DIP-based anisotropic total variation regularization for image denoising

• Published in: Advances in continuous and discrete models Vol. 2025; no. 1; p. 126
• Main Authors: Pang, Zhi-Feng, ShangGuan, Yi, Jiang, Fuyang, Tai, Xue-Cheng
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2025; Springer Nature B.V
• Subjects: Algorithms; Analysis; Artificial Intelligence and Machine Learning in Imaging Science; Artificial neural networks; Difference and Functional Equations; Experiments; Functional Analysis; Image processing; Machine learning; Mathematics; Mathematics and Statistics; Methods; Noise reduction; Numerical analysis; Ordinary Differential Equations; Partial Differential Equations; Random variables; Regularization; Sparsity; Deep image prior (DIP); Alternating direction multiplier method (ADMM); Learned perceptual image patch similarity (LPIPS); Anisotropic total variation (ATV); Image denoising
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-025-03984-y

Image denoising is a fundamental problem in image processing, with the primary objective of eliminating noise while effectively preserving image details and structural features. Recent advances in convolutional neural networks (CNNs) have led to the widespread adoption of deep learning-based denoising methods. However, the representative deep image prior (DIP) exhibits limitations in capturing structural features, resulting in insufficient detail preservation during denoising. To address this issue, we propose a novel denoising model that integrates DIP with anisotropic total variation (ATV) regularization, termed DIP-ATV. In the ATV term, a weighted matrix is introduced to couple the gradient operator, enhancing the regularization term’s ability to characterize local image structures. To decouple the weighted matrix and gradient operator from the ℓ 1 -norm, we employ the alternating direction method of multipliers (ADMM), decomposing the proposed model into several efficiently solvable subproblems. Experimental results demonstrate that DIP-ATV achieves superior visual quality in qualitative evaluations and outperforms state-of-the-art unsupervised denoising methods in quantitative metrics, including PSNR, SSIM, and LPIPS.