Multiple‐parameter fractional quaternion Fourier transform and its application in colour image encryption. Issue 12 (1st December 2018)

• Record Type: Journal Article
• Authors: Chen, Beijing; Yu, Ming; Tian, Yuhang; Li, Leida; Wang, Dingcheng; Sun, Xingming
• Is Part Of: IET image processing. Volume 12:Issue 12(2018)
• Page Start: 2238
• Page End: 2249
• Publication Date: 2018-12-01
• Subjects: image coding -- Fourier transforms -- image colour analysis -- cryptography -- signal processing -- inverse transforms; quaternion algebra -- quaternion signal processing -- colour image encryption algorithm -- MPFrQFT‐based encryption algorithm -- sensitive key transform orders -- multiple‐parameter fractional quaternion Fourier transform -- inverse transform -- double random phase encoding; Image processing -- Periodicals; 621.36705
• DOI: 10.1049/iet-ipr.2018.5440
• Languages: English
• ISSNs: 1751-9659

Abstract

Abstract : In this study, by using the quaternion algebra, multiple‐parameter fractional quaternion Fourier transform (MPFrQFT) is proposed to generalise the conventional multiple‐parameter fractional Fourier transform (MPFrFT) to quaternion signal processing in a holistic manner. First, the new transform MPFrQFT and its inverse transform are defined. An efficient discrete implementation method of MPFrQFT is then proposed, in which the relationship between MPFrQFT and MPFrFT of four components is utilised for a quaternion signal. Finally, a new colour image encryption algorithm based on the proposed MPFrQFT and the double random phase encoding technique is proposed to evaluate the performance of the proposed MPFrQFT. Experimental results demonstrate that: (i) the computational time of the proposed implementation method is almost a half of the direct method's time; (ii) the proposed MPFrQFT‐based encryption algorithm has an overall better performance than eight compared algorithms in security test and robustness test: it is more secure than the compared frequency‐based algorithms due to the larger key space and the more sensitive key 'transform orders'; it is also more robust than the compared spatial‐domain algorithms.