Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing

TL;DR

This paper introduces DCS-AMP, an efficient Bayesian algorithm for dynamic compressive sensing that accurately recovers time-varying sparse signals from limited measurements, with adaptive learning and near-oracle performance.

Contribution

It proposes a novel probabilistic model and an approximate message passing algorithm capable of high-dimensional, real-time dynamic signal recovery with adaptive parameter learning.

Findings

DCS-AMP achieves within 3 dB of oracle bounds on synthetic data.

The algorithm performs well on real datasets and frequency estimation tasks.

DCS-AMP offers state-of-the-art accuracy and computational efficiency.

Abstract

In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.