Image restoration method based on fractional variable order differential

• Published in: Multidimensional systems and signal processing Vol. 29; no. 3; pp. 999 - 1024
• Main Authors: Zhang, Yan-Shan, Zhang, Feng, Li, Bing-Zhao
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2018; Springer Nature B.V
• Subjects: Artificial Intelligence; Circuits and Systems; Differential equations; Electrical Engineering; Engineering; Fourier transforms; Image restoration; Iterative methods; Numerical analysis; Signal to noise ratio; Signal,Image and Speech Processing; Test procedures; Visual effects; Visual signals; Total variation; Fractional; Image restoration; Combined image similarity index; Variable order differential
• ISSN: 0923-6082; 1573-0824
• DOI: 10.1007/s11045-017-0482-z

In this paper, we study image restoration problem by using fractional variable order differential technique. Our idea is to make use of fractional order differential diffusion equation of evolution procedure into the image restoration problem. An image often exists different low-frequency and high-frequency components, such as flat, texture and edge, etc. Because fractional order differential can enhance the high-frequency components of a signal, meanwhile, nonlinearly preserve the low-frequency components of the signal, we can adapt suitable fractional differential orders to restore their components. In particular, different differential orders can be used in an image at the same time. In order to obtain the restored image automatically, we choose the fractional differential orders by the value of gradient modulus of the image and use the discrete Fourier transform to implement the numerical algorithm. We also provide an iterative scheme in the frequency domain. Experimental results are reported to demonstrate that the visual effects, the combined image similarity index and the peak signal to noise ratio of restored images by using the proposed method are very good, and are competitive with the other testing methods.