A note on support recovery of sparse signals using linear programming

A new theory known as compressed sensing considers the problem to acquire and recover a sparse signal from its linear measurements. In this paper, we propose a new support recovery algorithm from noisy measurements based on the linear programming (LP). LP is widely used to estimate sparse signals, however, we focus on the problem to recover the support of sparse signals rather than the problem to estimate sparse signals themselves. First, we derive an integer linear programming (ILP) formulation for the support recovery problem. Then we obtain the LP based support recovery algorithm by relaxing the ILP. The proposed LP based recovery algorithm has an attracting property that the output of the algorithm is guaranteed to be the maximum a posteiori (MAP) estimate when it is integer valued. We compare the performance of the proposed algorithm to a state-of-the-art algorithm named sparse matching pursuit (SMP) via numerical simulations.