Image denoising algorithms based on fractional sinc_α with the covariance of fractional Gaussian fields

Abstract

Image denoising has been considered as an essential image processing problem that is difficult to address. In this study, two image denoising algorithms based on fractional calculus operators are proposed. The first algorithm uses the convolution of covariance of fractional Gaussian fields with the fractional sinc_α (FS) (sinc function of order α). The second algorithm uses the convolution of covariance of fractional Gaussian fields with the fractional differential Heaviside function, which is the limit of FS. In the proposed algorithms, the given noisy image is processed in a blockwise manner. Each processed pixel is convolved with the mask windows on four directions. The final filtered image based on either FS or fractional differential Heaviside function (FDHS) can be obtained by determining the average magnitude of the four convolution test results for each filter mask windows. The outcomes are evaluated using visual perception and peak signal to noise ratio. Experiments prove the effectiveness of the proposed algorithms in removing Gaussian and Speckle noise. The proposed FS and FDHS achieved average PSNR of 28.88, 28.26 dB, respectively, for Gaussian noise. The improvements outperform those achieved with the use of Gaussian and Wiener filters.

Keywords:

• Fractional calculus
• Fractional Heaviside function
• Sinc function
• Fractional Gaussian fields
• Image denoising

Acknowledgments

The authors would like to thank the reviewers for their comments that help improve the paper. This research has been funded by university of Malaya. Project Number: RG312-14AFR.

ORCID

H. A. Jalab http://orcid.org/0000-0002-4823-6851

R. W. Ibrahim http://orcid.org/0000-0001-9341-025X