Fast sensing matrix construction method oriented towards frequency‐sparse signal. Issue 22 (1st October 2014)

• Record Type: Journal Article
• Authors: Fu, Ning; Song, Pingfan; Qiao, Liyan
• Is Part Of: Electronics letters. Volume 50:Issue 22(2014)
• Page Start: 1600
• Page End: 1602
• Publication Date: 2014-10-01
• Subjects: compressed sensing -- discrete Fourier transforms -- matrix algebra; FFT -- fast Fourier transform -- matrices transpose rule -- IDFT matrix -- inverse discrete Fourier transform -- measurement matrix -- compressive sensing -- frequency‐sparse signal recovery -- FSMC -- fast sensing matrix construction method; Electronics -- Periodicals; 621.381
• DOI: 10.1049/el.2014.2022
• Languages: English
• ISSNs: 0013-5194

Abstract

Abstract : 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.