A Fractal Deep Image Prior with Reliability-Weighted Charbonnier Fidelity for Salt-and-Pepper Image Denoising

Abstract

Salt-and-pepper noise (SPN) is a challenging impulsive degradation because a small fraction of severely corrupted pixels can dominate quadratic observation models. However, quadratic data-fidelity terms remain common in unsupervised and hybrid approaches used for SPN removal, despite their sensitivity to sparse extreme residuals. In this paper, we propose RWFracDIP, an unsupervised Fractal Deep Image Prior with Reliability-Weighted Charbonnier Fidelity for SPN removal. RW-FracDIP combines Fractal Image Coding (FIC), Total Variation (TV) regularization, and DIP within a unified formulation, in which the quadratic observation term is replaced by a reliability-weighted Charbonnier fidelity and the reliability map is estimated directly from the noisy image to downweight suspected impulse pixels. The resulting formulation is optimized by an ADMM-style alternating scheme that preserves the complementary roles of fractal self-similarity, TV regularization, and the deep prior. Across five standard grayscale images and four SPN levels, RW-FracDIP achieves the best PSNR in all tested settings and the best SSIM in most of them against DnCNN, DIP, L1/TV, and a FIC+DIP+TV baseline, indicating robustness under impulsive corruption.