Quaternion discrete fractional Krawtchouk transform and its application in color image encryption and watermarking

Liu, Xilin; Wu, Yongfei; Zhang, Hao; Wu, Jiasong; Zhang, Liming

doi:10.1016/j.sigpro.2021.108275

Cited by 32 publications

(11 citation statements)

References 54 publications

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“…( Then, the QFr-PHFMs for the original color image can be expressed as follows: (4) According to Equation( 4), the QFr-PHFMs has rotation invariance inherently, and the proof process mainly includes the following steps: Firstly, let the rotated color image be ) , (…”

Section: Wavelet Transformmentioning

confidence: 99%

“…By adding watermarks to the original data, traditional digital watermarking establishes the ownership of multimedia creations. Most of these techniques achieve their goal of embedding the watermark information by altering the image's spatial or frequency domain information [3][4]. The encoded watermark information is then altered to prevent tampering.…”

Section: Introductionmentioning

confidence: 99%

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Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Jing

Ang

Palaniappan

et al. 2023

JIWE

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This study presents a zero-watermarking algorithm that can resist rotation attacks. The algorithm uses quaternion fractional-order polar harmonic-Fourier moments (QFr-PHFMs) based on wavelet-transformation. First, the wavelet-transformation is applied to each component of the host image, which is in RGB three-channel color. The low-frequency sub-bands of each component are then extracted and represented using quaternion algebra. Multiple QFr-PHFMs are calculated, and the invariants of the QFr-PHFMs are utilized to establish the watermark system. The watermark extraction process is also simplified. The detection of the image requires a two-level wavelet transformation, followed by the calculation of multiple invariant moments of the low-frequency sub-image. The experimental results are shown and compared with similar methods. Simulations show that this method can produce high-quality visual effects and withstand noise, filtering, JPEG compression, and cropping attacks.

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Section: Wavelet Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Jing

Ang

Palaniappan

et al. 2023

JIWE

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show abstract

“…More recently, some fractional order transforms are extended to quaternion space using the quaternion theory. Indeed, Liu et al extend the fractional order Krawtchouk transform to the quaternion fractional order Krawtchouk transform based on quaternion theory [36]. Yamni et al extend the fractional-order Charlier and Hahn transforms to the quaternion fractional order Charlier transform [37] and quaternion fractional-order Hahn transform [38].…”

Section: Related Workmentioning

confidence: 99%

“…Separable fractional order Charlier-Krawtchouk [2] Signal reconstruction and zero-watermarking Quaternion fractional order Krawtchouk transform [36] Color image encryption and watermarking Quaternion fractional order…”

Section: Multiple Inputsmentioning

confidence: 99%

Biomedical Multimedia Encryption by Fractional-Order Meixner Polynomials Map and Quaternion Fractional-Order Meixner Moments

et al. 2022

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Chaotic systems are widely used in signal and image encryption schemes. Therefore, the design of new chaotic systems is always useful for improving the performance of encryption schemes in terms of security. In this work, we first demonstrate the chaotic behavior of fractional order Meixner polynomials (FrMPs) for introducing a new two-dimensional (2D) chaotic system called FrMPs map. This system is very sensitive to any variation by 15 10 − of its control parameters ( and µ β ).Next, we use FrMPs to introduce a new type of orthogonal transforms called quaternion fractional order Meixner moments (QFrMMs). The latter generalize the existing fractional order Meixner moments. To demonstrate the relevance of the proposed FrMPs map and QFrMMs in the field of signal and image processing, they are applied in the development of a new encryption scheme. The main advantage of this scheme is its applicability to the encryption of different types of biomedical data such as multi-biomedical signals, multiple grayscale medical images, color medical image, and grayscale medical image. Several simulation analysis (visual, histogram, runtime, correlation, robustness, etc.) are conducted to verify the efficiency of the proposed scheme. Simulation and comparison results confirm that our encryption method is effective in terms of high security level, high quality of the decrypted information, strong resistance to different types of attacks, etc. These findings support the suitability of the proposed scheme for the secure exchange of biomedical multimedia via a public communication channel.

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“…For more detailed significant results of quaternion integral transforms, including QLCT, we may refer to earlier studies [20][21][22][23]. The implementation of integral transforms for quaternion-valued signals has found several developments in 3D computer graphics, aerospace engineering, artificial intelligence, and color image processing [24,25].…”

Section: Introductionmentioning

confidence: 99%

Pseudo‐differential operator in quaternion space

Kundu

Prasad

2023

Math Methods in App Sciences

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This paper introduces the quaternion Schwarz type space, and quaternion linear canonical transform (QLCT) mapping properties are also discussed. Further, the quaternion pseudo-differential operator (QPDO) associated with QLCT is described. Some of its characteristics, including estimates, boundedness, and integral representation in quaternion Sobolev type space, are derived. Some applications of QLCT, quaternion differential equations, are also discussed.

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Quaternion discrete fractional Krawtchouk transform and its application in color image encryption and watermarking

Cited by 32 publications

References 54 publications

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Robust Image Watermarking With Quaternion Fractional-Order Polar Harmonic-Fourier Moments Based On Wavelet Transformation: Resistance Against Rotation Attacks

Biomedical Multimedia Encryption by Fractional-Order Meixner Polynomials Map and Quaternion Fractional-Order Meixner Moments

Pseudo‐differential operator in quaternion space

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