Total Fractional-Order Variation-Based Constraint Image Deblurring Problem

Shahid Saleem, Shahbaz Ahmad and Junseok Kim ()
Additional contact information
Shahid Saleem: Abdus Salam School of Mathematical Sciences (AS-SMS), Government College University, Lahore 54000, Pakistan
Shahbaz Ahmad: Abdus Salam School of Mathematical Sciences (AS-SMS), Government College University, Lahore 54000, Pakistan
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Republic of Korea

Mathematics, 2023, vol. 11, issue 13, 1-26

Abstract: When deblurring an image, ensuring that the restored intensities are strictly non-negative is crucial. However, current numerical techniques often fail to consistently produce favorable results, leading to negative intensities that contribute to significant dark regions in the restored images. To address this, our study proposes a mathematical model for non-blind image deblurring based on total fractional-order variational principles. Our proposed model not only guarantees strictly positive intensity values but also imposes limits on the intensities within a specified range. By removing negative intensities or constraining them within the prescribed range, we can significantly enhance the quality of deblurred images. The key concept in this paper involves converting the constrained total fractional-order variational-based image deblurring problem into an unconstrained one through the introduction of the augmented Lagrangian method. To facilitate this conversion and improve convergence, we describe new numerical algorithms and introduce a novel circulant preconditioned matrix. This matrix effectively overcomes the slow convergence typically encountered when using the conjugate gradient method within the augmented Lagrangian framework. Our proposed approach is validated through computational tests, demonstrating its effectiveness and viability in practical applications.

Keywords: image deblurring; constrained problem; TFOV; ill-posed problem; augmented Lagrangian method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/13/2869/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/13/2869/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:13:p:2869-:d:1179994

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().