Sequential Sparse Matching Pursuit

We propose a new algorithm, called sequential sparse matching pursuit (SSMP), for solving sparse recovery problems. The algorithm provably recovers a k-sparse approximation to an arbitrary n-dimensional signal vector x from only O(k log(n/k)) linear measurements of x. The recovery process takes time that is only near-linear in n. Preliminary experiments indicate that the algorithm works well on synthetic and image data, with the recovery quality often outperforming that of more complex algorithms, such as ¿₁ minimization.