Regularization of an ill-posed problem in corneal topography. (English) Zbl 1308.35326

Płociniczak, Ł.; Okrasiński, W.

Inverse Probl. Sci. Eng. 21, No. 6, 1090-1097 (2013).

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

Keywords:

corneal topography; mathematical model; partial differential equation; Tikhonov regularization; ill-posed problem

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