Orthogonal Matching Pursuit with Dictionary Refinement for Multitone Signal Recovery

In this paper, we propose a low-cost algorithm for recovering multitone signals from compressive measurements. We introduce a simple and efficient modification to orthogonal matching pursuit. Our approach uses a DFT basis, but refines the frequency estimate obtained at each iteration via a simple gradient descent. We find that by adapting the dictionary in this manner we can realize the benefits of an overcomplete DFT frame without incurring the increased computation. Numerical simulations show that this approach not only outperforms traditional OMP, it even outperforms `1-minimization unless we incur the computational cost of using a highly overcomplete DFT frame.