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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.

MSC:
35R30 Inverse problems for PDEs
92C55 Biomedical imaging and signal processing
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
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References:
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