# Hankel Matrix Nuclear Norm Regularized Tensor Completion for N-dimensional Exponential Signals

arXiv: https://arxiv.org/abs/1604.02100 · HTML: https://mlsanity.com/paper/1604.02100/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2016.

## Built on by (most cited first, 5 of 5)

- [Implicit Regularization in Deep Tensor Factorization](https://mlsanity.com/paper/2105.01346/) (2021)
- [Network Topology Inference with Sparsity and Laplacian Constraints](https://mlsanity.com/paper/2309.00960/) (2023)
- [TVCondNet: A Conditional Denoising Neural Network for NMR Spectroscopy](https://mlsanity.com/paper/2405.11064/) (2024)
- [Identifying the fragment structure of the organic compounds by deeply learning the original NMR data](https://mlsanity.com/paper/2107.11740/) (2021)
- [Structured Low-Rank Tensor Learning](https://mlsanity.com/paper/2305.07967/) (2023)

## Abstract (arXiv)

Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic. But existing approaches can not efficiently recover N-dimensional exponential signals with N≥ 3. In this paper, we study the problem of recovering N-dimensional (particularly N≥ 3) exponential signals from partial observations, and formulate this problem as a low-rank tensor completion problem with exponential factor vectors. The full signal is reconstructed by simultaneously exploiting the CANDECOMP/PARAFAC structure and the exponential structure of the associated factor vectors. The latter is promoted by minimizing an objective function involving the nuclear norm of Hankel matrices. Experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank.