Bound for Simultaneous Orthogonal Matching Pursuit

The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner product of any atom of a suitable dictionary and the current signal residual, which is formed by the subtraction of previously selected atoms. This inner product, or correlation, is a key metric to determine the best atom to pick at each iteration. This letter provides, for each iteration of SOMP, a novel lower bound of the aforementioned metric for the atoms belonging to the correct and common joint support of the multiple signals. Although the bound is obtained for the noiseless case, its main purpose is to intervene in noisy analyses of SOMP. Finally, it is shown for specific signal patterns that the proposed bound outperforms state-of-the-art results for SOMP and orthogonal matching pursuit (OMP) as a special case

A travelling salesman problem for a class of heterogeneous multi-vehicle systems

In this work we formulate and study a Travelling Salesman Problem (TSP) for a scenario in which two different vehicles cooperate so as to perform a desired task in an optimal way. In particular we consider the problem where a fast vehicle with a short operative range has to be coordinated with a carrier vehicle, typically slower but with virtually infinite operativity range, in order to visit in the shortest time a given collection of points