Local orthogonal greedy pursuits for scalable sparse approximation of large signals with shift-invariant dictionaries

We propose a way to increase the speed of greedy pursuit algorithms for scalable sparse signal approximation. It is designed for dictionaries with localized atoms, such as timefrequency dictionaries. When applied to OMP, our modification leads to an approximation as good as OMP while keeping the computation time close to MP. Numerical experiments with a large audio signal show that, compared to OMP and Gradient Pursuit, the proposed algorithm runs in over 500 less time while leaving the approximation error almost unchanged.