Intelligent greedy pursuit model for sparse reconstruction based on l0 minimization

• We propose a novel optimization function for the sparse reconstruction without knowing the sparsity level as a prior.
• We develop a two-cycle optimization algorithm to solve l0 minimization essentially.
• The proposed IGP model is as simple as greedy algorithm, while it can overcome the common shortcoming that greedy algorithm is easy to obtain a sub-optimal solution.
• The proposed IGP model can reconstruct signal accurately with fewer measurements than the state-of-the-art algorithms.

l0 minimization based sparse reconstruction is an NP-hard problem with very high computational complexity, which is difficult to be achieved by traditional algorithms. Although greedy algorithm aims at solving l0 minimization, it is more likely to obtain a sub-optimal solution. In this paper, we propose an intelligent greedy pursuit (IGP) algorithm to solve the l0 minimization essentially. Firstly, we propose a novel optimization function for the sparse reconstruction problem with the sparsity level unknown as a prior. Then, a two-cycle optimization algorithm is designed, whose object is to estimate the support collection and its corresponding coefficients intelligently and accurately by searching for the global optimal solution. To this end, we take advantage of intelligent optimization algorithm in global searching and solving combinatorial optimization problems to guide the intelligent estimation. Also, the principle of estimation is designed by the matching strategies of greedy algorithm which performs quite well in reconstruction speed. The so-called IGP model is as simple as greedy algorithm, while it has been proved through experiments that the performance of IGP for signal reconstruction and image reconstruction outperforms the state-of-the-art reconstruction algorithms. Moreover, IGP can reconstruct signal accurately with a relatively small measurement rate.