Medical Image Denoising Using Non-Convex TV Regularization with Chebyshev-Optimized ADMM

High-quality medical imaging is fundamental to accurate diagnosis and effective clinical decision-making, yet real-world acquisitions are frequently degraded by noise, artifacts, and loss of detail. To address these challenges, we propose a novel non-convex total variation (TV) regularization model that leverages a hyper-Laplacian prior to enhance sparsity and preserve structural edges. The model is formulated using an ℓp-quasi norm (0<p<1) and is efficiently solved via the Alternating direction method of multipliers framework integrated with the Chebyshev iterative method. This hybrid optimization strategy decomposes the complex problem into tractable subproblems, significantly improving convergence speed and computational efficiency. Extensive experiments on real medical images with varying noise levels demonstrate that the proposed method consistently outperforms state-of-the-art techniques in PSNR, SSIM, edge preservation, and spectral fidelity. The results highlight the method’s robustness, precision, and practical value for clinical image enhancement. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.