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Joint sensing matrix and sparsifying dictionary optimization for tensor compressive sensing

Accepted version
Peer-reviewed

Type

Article

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Authors

Ding, X 
Chen, W 
Wassell, IJ 

Abstract

Tensor compressive sensing (TCS) is a multidimensional framework of compressive sensing (CS), and it is advantageous in terms of reducing the amount of storage, easing hardware implementations, and preserving multidimensional structures of signals in comparison to a conventional CS system. In a TCS system, instead of using a random sensing matrix and a predefined dictionary, the average-case performance can be further improved by employing an optimized multidimensional sensing matrix and a learned multilinear sparsifying dictionary. In this paper, we propose an approach that jointly optimizes the sensing matrix and dictionary for a TCS system. For the sensing matrix design in TCS, an extended separable approach with a closed form solution and a novel iterative nonseparable method are proposed when the multilinear dictionary is fixed. In addition, a multidimensional dictionary learning method that takes advantages of the multidimensional structure is derived, and the influence of sensing matrices is taken into account in the learning process. A joint optimization is achieved via alternately iterating the optimization of the sensing matrix and dictionary. Numerical experiments using both synthetic data and real images demonstrate the superiority of the proposed approaches.

Description

Keywords

Multidimensional system, Compressive sensing, Tensor compressive sensing, Dictionary learning, Sensing matrix optimization

Journal Title

IEEE Transactions on Signal Processing

Conference Name

Journal ISSN

1053-587X
1941-0476

Volume Title

65

Publisher

IEEE
Sponsorship
Engineering and Physical Sciences Research Council (EP/K033700/1)
This work was supported in part by the EPSRC Research under Grant EP/K033700/1, in part by the Natural Science Foundation of China (61671046, 61401018), and in part by the State Key Laboratory of Rail Traffic Control and Safety (RCS2016ZT014) of Beijing Jiaotong University.