Distributed Compressed Sensing For Static and Time-Varying Networks

Abstract

We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal $x$, and the objective is for the agents to recover $x$ from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute in-network computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with time-varying topologies. The network dynamics necessarily introduce inaccuracies to our in-network computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for time-varying networks. Evaluations show that our distributed algorithms for both static and time-varying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude.

References in corpus (1)

• Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems

Cited by in corpus (16)

• Decentralized Frank-Wolfe Algorithm for Convex and Non-convex Problems
• Decentralized and Collaborative Subspace Pursuit: A Communication-Efficient Algorithm for Joint Sparsity Pattern Recovery with Sensor Networks
• Application of Compressive Sensing Techniques in Distributed Sensor Networks: A Survey
• Distributed Adaptive Gradient Algorithm with Gradient Tracking for Stochastic Non-Convex Optimization
• On Nonconvex Decentralized Gradient Descent
• Multi-Processor Approximate Message Passing Using Lossy Compression
• Federated Nonconvex Sparse Learning
• Performance Trade-Offs in Multi-Processor Approximate Message Passing
• Statistical Physics and Information Theory Perspectives on Linear Inverse Problems
• NEXT: In-Network Nonconvex Optimization
• Optimal Trade-offs in Multi-Processor Approximate Message Passing
• An Overview of Multi-Processor Approximate Message Passing
• Multi-frequency calibration for DOA estimation with distributed sensors
• Asynchronous Decentralized 20 Questions for Adaptive Search
• Locally Convex Sparse Learning over Networks
• Deterministic and Randomized Diffusion based Iterative Generalized Hard Thresholding (DiFIGHT) for Distributed Sparse Signal Recovery