Low-Cost HOSVD Reconstructs Urban Flow and Air Quality from Sparse Sensors

Reconstructing complex environmental fields, such as urban flow and air quality, from limited sensor data is a significant challenge in environmental monitoring and digital twin applications. Traditional low-cost reconstruction methods often rely on matrix decompositions, which flatten multi-dimensional datasets and discard crucial structural information. This new research proposes a solution called low-cost High-Order Singular Value Decomposition (lcHOSVD). lcHOSVD is a novel tensor-based framework designed for sparse-sensing reconstruction of high-dimensional environmental fields. A key advantage is its ability to maintain the natural tensor structure of the data, allowing it to exploit correlations across spatial, temporal, and various physical dimensions. This approach significantly reduces the computational demands compared to conventional HOSVD while offering superior data representation. The methodology was applied to urban flow and air-quality datasets, successfully reconstructing three-dimensional velocity and pollutant concentration fields using only 1-4% of available spatial sensor locations. While a simpler lcSVD offered faster computations, lcHOSVD consistently achieved lower reconstruction errors, particularly in scenarios with strong multidimensional coupling and heterogeneous dynamics. Furthermore, the tensor formulation proved more robust to uneven sensor distributions, a common issue in real-world environmental monitoring networks.