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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 5 — May. 1, 1988
  • pp: 660–665

Bidiagonalization for linear inverse problems

M. C. Jones and C. H. Travis  »View Author Affiliations


JOSA A, Vol. 5, Issue 5, pp. 660-665 (1988)
http://dx.doi.org/10.1364/JOSAA.5.000660


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Abstract

The inversion of a linear transformation requires a stable algorithm. The algorithm should also permit regularization for noisy measurement data. The singular-value decomposition satisfies these requirements at a significant computational cost. We propose that bidiagonalization of the transformation also achieves the desired characteristics but at a much lower cost. We employ a modified Lanczos method rather than Householder transformations, as this method produces the basis vectors more directly and is more suitable for our exposition. We demonstrate the method with data previously used in the literature.

© 1988 Optical Society of America

History
Original Manuscript: October 2, 1986
Manuscript Accepted: December 1, 1987
Published: May 1, 1988

Citation
M. C. Jones and C. H. Travis, "Bidiagonalization for linear inverse problems," J. Opt. Soc. Am. A 5, 660-665 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-5-660

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