The presence of noise is an intrinsic problem in acquisition processes for digital images. One way to enhance images is to combine the forward and backward diffusion equations. However, the latter problem is well known to be exponentially unstable with respect to any small perturbations on the final data. In this scenario, the final data can be regarded as a blurred image obtained from the forward process, and that image can be pixelated as a network. Therefore, we study in this work a regularization framework for the backward diffusion equation on graphs. Our aim is to construct a spectral graph-based solution based upon a cut-off projection. Stability and convergence results are provided together with some numerical experiments.
翻译：噪音的存在是数码图像获取过程中的一个内在问题。加强图像的一种方法是将前向和后向扩散方程式结合起来。然而,后一问题众所周知,在最终数据的任何小扰动方面,最后数据极不稳定。在这种情况下,最后数据可被视为从前向进程中取得的模糊图像,图像可作为一个网络混凝土。因此,我们在此研究一个在图形上进行后向扩散方程式的正规化框架。我们的目标是在截断预测的基础上构建一个光谱图解解决方案。稳定与趋同的结果与一些数字实验一起提供。
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