Effects of basis-mismatch in compressive sampling of continuous sinusoidal signals

The theory of compressive sampling (or compressed sensing) is very attractive in that it is possible to reconstruct some signals with a sub-Nyquist sampling rate provided that they are sparse in some basis domain. But if there exists a mismatch between the signal basis and the pre-defined reconstruction basis, the reconstruction performance is significantly degraded even if the signal is sparse enough. In this paper, the degradation due to this basis mismatch is investigated and a way to minimize the effects of basis mismatch in compressive sampling of continuous sinusoidal signals is discussed.