Loss-Level Stabilization in Deep Image Denoising via Fractional-Inspired Memory-Weighted Regularization

Abstract

This study investigates the role of memory-weighted (fractional-inspired) regularization in stabilizing training dynamics for deep image denoising. Unlike conventional loss functions that rely solely on instantaneous residuals, the proposed approach introduces a loss-level aggregation mechanism in which past residuals are incorporated through a weighted memory structure. Specifically, a memory-weighted regularization term is combined with a base loss function, where historical residuals are aggregated using a power-law decay weighting scheme. This formulation does not correspond to a strict fractional derivative operator, but is inspired by the long-memory characteristics of fractional calculus. The method is evaluated under controlled experimental settings across multiple noise intensities and noise types, including Gaussian and impulsive noise. All experiments are conducted using identical network architectures and training configurations to ensure fair comparison. The results show that, while improvements in reconstruction metrics such as PSNR and SSIM are modest, the proposed formulation consistently reduces late-stage fluctuation and yields smoother convergence behaviour. In particular, the reduction in PSNR standard deviation indicates improved optimization stability under high-noise conditions. These findings suggest that memory-aware loss design provides a complementary perspective for improving convergence stability in deep learning-based image denoising.