Jean-François Determe

On the Noise Robustness of Simultaneous Orthogonal Matching Pursuit

In this paper, the joint support recovery of several sparse signals whose supports exhibit similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analyzed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results.

Generalized Traveling Salesman Problem for Carrier-Vehicle Systems

In this paper, a mission planning problem for a team of collaborating vehicles is presented. The team consists of two vehicles: an aircraft, typically fast but with short flight endurance, and a marine carrier, typically slow but with negligible endurance limitations. The carrier is able to transport, deploy, recover, and service the aircraft. This paper focuses on the problem of determining the team’s trajectory that minimizes the time to visit a given set of locations. Since the resulting optimization problem is computationally difficult, a low-complexity heuristic is proposed. The proposed heuristic is obtained by decomposing the original problem into three easier subproblems. The effectiveness of the proposed method is validated through extensive numerical simulations.

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.