Oblique projections and standard-form transformations for discrete inverse problems

Authors

  • Per Christian Hansen

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    • Department of Informatics and Mathematical Modelling, Technical University of Denmark, Kongens Lyngby, Denmark
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Correspondence to: P. C. Hansen, Department of Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, DK-2800 Kongens Lyngby, Denmark.

E-mail:pch@imm.dtu.dk

SUMMARY

This tutorial paper considers a specific computational tool for the numerical solution of discrete inverse problems, known as the standard-form transformation, by which we can treat general Tikhonov regularization problems efficiently. In the tradition of B. N. Datta's expositions of numerical linear algebra, we use the close relationship between oblique projections, pseudoinverses, and matrix computations to derive a simple geometric motivation and algebraic formulation of the standard-form transformation. Copyright © 2011 John Wiley & Sons, Ltd.

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