Performance Limits of Segmented Compressive Sampling: Correlated Measurements Versus Bits

This paper discusses performance limits of the segmented compressive sampling (CS) system that collects correlated measurements. It is shown that the effect of correlation among measurements for the segmented CS can be characterized by a penalty term in the corresponding bounds on the measurement rate. Moreover, this penalty term is vanishing as the signal dimension increases. It means that the performance degradation due to the fixed correlation among measurements obtained by the segmented CS (as compared to the standard CS with equivalent size measurement matrix) is negligible for a high-dimensional signal. In combination with the fact that the signal reconstruction quality improves with additional measurements obtained by the segmented CS (as compared to the standard CS without additional measurements), the fact that the additional correlated measurements also provide new information about a signal is a strong argument for the segmented CS.