On Collaborative Compressive Sensing Systems: The Framework, Design and Algorithm

TL;DR

This paper introduces a collaborative compressive sensing framework that combines multiple estimators sharing the same sensing matrix but different dictionaries, leading to improved signal recovery accuracy with efficient parallel computation.

Contribution

It proposes a novel collaborative CS scheme with an optimal design method for sensing matrices and dictionaries, supported by an convergent alternating minimization algorithm.

Findings

Significant improvement in signal recovery accuracy over existing CS systems.

Efficient parallel implementation with the same computational time as individual CS systems.

Theoretical convergence of the proposed optimization algorithm.

Abstract

Based on the maximum likelihood estimation principle, we derive a collaborative estimation framework that fuses several different estimators and yields a better estimate. Applying it to compressive sensing (CS), we propose a collaborative CS (CCS) scheme consisting of a bank of $K$ CS systems that share the same sensing matrix but have different sparsifying dictionaries. This CCS system is expected to yield better performance than each individual CS system, while requiring the same time as that needed for each individual CS system when a parallel computing strategy is used. We then provide an approach to designing optimal CCS systems by utilizing a measure that involves both the sensing matrix and dictionaries and hence allows us to simultaneously optimize the sensing matrix and all the $K$ dictionaries. An alternating minimization-based algorithm is derived for solving the corresponding optimal design problem. With a rigorous convergence analysis, we show that the proposed algorithm is convergent. Experiments are carried out to confirm the theoretical results and show that the proposed CCS system yields significant improvements over the existing CS systems in terms of the signal recovery accuracy.