Statistical signal processing: applications to beamforming, detection, and estimation

Louis L. Scharf

doi:10.1117/12.541397

28 April 2004 Statistical signal processing: applications to beamforming, detection, and estimation

Louis L. Scharf

Author Affiliations +

Proceedings Volume 5373, Medical Imaging 2004: Ultrasonic Imaging and Signal Processing; (2004) https://doi.org/10.1117/12.541397
Event: Medical Imaging 2004, 2004, San Diego, California, United States

Abstract

Behind the algebra of statistical signal processing there lies a fascinating geometry. Our aim in this keynote talk is to develop this geometry, and use it to illuminate a number of problems in beamforming, detection, and estimation. In the realm of beamforming, we revisit the Capon, or MVDL beamformer, and establish its connections to more conventional beamformers like the Bartlett. We then offer several extensions to the Capon beamformer, making it suitable for the imaging of distributed targets from broadband data. For detection, we review the geometry of matched and adaptive subspace detectors. These detectors are matched to multidimensional subspaces, making them suitable for detecting distributed or broadband sources. They generalize much of what is known about matched filters, which are matched only to one-dimensional subspaces. Our review of estimation exploits the geometry of oblique projections. These processors have the virtue that they image sources with perfect nulling of nearby sources. Of course there is a price to pay in noise gain. This price depends on principal angles between subspaces, explaining why super-resolution is a risky enterprise.

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Louis L. Scharf "Statistical signal processing: applications to beamforming, detection, and estimation", Proc. SPIE 5373, Medical Imaging 2004: Ultrasonic Imaging and Signal Processing, (28 April 2004); https://doi.org/10.1117/12.541397

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KEYWORDS

Statistical analysis

Statistical signal processing

Ultrasonography

Phased arrays

Signal processing

Beam analyzers

Sensors

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