A novel mean curvature-based model for positive image restoration and blur kernel estimation in blind image deblurring

Azhar  Iqbal; Shahid  Saleem; Shahbaz  Ahmad; Adel M.  Al-Mahdi; Faisal  Fairag

doi:10.59400/adecp2805

A novel mean curvature-based model for positive image restoration and blur kernel estimation in blind image deblurring

Azhar Iqbal
Abdus Salam School of Mathematical Sciences (ASSMS), Government College University, Lahore 54000, Pakistan
Shahid Saleem
Department of Mathematics, The University of Chenab, Gujrat 50700, Pakistan
Shahbaz Ahmad
Abdus Salam School of Mathematical Sciences (ASSMS), Government College University, Lahore 54000, Pakistan
Adel M. Al-Mahdi
Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Faisal Fairag
Department of Mathematics, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Article ID: 2805

DOI: https://doi.org/10.59400/adecp2805

Keywords: blind image deblurring; ill-posed problem; mean curvature; constrained problem; augmented Lagrangian method

Abstract

The premise of blind image deblurring revolves around the restoration of a clear image from a blurred one without prior knowledge of the specific blur kernel employed. Within this realm, various image priors have been extensively investigated and applied to address this inherently challenging problem. Throughout the image deblurring process, ensuring the resulting image intensities remain strictly non-negative is often imperative. However, prevalent numerical methodologies utilized to solve this issue have shown instances where the outcomes are not consistently favorable, leading to undesirable negative intensities that contribute to significant areas of darkness in the restored images. This study introduces a novel model designed to tackle the blind image deblurring problem by leveraging mean curvature. The proposed model not only assures positive outcomes but also confines the upper limit of image intensity values, thereby maintaining them within a predefined range. Additionally, new numerical algorithms are introduced, which not only restore the image but also estimate the blur kernel. Comparative analyses between these proposed algorithms and existing numerical techniques have been conducted to showcase the effectiveness and feasibility of our suggested approach.

Published

2026-05-20

How to Cite

Iqbal, A., Saleem, S., Ahmad, S., Al-Mahdi, A. M., & Fairag, F. (2026). A novel mean curvature-based model for positive image restoration and blur kernel estimation in blind image deblurring. Advances in Differential Equations and Control Processes, 33(2). https://doi.org/10.59400/adecp2805

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Vol. 33 No. 2 (2026): In Progress

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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