论文标题
图表上的初始状态重建
Initial state reconstruction on graphs
论文作者
论文摘要
噪声的存在是数字图像采集过程中的固有问题。增强图像的一种方法是将前向和向后扩散方程组合。但是，众所周知，对于最终数据上的任何小扰动，众所周知，这是指数不稳定的。在这种情况下，最终数据可以被视为从正向过程获得的模糊图像，并且可以将图像像素化为网络。因此，我们在这项工作中研究了图形上向后扩散方程的正则化框架。我们的目的是基于截止投影构建基于光谱图的解决方案。稳定性和收敛结果与一些数值实验一起提供。
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.
