Online search Orthogonal Matching Pursuit

The recovery of a sparse signal x from y= Φx, where Φ is a matrix with more columns than rows, is a task central to many signal processing problems. In this paper we present a new greedy algorithm to solve this type of problem. Our approach leverages ideas from the field of online search on state spaces. We adopt the "agent perspective" and consider the set of possible supports of x as the state space. Under this setup, finding a solution is equivalent to finding a path from the empty support set to the state whose support has both the desired cardinality and the capacity to explain the observation vector y. An empirical investigation on Compressive Sensing problems shows that this new approach outperforms the classic greedy algorithm Orthogonal Matching Pursuit (OMP) while maintaining a reasonable computational complexity.