Abstract and Applied Analysis

Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image

Yi-Fei Pu, Ji-Liu Zhou, Patrick Siarry, Ni Zhang, and Yi-Guang Liu

Full-text: Open access

Abstract

The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 483791, 19 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450389

Digital Object Identifier
doi:10.1155/2013/483791

Mathematical Reviews number (MathSciNet)
MR3126733

Zentralblatt MATH identifier
1381.35231

Citation

Pu, Yi-Fei; Zhou, Ji-Liu; Siarry, Patrick; Zhang, Ni; Liu, Yi-Guang. Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 483791, 19 pages. doi:10.1155/2013/483791. https://projecteuclid.org/euclid.aaa/1393450389


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