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Efficient image restoration using generalized non-convex total variation regularization and Chebyshev-accelerated ADMM.

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Title: Efficient image restoration using generalized non-convex total variation regularization and Chebyshev-accelerated ADMM.
Authors: Kumar, Narendra1 (AUTHOR), Sonkar, Munnu2 (AUTHOR), Bhatnagar, Gaurav1 (AUTHOR) goravb@iitj.ac.in
Source: Computers & Mathematics with Applications. Aug2026, Vol. 216, p18-51. 34p.
Subjects: Optimization algorithms, Algorithms, Image reconstruction, Constrained optimization
Abstract: This paper introduces an efficient image deblurring model that integrates a generalized non-convex total variation (TV) regularization with a hyper-Laplacian gradient prior. The proposed method aims to enhance edge retention and sparsity while preserving natural image statistics. An efficient Alternating Direction Method of Multipliers (ADMM) algorithm is developed, leveraging the Chebyshev method to solve the l p minimization problem with rapid convergence. A theoretical convergence analysis of the proposed algorithm is also provided. Extensive experiments on various real test images demonstrate that the proposed method outperforms existing techniques in both qualitative and quantitative measures. It achieves Peak Signal-to-Noise Ratio (PSNR) values between 37 dB and 42.1 dB, Structural Similarity Index (SSIM) values from 0.95 to 1, and near-perfect Feature Similarity Index (FSIM) values, with notable performance improvements observed for p in the range of 0.45 to 0.7. The proposed approach excels in preserving edge details, converges in at most 30 iterations, and proves superior to the state-of-the-art methods. The implementation of the proposed algorithm can be accessed via https://github.com/nadr123/Image_Restoration. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:This paper introduces an efficient image deblurring model that integrates a generalized non-convex total variation (TV) regularization with a hyper-Laplacian gradient prior. The proposed method aims to enhance edge retention and sparsity while preserving natural image statistics. An efficient Alternating Direction Method of Multipliers (ADMM) algorithm is developed, leveraging the Chebyshev method to solve the l p minimization problem with rapid convergence. A theoretical convergence analysis of the proposed algorithm is also provided. Extensive experiments on various real test images demonstrate that the proposed method outperforms existing techniques in both qualitative and quantitative measures. It achieves Peak Signal-to-Noise Ratio (PSNR) values between 37 dB and 42.1 dB, Structural Similarity Index (SSIM) values from 0.95 to 1, and near-perfect Feature Similarity Index (FSIM) values, with notable performance improvements observed for p in the range of 0.45 to 0.7. The proposed approach excels in preserving edge details, converges in at most 30 iterations, and proves superior to the state-of-the-art methods. The implementation of the proposed algorithm can be accessed via https://github.com/nadr123/Image_Restoration. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2026.04.034