Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

Lian Yuefang; Zhou Jinchuan; Tang JingyongSun Zhongfeng

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Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

机译：Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

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1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2020年第43期|8849395.1-8849395.14|共14页
作者
Lian Yuefang; Zhou Jinchuan; Tang JingyongSun Zhongfeng;
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Shandong Univ Technol, Sch Math & Stat, Dept Stat, Zibo 255000, Peoples R China;

Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China;

Shandong Univ Technol, Sch Math & Stat, Dept Informat & Comp Sci, Zibo 255000, Peoples R China;

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Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

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