Open AccessA Reconstruction Method for Compressed Sampling in Shift-Invariant Spaces
Author(s) -
Junyi Luo,
Yuting Yang
Publication year - 2016
Publication title -
journal of engineering and technological sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.202
H-Index - 14
eISSN - 2338-5502
pISSN - 2337-5779
DOI - 10.5614/j.eng.technol.sci.2016.48.2.5
Subject(s) - compressed sensing , mathematics , signal reconstruction , bandwidth (computing) , sampling (signal processing) , invariant (physics) , norm (philosophy) , algorithm , signal processing , computer science , detector , telecommunications , radar , political science , law , mathematical physics
A traditional sampling method is that the signal should be sampled at a rate exceeding twice the highest frequency. This is based on the assumption that the signal occupies the entire bandwidth. In practice, however, many signals are sparse so that only part of the bandwidth is used. Compressed sampling has been developed for low-rate sampling of continuous time sparse signals in shift-invariant spaces generated by m kernels with period T. However, in general the reconstruction of compressed sampling signals is unstable. To reconstruct the signal, continuous reconstruction is replaced by generalized inverse. In this paper, periodic non-uniform sampling and the reconstruction of functions in shift-invariant spaces are discussed, the unique sparse expression is obtained by using the minimal L1 norm. Also, necessary condition and error of reconstruction were analyzed. Finally, the method was validated via simulation and it was shown that the method was effective