图上的初始状态重构
Initial state reconstruction on graphs
AI总结：
针对数字图像采集中的噪声问题及反向扩散方程的指数不稳定性，本研究提出图上反向扩散方程的正则化框架，基于截断投影构建图谱求解方法，给出稳定性与收敛性结果并辅以数值实验。
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结合正向和反向扩散方程。但众所周知，后者问题对于最终数据上的任何微小扰动都具有指数不稳定性。在这种场景下，最终数据可被视为由正向过程得到的模糊图像，且该图像可被像素化为一个网络。因此，我们在本研究中提出了一种用于图上反向扩散方程的正则化框架。我们的目标是基于截断投影构建一种基于图谱的求解方法。本文给出了稳定性和收敛性结果，并附上了若干数值实验。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
