论文标题
通过插值辅助矩阵完成的繁殖图重建
Propagation Map Reconstruction via Interpolation Assisted Matrix Completion
论文作者
论文摘要
从一组分散的测量值中构建传播图在许多领域（例如本地化，频谱监视和管理）中找到了重要的应用。经典的插值方法在测量非常稀疏的地区的性能较差。矩阵完成的最新进展有可能从稀疏测量值重建传播图，但是空间分辨率有限。本文提议将插值与矩阵的完成整合，以利用空间相关性和传播图的潜在低等级结构。提出的方法首先使用插值富集矩阵观测，并基于局部多项式回归模型开发插值误差的统计数据。然后，开发了两种不确定性矩阵完成算法来利用插值误差统计信息。从数值上证明，所提出的方法的表现优于Kriging和其他最先进的方案，并将中等至大量测量值的繁殖地图重建的平均平方误差（MSE）减少了10％-50％。
Constructing a propagation map from a set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance in regions with very sparse measurements. Recent advance in matrix completion has the potential to reconstruct a propagation map from sparse measurements, but the spatial resolution is limited. This paper proposes to integrate interpolation with matrix completion to exploit both the spatial correlation and the potential low rank structure of the propagation map. The proposed method first enriches matrix observations using interpolation, and develops the statistics of the interpolation error based on a local polynomial regression model. Then, two uncertainty-aware matrix completion algorithms are developed to exploit the interpolation error statistics. It is numerically demonstrated that the proposed method outperforms Kriging and other state-of-the-art schemes, and reduces the mean squared error (MSE) of propagation map reconstruction by 10%-50% for a medium to large number of measurements.
