Abstract: Quaternion algebra has been used to apply the fractional Fourier transform (FrFT) to color images in a comprehensive approach. However, the discrete fractional random transform (DFRNT) with adequate basic randomness remains to be examined. This paper presents a novel multistage privacy system for color medical images based on discrete quaternion fractional Fourier transform (DQFrFT) watermarking and three-dimensional chaotic logistic map (3D-CLM) encryption. First, we describe quaternion DFRNT (QDFRNT), which generalizes DFRNT to handle quaternion signals effectively, and then use QDFRNT to perform color medical image adaptive watermarking. To efficiently evaluate QDFRNT, this study derives the relationship between the QDFRNT of a quaternion signal and the four components of the DFRNT signal. Moreover, it uses the human vision system’s (HVS) masking qualities of edge, texture, and color tone immediately from the color host image to adaptively modify the watermark strength for each block in the color medical image using the QDFRNT-based adaptive watermarking and support vector machine (SVM) techniques. The limitations of watermark embedding are also explained to conserve watermarking energy. Second, 3D-CLM encryption is employed to improve the system’s security and efficiency, allowing it to be used as a multistage privacy system. The proposed security system is effective against many types of channel noise attacks, according to simulation results.

Key words: Color medical image; Quaternion; Adaptive watermarking; Encryption; Fractional transform; Three-dimensional chaotic logistic map (3D-CLM)

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