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Regularization of an ill-posed problem in corneal topography

Author: Płociniczak Ł   Okrasiński W  

Publisher: Taylor & Francis Ltd

ISSN: 1741-5977

Source: Inverse Problems in Science and Engineering, Vol.21, Iss.6, 2013-09, pp. : 1090-1097

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Abstract

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.