Performance Limits of Segmented Compressive Sampling: Correlated Samples versus Bits

Abstract

This paper gives performance limits of the segmented compressive sampling (CS) which collects correlated samples. It is shown that the effect of correlation among samples for the segmented CS can be characterized by a penalty term in the corresponding bounds on the sampling rate. Moreover, this penalty term is vanishing as the signal dimension increases. It means that the performance degradation due to the fixed correlation among samples obtained by the segmented CS (as compared to the standard CS with equivalent size sampling matrix) is negligible for a high-dimensional signal. In combination with the fact that the signal reconstruction quality improves with additional samples obtained by the segmented CS (as compared to the standard CS with sampling matrix of the size given by the number of original uncorrelated samples), the fact that the additional correlated samples also provide new information about a signal is a strong argument for the segmented CS.