Target Detection Performance Bounds in Compressive Imaging

TL;DR

This paper introduces computationally efficient detection methods for known targets and anomalies in compressive imaging, providing theoretical bounds and practical validation without requiring signal reconstruction.

Contribution

It presents novel detection algorithms with performance guarantees that do not rely on sparse signal representations, leveraging dictionary structure and measurement properties.

Findings

Performance bounds reveal tradeoffs among measurements, background noise, and target similarity.

Detection methods effectively control false discoveries in anomaly detection.

Simulation results demonstrate practical effectiveness of the proposed approaches.

Abstract

This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches accommodate signals of different strengths contaminated by a colored Gaussian background, and perform detection without reconstructing the underlying signals from the observations. The theoretical performance bounds of the target detector highlight fundamental tradeoffs among the number of measurements collected, amount of background signal present, signal-to-noise ratio, and similarity among potential targets coming from a known dictionary. The anomaly detector is designed to control the number of false discoveries. The proposed approach does not depend on a known sparse representation of targets; rather, the theoretical performance bounds exploit the structure of a known dictionary of targets and the distance preservation property of the measurement matrix. Simulation experiments illustrate the practicality and effectiveness of the proposed approaches.