Nonlinear parameter identification in a corneal geometry model

In this paper, we apply an iterative regularization technique based on Newton’s method to the ill-posed problem of parameter identification in a differential equation describing corneal surface. This equation is based on our previously derived model of corneal topography. We prove the convergence of the proposed method along with some stability estimates. When compared with real corneal data, this method gives reasonable results with error of the same order of magnitude as is introduced by measuring equipment in data acquisition. Moreover, the iteration converges very quickly to the parameters associated with the intra-ocular pressure and the elasticity of the cornea.

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