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