Multi-variable intelligent matching pursuit algorithm using prior knowledge for image reconstruction by l0 minimization

• We propose an MIMP method by taking advantage of intelligent optimization algorithm in combinatorial optimization problems to solve l0 minimization essentially and improve the reconstruction accuracy significantly.
• A novel optimization function is proposed with the sparsity level unknown as a prior.
• Multi-variable scheme is introduced to improve the reconstruction performance significantly with a relatively small measurement number.
• Edge information is applied as the prior knowledge to reduce the computation complexity and improve the reconstruction performance.

Image reconstruction by l0 minimization is an NP-hard problem that requires exhaustively listing all possibilities of the original signal with a 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 fall into a suboptimal solution. In this paper, we propose a multi-variable intelligent matching pursuit algorithm (MIMP), which can solve l0 minimization problem essentially by taking the advantage of the intelligent optimization algorithm in solving combinatorial optimization problems and searching for the global optimal solution to improve the performance of image reconstruction. The updating mechanism of MIMP is designed by introducing the matching strategies of greedy algorithm to accelerate the reconstruction speed. Also, the multi-variable scheme is utilized to sample images and then the joint reconstruction is implemented to the measurements, which can not only improve the reconstruction accuracy but also reduce the computational complexity. Moreover, the edge saliency can be obtained as the prior knowledge to guide the compressive sensing reconstruction, which contributes a lot to reduce the computational complexity and accelerate the reconstruction speed. As the sparsity level of image is hard to be estimated, a new optimization function is proposed to solve this problem without knowing the sparsity level as a prior. Compared with other state-of-the-art algorithms, the proposed method MIMP can achieve a better reconstruction accuracy by solving l0 minimization essentially with intelligent optimization algorithms. Also, MIMP has a reasonable relatively faster reconstruction speed by introducing the matching strategies of greedy algorithm and using the edge saliency as a prior knowledge. Numerical experiments on several images demonstrate that the proposed method MIMP significantly outperforms the state-of-the-art algorithms and the structure based reconstruction algorithms in PSNR, SSIM and visual quality.