MIXED-NOISE REMOVAL WITH COUPLED NONLOCAL FRACTAL PRIOR AND DEEP IMAGE PRIOR FOR HIGH-DIMENSIONAL IMAGES

Images acquired in real-world applications such as medical imaging, remote sensing and hyperspectral imaging are frequently degraded by mixed noise, where Gaussian perturbations, impulsive outliers, and structured artifacts coexist. Conventional restoration methods, typically developed and evaluated on grayscale or RGB images with only one or three channels, often struggle to handle such heterogeneous degradations. In this work, we propose a denoising framework that integrates fractal priors and Deep Image Prior (DIP) for mixed-noise image restoration, which can be naturally applied to multi-channel data such as Hyper Spectral Images (HSI). Specifically, the noisy observation is decomposed into four components: the clean image, Gaussian noise, sparse impulsive noise, and structured stripe noise. Each component is penalized with tailored regularizations, including a Frobenius norm for Gaussian noise, an [Formula: see text] norm for impulsive noise, and a mixed [Formula: see text] norm for structured noise. By combining the complementary capabilities of DIP and fractal modeling, a fractal regularization term enforces nonlocal self-similarity, whereas DIP provides a strong implicit prior that captures global image structure for faithful reconstruction. The overall problem is formulated as a constrained variational optimization and efficiently solved using the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on grayscale, RGB and hyperspectral datasets demonstrate that the proposed framework effectively suppresses diverse noise types while preserving fine structural details, achieving superior robustness compared with existing approaches.