Measurement Bounds for Sparse Signal Ensembles via Graphical Models

TL;DR

This paper introduces a bipartite graph-based framework for modeling dependencies in sparse signal ensembles, establishing fundamental measurement bounds for joint recovery in distributed compressive sensing.

Contribution

It presents a novel graphical model framework that quantifies intra- and inter-signal dependencies, deriving bounds on measurements needed for accurate joint recovery.

Findings

Framework quantifies intra- and inter-signal dependencies.

Provides bounds on the number of measurements for joint recovery.

Uses bipartite graph representation for modeling sparse ensembles.

Abstract

In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra- and inter-signal dependencies within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.