This paper proposes a new anisotropic diffusion model in image restoration that is understood from a variational optimization of an energy functional. Initially, a family of new diffusion functions based on cubic Hermite spline is provided for optimal image denoising. After that, the existence and uniqueness of weak solutions for the corresponding Euler–Lagrange equation are proven in an appropriate functional space, and a consistent and stable numerical model is also shown. We complement this work by illustrating some experiments on different actual brain Magnetic Resonance Imaging (MRI) scans, showing the proposed model’s impressive results.

中文翻译：

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一类新的与图像分析相关的凸优化问题的弱解的存在性和唯一性

本文提出了一种新的各向异性扩散模型，该模型可以通过能量函数的变分优化来理解。最初，提供了一组基于三次Hermite样条的新扩散函数，以实现最佳图像降噪。此后，在适当的函数空间中证明了相应的Euler-Lagrange方程的弱解的存在性和唯一性，并且还显示了一致且稳定的数值模型。我们通过在不同的实际脑磁共振成像（MRI）扫描上进行一些实验来补充这项工作，从而显示出该模型令人印象深刻的结果。