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Abstract <p>The inverse problem of recovering a multichannel image distorted as a result of defocusing and the associated chromatic aberration is considered. This problem arises in applied problems of ophthalmology related to in vivo diagnostics of living structures of the human eye using optical methods. A mathematical model describing the formation of a multichannel image based on a system of integral equations of convolution type is proposed. To solve the ill-posed inverse problem of multichannel image recovery, an algorithm based on a modified implicit iterative Tikhonov regularization method in combination with a selection rule for a frequency-localized regularization parameter and a stopping criterion has been developed. The results of the software implementation of the proposed method make it possible to evaluate its effectiveness in the inverse problem of multichannel image recovery, including the case of high-resolution images characteristic of medical applications.</p>

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Inverse Problem of Image Recovery in a Multichannel Optical System

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • E. I. Kiselyov,
  • A. V. Razgulin,
  • N. G. Iroshnikov

摘要

Abstract

The inverse problem of recovering a multichannel image distorted as a result of defocusing and the associated chromatic aberration is considered. This problem arises in applied problems of ophthalmology related to in vivo diagnostics of living structures of the human eye using optical methods. A mathematical model describing the formation of a multichannel image based on a system of integral equations of convolution type is proposed. To solve the ill-posed inverse problem of multichannel image recovery, an algorithm based on a modified implicit iterative Tikhonov regularization method in combination with a selection rule for a frequency-localized regularization parameter and a stopping criterion has been developed. The results of the software implementation of the proposed method make it possible to evaluate its effectiveness in the inverse problem of multichannel image recovery, including the case of high-resolution images characteristic of medical applications.