A Method of Image Reconstruction Based on Sub-Gaussian Random Projection

In this paper, sub-Gaussian random projection is introduced into compressed sensing （CS） theory and two new kinds of CS measurement matrix: sparse projection matrix and very sparse projection matrix are presented By the tail bounds for sub-Gaussian random projections, the proof of how these new matrices satisfy the necessary condition for CS measurement matrix is provided Then, it is expatiated that owing to their sparseness, new kinds of matrices greatly simplify the projection operation during image reconstruction, which simultaneously greatly improves the speed of reconstruction Further, it can be easily proved that Gaussian matrix and Bernoulli matrix are special matrices obeying sub-Gaussian random distribution, which indicates that new measurement matrices extend the current results on CS measurement matrix Both the results of simulated and real experiments show that with a certain number of measurements, new matrices have good measurement effect and can acquire exact reconstruction Finally, the comparison and analysis of reconstruction results respectively adopting new matrices and Gaussian measurement matrix is conducted Compared with Gaussian measurement matrix, new matrices have lesser average over-sampling factor, which indicates lower complexity of reconstruction.