Complexity reduction in compressive sensing using Hirschman uncertainty structured random matrices

Compressive Sensing (CS) increases the computational complexity of decoding while simplifying the sampling process. In this paper, we apply our previously discussed Hirschman Optimal Transform to develop a series of measurement matrices that reduce the computational complexity of decoding while preserving the recovery performance. In addition, this application provides us alternative choices when we need different accuracy levels for the recovered image. Our simulation results show that with only 1/4 the computational resources of the partial DFT sensing basis, our proposed new sensing matrices achieve the best PSNR performance, which is fully 5dB superior to other commonly used sensing bases.