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Some applications of a decomposition for five quaternion matrices in control system and color image processing

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Abstract

In this paper, some applications of a decomposition for five quaternion matrices in control system and color image processing are given. A system of Sylvester-type quaternion matrix equations with five equations is considered. Some necessary and sufficient conditions for the existence of a solution to the system is derived. The general solution to the system is presented. The maximal and minimal ranks of the general solution to the system is provided. New frameworks for simultaneous embedding and extraction of five watermarks through this decomposition is proposed. Some algorithms and examples are given to illustrate the main result.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Zhuo-Heng He & Wei-Lu Qin

  2. Department of Mathematics and Statistics, University of Nevada, Reno, NV, 89557, USA

    Xiang-Xiang Wang

Authors
  1. Zhuo-Heng He
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  2. Wei-Lu Qin
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  3. Xiang-Xiang Wang
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Correspondence to Zhuo-Heng He.

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Communicated by Jinyun Yuan.

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This research was supported by the National Natural Science Foundation of China (Grant nos. 11801354 and 11971294)

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He, ZH., Qin, WL. & Wang, XX. Some applications of a decomposition for five quaternion matrices in control system and color image processing. Comp. Appl. Math. 40, 205 (2021). https://doi.org/10.1007/s40314-021-01579-3

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