https://doi.org/10.26089/NumMet.v27r334

On the inverse problem of optical sectioning in a confocal system model for ophthalmological applications

Authors

  • Sergey D. Bazhitov
  • Alexander V. Razgulin
  • A. V. Larichev

Keywords:

sectioning
confocal system
convolution
inverse problem
Tikhonov functional
Fourier filtering

Abstract

The problem of reconstructing 3-D translucent objects for a nonlinear confocal optical system model is posed based on minimizing the Tikhonov functional with a Fourier filter in the stabilizer. Fr´echet differentiability of the Tikhonov functional in Sobolev space is established, and estimates for the Lipschitz constant for its gradient are obtained. A method for minimizing the Tikhonov functional is proposed that allows for an efficient implementation. The presented results of numerical experiments on fundus images and simulated images demonstrate the effectiveness of using a variational approach based on the gradient method for minimizing the Tikhonov functional with a Fourier filter in the stabilizer.


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Published

2026-09-16

Issue

Vol. 27 (2026): Issue 3.

Section

Methods and algorithms of computational mathematics and their applications

Authors

Sergey D. Bazhitov

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

• PhD Student

Alexander V. Razgulin

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

• Head of Department

A. V. Larichev

Lomonosov Moscow State University, Faculty of Physics

• Associate Professor

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