Quasi-Newton Iterative Projection Algorithm for Sparse Recovery

A computationally simple and efficient algorithm for compressed sensing is proposed. The algorithm, a simple combination of the orthogonal projection algorithm and of a novel quasi-Newton optimization scheme, is termed Quasi-Newton Iterative Projection (QNIP). There are two main advantages of the proposed algorithm. First, the computation of the proposed algorithm is very simple, which involves the application of the sampling matrix and its transpose at each iteration. Second, the algorithm appears to require a fewer number of iterations for convergence, whilst it provides a higher rate of perfect recovery compared with the reference algorithms. The performance of the proposed algorithm is validated via theoretical analysis as well as some numerical examples.