Structured linear algebra problems in adaptive optics imaging

Authors:
Johnathan M. Bardsley;Sarah Knepper;James Nagy
Affiliations:
Department of Mathematical Sciences, University of Montana, Missoula, USA 59812;Department of Mathematics and Computer Science, Emory University, Atlanta, USA 30322;Department of Mathematics and Computer Science, Emory University, Atlanta, USA 30322
Venue:
Advances in Computational Mathematics
Year:
2011

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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.