Sparse Trinary Circulant Measurement Matrices with Random Spacing in Compressive Imaging

Compressive imaging is a novel imaging method based on compressive sensing theory, the key idea is that it can reconstruct original scene precisely with far fewer measurements than Nyquist samples if the scene is sparse/compressible; Constructing an appropriate measurement matrix easy to realize random linear measurement of an image is one of the key points of practical compressive sensing. In this paper, analyzing the existing Bernoulli and Circulant matrices, a novel sparse trinary circulant measurement matrix with random spacing for phase mask is proposed. Simulation results show that novel phase mask matrices, compared to Bernoulli and Bernoulli-Circulant (BC) phase mask matrices, have the same signal-to-noise ratio; But with the number of independent random variables and the number of non-zeros entries a dramatically reduction, which is more conducive to data transmission and storage; more importantly that is easy to hardware implementation and the reconstructed time is only about 20%~50% of that of original matrices, which has a significance effects on practical compressive sensing.