Structured linear algebra problems in adaptive optics imaging

Advances in Computational Mathematics

Volumn 35, Issue 2, 2011, Pages 103-117

  Bardsley, Johnathan M ^a   Knepper, Sarah ^b   Nagy, James ^b  

^a UNIVERSITY OF MONTANA   (United States)

^b EMORY UNIVERSITY   (United States)

Author keywords

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

Indexed keywords

EID: 80051864161     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-011-9172-9     Document Type: Article

References (18)

1. Barbero, S., Rubinstein, J., Thibos, L. N.: Wavefront sensing and reconstruction from gradient and Laplacian data measured with a Hartmann-Shack sensor. Opt. Lett. 31(12), 1845-1847 (2006).
2. Bardsley, J. M.: Wavefront reconstruction methods for adaptive optics systems on ground-based telescopes. SIAM J. Matrix Anal. Appl. 30(1), 67-83 (2008).
3. Barrett, H. H., Dainty, C., Lara, D.: Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions. J. Opt. Soc. Am. A, Opt. Image Sci. Vis. 24(2), 391-414 (2007).
4. Cannon, R. C.: Global wave-front reconstruction using Shack-Hartmann sensors. J. Opt. Soc. Am. A 12, 2031-2039 (1995).
5. Ellerbroek, B. L.: Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques. J. Opt. Soc. Am. A 19(9), 1803-1816 (2002).
6. Ettl, S., Kaminski, J., Knauer, M. C., Husler, G.: Shape reconstruction from gradient data. Appl. Opt. 47(12), 2091-2097 (2008).
7. Fried, D. L.: Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements. J. Opt. Soc. Am. 67(3), 370-375 (1977).
8. Gilles, L.: Order-n sparse minimum-variance open-loop reconstructor for extreme adaptive optics. Opt. Lett. 28(20), 1927-1929 (2003).
9. Golub, G. H., van Loan, C.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996).
10. Goodman, J. W.: Introduction to Fourier Optics, 2nd edn. McGraw-Hill, New York (1996).
11. Hudgin, R. H.: Wave-front reconstruction for compensated imaging. J. Opt. Soc. Am. 67(3), 375-378 (1977).
12. Hunt, B. R.: Matrix formulation of the reconstruction of phase values from phase differences. J. Opt. Soc. Am. 69(3), 393-399 (1979).
13. van Loan, C.: The ubiquitous Kronecker product. J. Comput. Appl. Math. 123(1), 85-100 (2000).
14. Paige, C. C., Saunders, M. A.: Algorithm 583 LSQR: sparse linear equations and least squares problems. ACM Trans. Math. Softw. 8(2), 195-209 (1982).
15. Paige, C. C., Saunders, M. A.: LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. 8(1), 43-71 (1982).
16. Ren, H., Dekany, R.: Fast wave-front reconstruction by solving the Sylvester equation with the alternating direction implicit method. Opt. Express 12(14), 3279-3296 (2004).
17. Ren, H., Dekany, R., Britton, M.: Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm. Appl. Opt. 44(13), 2626-2637 (2005).
18. Roggemann, M., Welsh, B.: Imaging Through Turbulence. CRC Press, Boca Raton (1996).