Performance Limits of Segmented Compressive Sampling: Correlated Samples versus Bits

TL;DR

This paper analyzes the performance limits of segmented compressive sampling with correlated samples, showing that correlation effects diminish with high-dimensional signals and that segmented CS can improve reconstruction quality by providing additional informative samples.

Contribution

It characterizes the impact of sample correlation in segmented CS and demonstrates that performance degradation is negligible in high dimensions, supporting the use of segmented CS for better signal reconstruction.

Findings

Correlation penalty term vanishes as signal dimension increases

Segmented CS provides additional informative samples

Performance degradation due to correlation is negligible in high dimensions

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.