Abstract—This paper introduces an image denoising algorithm based on generalized Srivastava-Owa fractional differential operator for removing Gaussian noise in digital images. The structures of n n × fractional masks are constructed by this algorithm. Experiments show that, the capability of the denoising algorithm by fractional differential-based approach appears efficient to smooth the Gaussian noisy images for different noisy levels. The denoising performance is measured by using peak signal to noise ratio (PSNR) for the denoising images. The results showed an improved performance (higher PSNR values) when compared with standard Gaussian smoothing filter. Keywords—Fractional calculus, fractional differential operator, fractional mask, fractional filter. I. INTRODUCTION RACTIONAL integration and fractional differentiation are generalizations of the notions of integer-order integration and differentiation and they include n th derivatives and n-fold integrals in particular cases. Many applications of fractional calculus in physics amount to replace the time derivative in an evolution equation with a derivative of fractional order. Fractional calculus has been applied to a variety of physical phenomena, including anomalous diffusion, transmission line theory, problems involving oscillations, nanoplasmonics, solid mechanics, astrophysics and viscoelasticity [1]-[6]. Currently, fractional calculus (integral and differential operators) is employed in signal processing and image possessing. The fractional calculus enhances the quality of images, with interesting possibilities in various image enhancement applications such as image denoising and texture enhancement [7]-[9]. In the past three decades a lot of studies have been conducted on fractional calculus and fractional differential equations, involving different operators such as Riemann- Liouville operators, Erdélyi-Kober operators, Weyl-Riesz operators, Caputo operators and Grünwald-Letnikov operators, with their applications in other fields. Moreover, the existence and uniqueness of holomorphic solutions for nonlinear fractional differential equations such as Cauchy problems and Hamid A. Jalab is with the Faculty of Computer Science & Information Technology University Malaya, 50603. Kuala Lumpur, Malaysia (e-mail: hamidjalab@um.edu.my). Rabha W. Ibrahim is with the Institute of Mathematical Sciences University Malaya, 50603. Kuala Lumpur, Malaysia (e-mail: rabhaibrahim@yahoo.com). diffusion problems in complex domain are established and posed [10]-[17]. Noise is any undesired signal that contaminates an image. The digital image acquisition is the primary process by which noise appears in digital images as this process converts an optical image into a continuous electrical signal. Noise, arising from a variety of sources, is inherent to all electronic image sensors and the electronic components in the image environment. In Gaussian noise, all the image pixels deviate from their original values following the bell-shaped curve distribution (Gaussian curve). Denoising is one of the most fundamental image restoration problems in computer vision and image processing. Image denoising refers to the process of recovering a digital image that has been contaminated by additive white Gaussian noise. There have been many attempts to construct digital filters to remove noise from digital images. Vijaykumar et al. in [18], presented a new fast and efficient algorithm capable in removing Gaussian noise with less computational complexity. R. H. Chan, in [19], proposed two-phase scheme for removing salt-and-pepper impulse noise. The concept of image fusion of filtered noisy images for impulse noise reduction is used in [20]. S. D. Ruikar and D. D. Doye [21] proposed different approaches of wavelet based image denoising methods. In [22] G. Vijaya and V. Vasudevan presented an interactive algorithm for image denoising and segmentation using soft computing techniques. Furthermore, A novel approach based on fractional calculus were employed in multi-scale texture segmentation [23]; design problems of variables and image denoising [24]; digital fractional order for different filters [25]. Finally, fractional differential masks based on the definitions of fractional differential operators due to Grümwald-Letnikov and Riemann-Liouvillewere introduced. Therefore, the fractional calculus in the field of image processing and signal prosecuting that has broad application prospect. In this paper, we have aimed introduce an image denoising algorithm named generalized fractional differential image denoising algorithm based on Srivastava-Owa fractional differential operator. Initially the structures of n n × fractional masks of this algorithm are constructed. The denoising performance is measured by conducting experiments according to subjective and objective standards of visual perception values. Compared to other methods the proposed method performs well with very less computational time. The outline of the paper is as follows: Section II explains Hamid A. Jalab, Rabha W. Ibrahim Fractional Masks Based On Generalized Fractional Differential Operator for Image Denoising F World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:7, No:2, 2013 308 International Scholarly and Scientific Research & Innovation 7(2) 2013 scholar.waset.org/1307-6892/9996971 International Science Index, Computer and Information Engineering Vol:7, No:2, 2013 waset.org/Publication/9996971