A fast global matching pursuit algorithm for sparse reconstruction by $l_{0}$ minimization

Abstract

Greedy algorithms, which are employed to solve the sparse reconstruction based on $l_{0}$ minimization, always present two main shortcomings. One is that they are easy to fall into sub-optimal solutions by utilizing fast searching strategies and perform relatively bad on reconstruction accuracy. The other is that they need a large number of iterations to be convergent by setting negative gradient as the searching direction. To improve the two shortcomings, this paper proposes a novel fast global matching pursuit algorithm (FGMP) for sparse reconstruction. Firstly, we design global matching pursuit strategies to solve the $l_{0}$ minimization essentially, which is more likely to find the global optimal solution accurately. Then, the global searching direction is designed based on Quasi-Newton projection to replace the negative gradient, which is efficient to reduce the iterations of convergence and avoid the long time-consuming least square implementation to accelerate the reconstruction speed. The proposed FGMP algorithm is as simple as greedy algorithms, while it has better performance on both reconstruction accuracy and reconstruction speed. Simulated experiments on signal reconstruction and image reconstruction demonstrate that FGMP outperforms the state-of-the-art greedy algorithms especially when the sparsity level is relatively large.