论文标题
关于时变图形信号的Sobolev规范的最小化：2019年新冠状病毒病例的估计
On the Minimization of Sobolev Norms of Time-Varying Graph Signals: Estimation of New Coronavirus Disease 2019 Cases
论文作者
论文摘要
传染病的数学建模是计划遏制暴发策略的基本研究领域。与该研究领域相关的模型通常在新案例的数量中具有指数性的先验假设，而在这些模型中，空间数据的探索很少分析。在本文中，我们对2019年冠状病毒病（COVID-19）的新病例的数量进行了建模，以此作为时间变化图信号的重建问题。为此，我们提出了一种基于图形信号处理中Sobolev Norm的最小化的新方法。我们的方法优于约翰·霍普金斯大学提供的两个COVID-19数据库中最先进的算法。以同样的方式，我们通过依靠与我们方法的基础优化问题相关的黑森的条件数来证明Sobolev重建方法的收敛速率的好处。
The mathematical modeling of infectious diseases is a fundamental research field for the planning of strategies to contain outbreaks. The models associated with this field of study usually have exponential prior assumptions in the number of new cases, while the exploration of spatial data has been little analyzed in these models. In this paper, we model the number of new cases of the Coronavirus Disease 2019 (COVID-19) as a problem of reconstruction of time-varying graph signals. To this end, we proposed a new method based on the minimization of the Sobolev norm in graph signal processing. Our method outperforms state-of-the-art algorithms in two COVID-19 databases provided by Johns Hopkins University. In the same way, we prove the benefits of the convergence rate of the Sobolev reconstruction method by relying on the condition number of the Hessian associated with the underlying optimization problem of our method.
