A Bayesian Denoising Framework with a Joint Local/Non-Local Prior Distribution

الملخص

This paper introduces a robust Bayesian framework for image denoising, designed to address the limitations of traditional local regularization methods. The approach is centered on a novel Joint Probabilistic Prior that synergistically integrates a local Markov Random Field (MRF) prior, which enforces smoothness, with a non-local prior derived from the Non-Local Means (NLM) principle, which preserves structural integrity. By combining these two complementary forces within a single energy function, the model can effectively suppress White Gaussian Noise while simultaneously preserving sharp edges and fine-grained textures. The optimal denoised image is estimated by minimizing the posterior energy function using a Maximum a Posteriori (MAP) approach, solved efficiently via a gradient descent algorithm. We conduct a comprehensive comparative analysis, evaluating our model against both a conventional MRF-only Bayesian model and the state-of-the-art BM3D algorithm across a wide spectrum of noise levels (σ=10 to 80). The results are conclusive: the proposed Joint Prior Model consistently and overwhelmingly outperforms the MRF-only, achieving, for instance, a remarkable +10.47 dB gain in PSNR at σ=60. Furthermore, the proposed model demonstrates highly competitive performance against BM3D, particularly in high-noise levels, validating the efficacy and robustness of the proposed framework. These findings establish the joint prior approach as a powerful and principled solution for high-fidelity image denoising.