Hankel Matrix Nuclear Norm Regularized Tensor Completion for Ndimensional Exponential Signals
Abstract
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 $N\geq 3$. In this paper, we study the problem of recovering Ndimensional (particularly $N\geq 3$) exponential signals from partial observations, and formulate this problem as a lowrank 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.
 Publication:

IEEE Transactions on Signal Processing
 Pub Date:
 July 2017
 DOI:
 10.1109/TSP.2017.2695566
 arXiv:
 arXiv:1604.02100
 Bibcode:
 2017ITSP...65.3702Y
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Information Theory;
 Mathematics  Numerical Analysis;
 Mathematics  Spectral Theory;
 Physics  Medical Physics
 EPrint:
 15 pages, 12 figures