关于时变图信号Sobolev范数的极小化：2019年新型冠状病毒病病例的估计
On the Minimization of Sobolev Norms of Time-Varying Graph Signals: Estimation of New Coronavirus Disease 2019 Cases
摘要：
传染病的数学建模是制定控制疫情策略的基础研究领域。与这一研究领域相关的模型通常在新案例数量上具有指数先验假设，而空间数据的探索在这些模型中很少被分析。在本文中，我们将2019年冠状病毒病（COVID-19）的新增病例数建模为时变图形信号的重建问题。为此，我们提出了一种基于图信号处理中Sobolev范数最小化的新方法。我们的方法在约翰霍普金斯大学提供的两个COVID-19数据库中的性能优于最先进的算法。以同样的方式，我们证明了索伯列夫重建方法的收敛速度的好处，依靠与我们的方法的底层优化问题相关联的海森的条件数。
英文摘要：
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.
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