This work introduces an innovative strategy for mitigating shadow effects in images through the utilization of a time-fractionated anisotropic osmosis equation. The method goes beyond conventional approaches by incorporating a newly derived bilateral total variation (BTV) term, coupled with a nonlinear anisotropic transport component. Theoretical insights are rigorously presented, accompanied by a meticulous exposition of the discretization scheme based on finite differences. In addition to the theoretical foundation, the paper conducts comprehensive numerical experiments to validate the proposed model's efficacy. These experiments not only affirm the qualitative advantages of the anisotropic osmosis model but also provide quantitative evidence of its superiority over existing state-of-the-art techniques.

中文翻译：

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具有双侧总变化的时间分向异性渗透，可在图像处理中有效缓解阴影


这项工作介绍了一种创新策略，通过利用时间分度各向异性渗透方程来减轻图像中的阴影效果。该方法通过结合新推导的双边总变分 （BTV） 项和非线性各向异性输运分量，超越了传统方法。严格地提出了理论见解，并对基于有限差分的离散化方案进行了细致的阐述。除了理论基础外，本文还进行了全面的数值实验，以验证所提模型的有效性。这些实验不仅肯定了各向异性渗透模型的定性优势，而且还提供了其优于现有最先进技术的定量证据。