Computational ghost imaging with 4-step iterative rank minimization

Highlights: • A rank-minimization-based computational ghost imaging scheme is proposed. • A 4-step iterative method is developed for ghost imaging image reconstruction. • A randomized SVD method is used to solve large matrix decomposition problems. • The proposed scheme can obtain clear images in sub-Nyquist sampling ratio conditions. • The proposed scheme can be deployed to other single-pixel imaging schemes. We propose a rank-minimization-based computational ghost imaging (CGI) scheme to acquire clear ghost images in sub-Nyquist sampling ratio (SR) conditions. The proposed scheme uses a 4-step iterative method that is composed of block matching, weighted nuclear norm minimization, aggregation and projection for the CGI image reconstruction. Both numerical and practical experiments are implemented, and the results are compared with those of four recently published works, "Russian dolls" CGI, 4-connected-region-based CGI, "Cake-Cutting" CGI, and compressive-sensing-based CGI. The comparison results demonstrate that the image quality of the proposed scheme is dramatically enhanced and outperforms the other four methods. The proposed scheme can be used in many practical application areas, such as remote sensing, underwater and X-ray CGI.