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A Deterministic Structure of 2D-Imagery Compressed Sensing Measurement Matrix

Zhen Li, Hong Zheng, Shiting Wang, Wenda Zeng

Abstract



In Compressed Sensing (CS) of two-dimensional imagery, a random measurement matrix has engineering applicability difficulty and performance instability, whereas deterministic measurement matrices have poor performance in reconstructing high-quality images. To solve those problems, this paper proposes a deterministic structure of measurement matrix based on polynomial matrices and the circulate block structure. To avoid structural defects of the standard Polynomial Measurement Matrix (PMM), multiple isomorphic polynomial measurement matrix are combined by the circulate block structure. This proposed construction can perform an better reconstruction results than those traditional ones and it requires a shorter CPU time when generating a matrix. This paper also proves the method obeying Restricted Isometry Property (RIP) and gives optimal analysis under complicated hypothesis. Simulation experiment results indicate that our algorithm is valid and stable.

Keywords


Compressed Sensing, Measurement Matrix, Polynomial Measurement Matrix.

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