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Linear models, signal detection, and the Grassmann manifold

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dc.contributor.authorSchwickerath, Anthony Norbert, author
dc.contributor.authorKirby, Michael, advisor
dc.contributor.authorPeterson, Chris, advisor
dc.contributor.authorScharf, Louis, committee member
dc.contributor.authorEykholt, Richard, committee member
dc.date.accessioned2007-01-03T05:57:39Z
dc.date.available2016-01-31T06:30:24Z
dc.date.issued2014
dc.description.abstractStandard approaches to linear signal detection, reconstruction, and model identification problems, such as matched subspace detectors (MF, MDD, MSD, and ACE) and anomaly detectors (RX) are derived in the ambient measurement space using statistical methods (GLRT, regression). While the motivating arguments are statistical in nature, geometric interpretations of the test statistics are sometimes developed after the fact. Given a standard linear model, many of these statistics are invariant under orthogonal transformations, have a constant false alarm rate (CFAR), and some are uniformly most powerful invariant (UMPI). These properties combined with the simplicity of the tests have led to their widespread use. In this dissertation, we present a framework for applying real-valued functions on the Grassmann manifold in the context of these same signal processing problems. Specifically, we consider linear subspace models which, given assumptions on the broadband noise, correspond to Schubert varieties on the Grassmann manifold. Beginning with increasing (decreasing) or Schur-convex (-concave) functions of principal angles between pairs of points, of which the geodesic and chordal distances (or probability distribution functions) are examples, we derive the associated point-to-Schubert variety functions and present signal detection and reconstruction algorithms based upon this framework. As a demonstration of the framework in action, we implement an end-to-end system utilizing our framework and algorithms. We present results of this system processing real hyperspectral images.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierSchwickerath_colostate_0053A_12798.pdf
dc.identifier.urihttp://hdl.handle.net/10217/88538
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectGrassmann manifold
dc.subjectSchubert variety
dc.subjectminimum distance
dc.subjectgeometric signal detection
dc.subjectgeometric signal recovery
dc.subjectlinear subspace model
dc.titleLinear models, signal detection, and the Grassmann manifold
dc.typeText
dcterms.embargo.expires2016-01-31
dcterms.embargo.terms2016-01-31
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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