A PDE model based on an image specific auto generated multi-well potential function and a 4th order anisotropic diffusion with good performance with respect to loss due to smoothing effects has been proposed for grayscale image inpainting. An unconditionally stable numerical scheme using the notion of convexity splitting in time and Fourier spectral method in space has been derived. The stable scheme is both consistent and convergent. Numerical computations are done for some standard test images and results are compared with the results of other existing models in the literature using image analysis specs such as PSNR, SNR, and SSIM.

中文翻译：

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用于图像修复的各向异性PDE模型

已经提出了基于图像特有的自动产生的多阱势函数和四阶各向异性扩散的PDE模型，该PDE模型对于由于平滑效应引起的损失具有良好的性能，用于灰度图像修补。利用时间上的凸度分裂概念和空间傅立叶谱方法，推导了一种无条件稳定的数值格式。稳定的方案既一致又收敛。对一些标准测试图像进​​行了数值计算，并将结果与​​文献中使用图像分析规范（例如PSNR，SNR和SSIM）的其他现有模型的结果进行比较。