In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function: E γ;q,c α,β (z) = ∞ ∑ n=0 Bp(γ+nq, c− γ)(c)nq B(γ, c− γ)Γ(αn+β) zn n! , (z,β,γ ∈ C), as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels. c ©2017 All rights reserved.

The extended Mittag-Leffler function via fractional calculus

An adaptive color image watermarking using RDWT-SVD and artificial bee colony based quality metric strength factor optimization

The aim of this paper is to establish an (presumably new) extension of generalized Bessel-Maitland function by using the extension of extended beta function. In addition, investigate several important properties namely integral representation, derivatives, recurrence relation, Beta transform and Mellin transform. Further, certain properties of the Riemann-Liouville fractional calculus associated with extended generalized Bessel-Maitland function are also investigated.

Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus

SVD-based Digital Image Watermarking Scheme

This paper presents a robust and secure image hash algorithm. The algorithm extracts robust image features in the Radon transform domain. A randomization mechanism is designed to achieve good discrimination and security. The hash value is dependent on a secret key. We evaluate the performance of the proposed algorithm and compare the results with those of one existing Radon transform-based algorithm. We show that the proposed algorithm has good robustness against contentpreserving distortion. It withstands JPEG compression, filtering, noise addition as well as moderate geometrical distortions. Additionally, we achieve improved performance in terms of discrimination, sensitivity to malicious tampering and receiver operating characteristics. We also analyze the security of the proposed algorithm using differential entropy and confusion/diffusion capabilities. Simulation shows that the proposed algorithm well satisfies these metrics.

https://lirias.kuleuven.be/bitstream/123456789/329830/2/article-2108.pdf

Radon Transform-Based Secure Image Hashing

Watermarking is proposed as solution to authentication, copyright protection and security requirements of multimedia objects (speech, image and video). In this paper a watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed. In the proposed scheme, image to be watermarked is first transformed by finite radon transform, the radon transformed image is further transformed by FRFT, and singular values of FRFT transformed image are modified to embed the watermark. Inverse transformation is applied to obtain watermarked image. Simulations are performed under various test conditions with different FRFT transform angles for improved robustness and visual transparence of watermarked image. Results of the proposed scheme are better in comparison to the existing schemes for most of the attacks. Proposed scheme provide additional degree of freedom in security, robustness, payload capacity and visual transparence. Proposed scheme can also be used to communicate or store the watermarked image as erasure code, to reduce communication errors over a network, due to the use of FRAT.

K.K. Sharma

Papers

Hybrid Watermarking Algorithm using Finite Radon and Fractional Fourier Transform