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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.04847 |
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Table of Contents:
- In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a low-rank Hankel tensor completion task, exploiting the spectral sparsity via the low multilinear rankness of the tensor. Furthermore, we design a scaled gradient descent algorithm for Hankel tensor completion (ScalHT), which integrates the low-rank Tucker decomposition with the Hankel structure. Crucially, we derive novel fast computational formulations that leverage the interaction between these two structures, achieving up to an $O(\min\{s,n\})$-fold improvement in storage and computational efficiency compared to the existing algorithms, where $n$ is the length of signal, $s$ is the number of measurement vectors. Beyond its practical efficiency, ScalHT is backed by rigorous theoretical guarantees: we establish both recovery and linear convergence guarantees, which, to the best of our knowledge, are the first of their kind for low-rank Hankel tensor completion. Numerical simulations show that our method exhibits significantly lower computational and storage costs while delivering superior recovery performance compared to prior arts.