Year: 2026
Type: preprint
Abstract: In this work, we consider a structured tensor approximation problem, where only a limited number of lateral slices are observed. The proposed algorithm , called Basis and Manifold prior Tensor Approximation (BMTA), exploits both global and local structures of the evolution of a global tensor. Specifically, BMTA integrates two signal models: (i) a quasi-basis model that captures smooth global variations along a physical trajectory, and (ii) a manifold-guided interpolation model that characterizes local relationships among tensor slices. A low-rank Tucker reconstruction framework is incorporated to efficiently capture the priors, resulting in coefficients for basis function estimation and a tensor optimization. In addition, we provide a theoretical analysis which establishes a non-asymptotic reconstruction error bound that characterizes the effects of sampling complexity, optimization convergence, and model mismatch. Numerical experiments are performed on both synthetic and real-world datasets, including quantum chemistry and spatiotemporal sensing applications.
Source: arXiv (Cornell University)
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7201870695
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