Journal of Computer Applications ›› 2017, Vol. 37 ›› Issue (7): 2067-2070.

### Variable exponent variational model for image interpolation

1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
• Received:2017-01-06 Revised:2017-03-01 Online:2017-07-10 Published:2017-07-18
• Supported by:
This work is partially supported by the Chongqing Research Program of Basic Research and Frontier Technology (cstc2015jcyjA40029), the Scientific Research Project of Chongqing Technology and Business University (2016-56-08).

### 图像插值的一个变指数变分模型

1. 重庆工商大学 数学与统计学院, 重庆 400067
• 通讯作者: 詹毅
• 作者简介:詹毅(1971-),男,重庆万州人,副教授,博士,主要研究方向:偏微分方程及其应用、变分法图像处理;李梦(1973-),女,四川开江人,副教授,博士,主要研究方向:偏微分方程图像处理、显著特征提取、概率图模型。
• 基金资助:
重庆市基础与前沿研究计划一般项目（cstc2015jcyjA40029）；重庆工商大学科研项目（2016-56-08）。

Abstract: To eliminate the zigzagging and blocky effects in homogeneous areas in an interpolated image, a variable exponent variational method was proposed for image interpolation. An exponent function with diffusion characteristic of image interpolution was introduced by analyzing the diffusion characteristic of variable exponent variational model. Two parameters in the exponent function act on interpolation: the one controlled the intensity of diffusion which eliminated the width of image edges while the other controlled the intensity of smoothness which retained the fine textures in the image. The new variable exponent variatonal model made the Total Variation (TV) variational diffuse along image contours and the heat diffusion on smooth areas. The numerical experiment results on real images show that image interpolated by the proposed method has better interpolated edges, especially for fine textures. Compared to the method proposed by Chen et al. (CHEN Y M, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration. SIAM Journal on Applied Mathematics, 2006, 66(4): 1383-1406) and robust soft-decision interpolation method, the visual improvement is prominent for retaining fine textures, and the Mean Structural SIMilarity (MSSIM) is increased by 0.03 in average. The proposed model is helpful to further study variable exponent variational model for specifical image processing and worthy to practical applications such as image network communication and print.

CLC Number: