Fast sensing matrix construction method oriented towards frequency-sparse signal

The sensing matrix is a crucial parameter in the recovery of frequency-sparse signals according to compressive sensing theory. Generally, it is calculated via multiplication of the measurement matrix and the inverse discrete Fourier transform (IDFT) matrix, which involves a large amount of computational work. To reduce the computational load, a fast sensing matrix construction (FSMC) method is developed. The matrices transpose rule, the symmetry property of the discrete Fourier transform (DFT) matrix, the conjugation relation between the DFT matrix and the IDFT matrix are exploited for the first time to develop this FSMC method in which the fast Fourier transform algorithm can be applied. Experiments demonstrate that the FSMC method can boost computational efficiency and contribute to a reduction in computational load without any loss of accuracy.