Image Reconstruction Based on Sub-Gaussian Random Projection

In this paper, we introduce the sub-Gaussian random projection into compressed sensing (CS) theory and present two new kinds of CS measurement matrices: sparse projection matrix and very sparse projection matrix. By the tail bounds for sub-Gaussian random projection, we present the proof of how these new matrices satisfying the necessary condition for CS measurement matrix. Further, we expatiate that owe to their sparsity, new matrices greatly simplify the projection operation during images reconstruction, which greatly improves the speed of reconstruction. The results of simulated and real experiments show that with a certain number of measurements, new matrices both achieve good measurement effect and can acquire exact reconstruction by them. Last, the comparison of reconstruction results respectively adopting new matrices and Gaussian measurement matrix is conducted.