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Structured linear algebra problems in adaptive optics imaging

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Abstract

A main problem in adaptive optics is to reconstruct the phase spectrum given noisy phase differences. We present an efficient approach to solve the least-squares minimization problem resulting from this reconstruction, using either a truncated singular value decomposition (TSVD)-type or a Tikhonov-type regularization. Both of these approaches make use of Kronecker products and the generalized singular value decomposition. The TSVD-type regularization operates as a direct method whereas the Tikhonov-type regularization uses a preconditioned conjugate gradient type iterative algorithm to achieve fast convergence.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Montana, Missoula, MT, 59812, USA

    Johnathan M. Bardsley

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    Sarah Knepper & James Nagy

Authors
  1. Johnathan M. Bardsley
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  2. Sarah Knepper
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  3. James Nagy
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Corresponding author

Correspondence to James Nagy.

Additional information

Communicated by Rafael Bru.

Research of first author was supported by the National Science Foundation under grant DMS-0915107. Research of third author was supported by the National Science Foundation under grant DMS-0811031, and the Air Force Office of Scientific Research under grant FA9550-09-1-0487.

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Bardsley, J.M., Knepper, S. & Nagy, J. Structured linear algebra problems in adaptive optics imaging. Adv Comput Math 35, 103–117 (2011). https://doi.org/10.1007/s10444-011-9172-9

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  • DOI: https://doi.org/10.1007/s10444-011-9172-9

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