Fast and Efficient Compressive Sensing Using Structurally Random Matrices

This paper introduces a new framework to construct fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we prerandomize the sensing signal by scrambling its sample locations or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the resulting transform coefficients to obtain the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable to that of completely random sensing matrices. Numerical simulation results verify the validity of the theory and illustrate the promising potentials of the proposed sensing framework.