Structured linear algebra problems in adaptive optics imaging

Johnathan M. Bardsley, Sarah Knepper, James Nagy

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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.

Original languageEnglish
Pages (from-to)103-117
Number of pages15
JournalAdvances in Computational Mathematics
Volume35
Issue number2
DOIs
StatePublished - Nov 2011

Keywords

  • Adaptive optics
  • Generalized singular value decomposition
  • Image deblurring
  • Kronecker product
  • LSQR
  • Preconditioning
  • Tikhonov regularization
  • Truncated singular value decomposition
  • Wavefront reconstruction

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