Adaptive Fractional-Order Total Variation and Minimax-Concave Based Image Denoising Model

Total variation (TV)-based image denoising effectively suppresses noise while preserving edges, but it often introduces staircase artifacts in flat regions. To address this limitation, we propose a novel denoising model that combines adaptive fractional-order total variation with a minimax-concave (MC) penalty in the regularization term. The adaptive fractional-order TV alleviates staircase effects in homogeneous areas while preserving fine details in textured regions. The MC penalty provides a more accurate estimation of image sparsity, improving restoration fidelity compared to traditional L1-based regularization. The resulting model, termed AFTVMC, is efficiently solved using an alternating direction method of multipliers (ADMM). Extensive numerical experiments on synthetic and natural images demonstrate that AFTVMC outperforms classical TV, higher-order LLT, adaptive ATV, and state-of-the-art MCFOTV models in both objective metrics—peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM)—and subjective visual quality, particularly in suppressing staircase artifacts and preserving complex texture details.