Low-Cost High-Order Singular Value Decomposition for Tensor-Based Reconstruction from Sparse Sensor Measurements: Urban Flow and Air-Quality Applications

• URL: http://arxiv.org/abs/2606.24989v1
• Date: Tue, 23 Jun 2026 14:39:50 GMT
• Title: Low-Cost High-Order Singular Value Decomposition for Tensor-Based Reconstruction from Sparse Sensor Measurements: Urban Flow and Air-Quality Applications
• Abstract summary: This work introduces a novel tensor-based sparse-sensing reconstruction framework for high-dimensional environmental fields.<n>To the authors' knowledge, this is the first methodology that combines sparse sensing and HOSVD for field reconstruction.<n>The methodology is applied to urban flow and air-quality datasets, where three-dimensional velocity and pollutant concentration fields are reconstructed using only 1-4% of the available spatial locations.
• Score: 7.808315103505624
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Urban flow and air-quality simulations generate high-dimensional datasets describing velocity and pollutant transport across multiple spatial, temporal, and physical-variable dimensions. Reconstructing these fields from sparse sensor measurements is a fundamental challenge in environmental monitoring, digital twins, forecasting, and data assimilation. Existing low-cost reconstruction approaches are commonly based on matrix decompositions, which require multidimensional datasets to be flattened into two-dimensional snapshot matrices, thereby discarding important structural information. This work introduces the low-cost High-Order Singular Value Decomposition (lcHOSVD), a novel tensor-based sparse-sensing reconstruction framework for high-dimensional environmental fields. To the authors' knowledge, this is the first methodology that combines sparse sensing and HOSVD for field reconstruction. Unlike matrix-based approaches, lcHOSVD preserves the natural tensor structure of the data, enabling the exploitation of correlations across spatial, temporal, and physical-variable dimensions while substantially reducing the computational requirements of conventional HOSVD. The methodology is applied to urban flow and air-quality datasets, where three-dimensional velocity and pollutant concentration fields are reconstructed using only 1-4% of the available spatial locations. While lcSVD provides larger computational speed-ups, lcHOSVD consistently achieves lower reconstruction errors in configurations characterized by strong multidimensional coupling and heterogeneous dynamics across dimensions. Additional sensor-anisotropy analyses demonstrate that the tensor formulation is significantly more robust to uneven sensor distributions, a common situation in practical environmental monitoring networks.

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