Performance Bounds for Grouped Incoherent Measurements in Compressive Sensing

TL;DR

This paper analyzes the impact of grouped, dependent measurement projections on compressive sensing performance, deriving measurement requirements and penalties compared to standard independent measurement schemes, with validation through simulations.

Contribution

It introduces theoretical bounds for measurement requirements in grouped incoherent measurements, extending compressive sensing guarantees to practical scenarios with dependent measurements.

Findings

Derived measurement bounds for grouped measurements

Identified penalty factor compared to independent schemes

Validated bounds through simulation results

Abstract

Compressive sensing (CS) allows for acquisition of sparse signals at sampling rates significantly lower than the Nyquist rate required for bandlimited signals. Recovery guarantees for CS are generally derived based on the assumption that measurement projections are selected independently at random. However, for many practical signal acquisition applications, including medical imaging and remote sensing, this assumption is violated as the projections must be taken in groups. In this paper, we consider such applications and derive requirements on the number of measurements needed for successful recovery of signals when groups of dependent projections are taken at random. We find a penalty factor on the number of required measurements with respect to the standard CS scheme that employs conventional independent measurement selection and evaluate the accuracy of the predicted penalty through simulations.