Geometric structure based intelligent collaborative compressive sensing for image reconstruction by l0 minimization

Image reconstruction by l0 minimization is an NP-hard problem with high computational complexity and the results are sometimes not accurate enough due to the down-sampled measurements. In this paper, we propose a novel geometric structure based intelligent collaborative compressive sensing (G-ICCS) method for image reconstruction by l0 minimization. Firstly, the local geometric structures of image are exploited to establish the geometric structure based sparsity models based on the geometric over-completed dictionaries, which aims to enhance the reconstruction accuracy of image structures. To reduce the computational complexity and achieve the better reconstruction accuracy, we utilize the nonlocal self-similarity property to obtain the geometric sparsity prior to guide the reconstruction for each geometric structure based sparsity model, respectively. Considering intelligent optimization algorithm has superior performance in solving combinatorial optimization problems and global searching and greedy algorithm performs well in reconstruction speed, we make a hybrid use of them to solve the l0 minimization essentially by designing the intelligent searching strategies. Finally, the image patches are estimated by the designed intelligent searching strategies under the guidance of the geometric sparsity prior to improve the reconstruction accuracy significantly especially when the measurement rate is relatively small. Some experiments test the proposed method G-ICCS on natural images, and the results demonstrate that G-ICCS outperforms its counterparts in both numerical measures and visual quality.