Structured linear algebra problems in adaptive optics imaging
作者： Johnathan M. Bardsley , Sarah Knepper , James Nagy
DOI: 10.1007/S10444-011-9172-9
关键词: Conjugate gradient method 、 Singular value decomposition 、 Iterative method 、 Mathematics 、 Algorithm 、 Regularization (mathematics) 、 Mathematical optimization 、 Kronecker product 、 Generalized singular value decomposition 、 Kronecker delta 、 Tikhonov regularization 、 Applied mathematics 、 Computational mathematics
摘要: A main problem in adaptive optics is to reconstruct the phase spectrum given noisy differences. We present an efficient approach solve least-squares minimization resulting from this reconstruction, using either a truncated singular value decomposition (TSVD)-type or Tikhonov-type regularization. Both of these approaches make use Kronecker products and generalized decomposition. The TSVD-type regularization operates as direct method whereas uses preconditioned conjugate gradient type iterative algorithm achieve fast convergence.
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