Nonconvex compressive sensing reconstruction for tensor using structures in modes

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Ding, X 
Chen, W 

This paper focuses on the reconstruction of a tensor captured using Compressive Sensing (CS). Instead of processing the signals via vectorization as is done in conventional CS, in tensor CS high dimensional signals are kept in their original formats, which benefits hardware implementation and eases memory requirements. In addition, more structures exist in a tensor along its various dimensions than in its vectorized format. Utilizing these various structures, this paper proposes a general reconstruction approach for tensor CS. Employing the proximity operator of a nonconvex norm function, a special case for a tensor with low rank and sparse structures is elaborated, which is shown to outperform the state-of-art tensor CS reconstruction methods when applied to magnetic resonance imaging and hyper-spectral imaging.

Compressive sensing, tensor reconstruction, sparse and low rank reconstruction
Journal Title
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Conference Name
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Journal ISSN
Volume Title
Engineering and Physical Sciences Research Council (EP/K033700/1)
This work is supported by EPSRC Research Grant EP/K033700/1; the Natural Science Foundation of China (61401018, U1334202); the Fundamental Research Funds for the Central Universities (No. 2014JBM149); the State Key Laboratory of Rail Traffic Control and Safety (RCS2016ZT014) of Beijing Jiaotong University; the Key Grant Project of Chinese Ministry of Education (313006).