Tensor Matched Subspace Detection
Cuiping Li, Xiao-Yang Liu, and Yue Sun

TL;DR
This paper introduces a novel tensor matched subspace detection method using transform-based tensor models, estimators, and detectors, applicable to high-dimensional tensor data, with theoretical analysis and simulation validation.
Contribution
It develops tensor matched subspace detection techniques based on tubal-sampling and elementwise-sampling, extending vector methods to tensor data with theoretical guarantees.
Findings
Estimators effectively estimate signal energy outside a subspace with sufficient samples.
Detectors perform well for both noiseless and noisy tensor data.
Simulation results confirm the approach's effectiveness.
Abstract
The problem of testing whether a signal lies within a given subspace, also named matched subspace detection, has been well studied when the signal is represented as a vector. However, the matched subspace detection methods based on vectors can not be applied to the situations that signals are naturally represented as multi-dimensional data arrays or tensors. Considering that tensor subspaces and orthogonal projections onto these subspaces are well defined in the recently proposed transform-based tensor model, which motivates us to investigate the problem of matched subspace detection in high dimensional case. In this paper, we propose an approach for tensor matched subspace detection based on the transform-based tensor model with tubal-sampling and elementwise-sampling, respectively. First, we construct estimators based on tubal-sampling and elementwise-sampling to estimate the energy…
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Taxonomy
TopicsTensor decomposition and applications · Sparse and Compressive Sensing Techniques · Direction-of-Arrival Estimation Techniques
