<p>Removing mixed Poisson–Gaussian noise remains a critical challenge in clinical MRI, where the two noise sources are physically coupled and statistically dependent. Conventional methods assuming independence or requiring large training datasets often fail on real MRI acquisitions with intense, texture-rich noise. We propose a fully unsupervised, training-free two-stage framework that explicitly models this inter-noise dependency via copulas. In the first stage, Gaussian noise is effectively suppressed using Structure-Adaptive Directional Total Variation (SA-DTV), a state-of-the-art anisotropic regularizer that delivers superior preservation of curvilinear structures and fine MRI textures. In the second stage, the residual is separated in a blind-source manner using a semiparametric copula model that captures the true joint statistics of the remaining Poisson-dominated noise without any restrictive assumptions. Extensive experiments on real clinical MRI datasets (brain, chest, abdominal, high-noise post-contrast, and tumor cases) demonstrate that the proposed method consistently outperforms current optimization-based and learning-based approaches in both PSNR/SSIM and visual quality, especially under severe noise conditions, establishing a new standard for dependency-aware mixed-noise removal in practical MRI applications.</p>