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Regularization of an ill-posed problem in corneal topography. (English) Zbl 1308.35326
Summary: In this paper, we use Tikhonov regularization and spectrum cutoff methods to regularize a solution of the inverse problem in a partial differential equation describing the corneal geometry. This solution is closely connected with some intrinsic parameters of cornea like elasticity and intra-ocular pressure which are important in applications. We obtain a stable solution which can give some new insight into biomechanical structure of cornea. Also, we provide an order of convergence estimates and a numerical comparison with the real corneal data. This method gives reasonable results with an error of order of a few per cent.

35R30 Inverse problems for PDEs
92C55 Biomedical imaging and signal processing
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
Full Text: DOI
[1] Trattler W, Cornea Handbook (2010)
[2] DOI: 10.1111/j.1475-1313.2006.00430.x · doi:10.1111/j.1475-1313.2006.00430.x
[3] DOI: 10.1364/AO.48.006594 · doi:10.1364/AO.48.006594
[4] DOI: 10.1098/rsif.2004.0002 · doi:10.1098/rsif.2004.0002
[5] DOI: 10.3928/1081597X-20090710-01 · doi:10.3928/1081597X-20090710-01
[6] DOI: 10.1109/10.900255 · doi:10.1109/10.900255
[7] DOI: 10.1109/TBME.2008.2006019 · doi:10.1109/TBME.2008.2006019
[8] Engl HW, Regularization of Inverse Problems (2000)
[9] Groetsch CW, Inverse Problems in the Mathematical Sciences (1993)
[10] Abramowitz M, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (1965) · Zbl 0171.38503
[11] DOI: 10.1007/978-1-4612-5338-9 · doi:10.1007/978-1-4612-5338-9
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