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Open Access Research

Target detection performance bounds in compressive imaging

Kalyani Krishnamurthy1*, Rebecca Willett1 and Maxim Raginsky2

Author Affiliations

1 Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA

2 Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

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EURASIP Journal on Advances in Signal Processing 2012, 2012:205  doi:10.1186/1687-6180-2012-205

Published: 25 September 2012

Abstract

This article 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.

Keywords:
Target detection; Anomaly detection; False discovery rate; ip-value; Incoherent projections; Compressive sensing