A modified bispectral method is proposed for solving the inverse problem of image reconstruction in ophthalmology. Modeling shows that the method produces stable results for typical symmetric aberrations of the human eye’s imaging system in the presence of turbulent distortions leading to a signalternating optical transfer function.
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References
A. Bol’shunov, N. Iroshnikov, E. Katalevskaya, and A. Larichev, “Adaptive optics and its application in diagnosis of diseases of the fundus of the eye,” in A. F. Bol’shunov, ed., Topics in Laser Ophthalmology [in Russian], Moscow (2013), pp. 66–82.
A. Goncharov, N. Iroshnikov, and A. Larichev, “Retinal imaging: adaptive optics,” in V. V. Tuchin, ed., Handbook of Coherent-Domain Optical Methods in Biomedical Diagnostics, New York, NY (2013), p. 1332.
H. Bartelt, A. W. Lohmann, and B. Wirnitzer, “Phase and amplitude recovery from bispectra,” Applied Optics, 23, 3121–3129 (1984).
P. Negrete-Regagnon, “Practical aspects of image recovery by means of the bispectrum,” J. Opt. Soc. Am. A, 13, No. 7, 1557–1577 (1996).
A. W. Lohmann, G. Weigelt, and B. Wirnitzer, “Speckle masking in astronomy: triple correlation theory and applications,” Applied Optics, 22, 869–891 (1983).
A. V. Koryabin and V. I. Shmal’gauzen, “Moving spatial filtering method for modeling turbulent atmosphere,” Optika Atmosfery i Okeana, 19, No. 10, 909–914 (2006).
A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys, 6, 85–87 (1970).
A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, Wiley (1977).
V. A. Morozov, Regularization Methods for Ill-Posed Problems, CRC Press, New York (1993).
N. Iroshnikov, A. Larichev, A. Potyagalova, and A. Razgulin, “Tikhonov-regularized bispectral variational method for optical signal reconstruction,” Computational Mathematics and Modeling, 24, No. 4, 505–516 (2013).
A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems, Kluwer (1995).
A. Bakushinsky and A. Goncharsky, Ill-Posed Problems: Theory and Applications, Kluwer (1994).
A. M. Denisov, Elements of the Theory of Inverse Problems, VSP, Utrecht (1999).
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Translated from Prikladnaya Matematika i Informatika, No. 47, 2014, pp. 82–98.
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Iroshnikov, N.G., Larichev, A.V., Razgulin, A.V. et al. A Modified Bispectral Image Reconstruction Method in Ophthalmology. Comput Math Model 26, 534–545 (2015). https://doi.org/10.1007/s10598-015-9290-1
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DOI: https://doi.org/10.1007/s10598-015-9290-1