高阶变分正则化的图像放大算法  

Image Zooming Method Based on High-order Variation

作　　者：刘晨华[1] 颜兵[2] 

机构地区：[1]太原科技大学应用科学学院,山西太原030024 [2]中北大学信息与通信工程学院,山西太原030051

出　　处：《信息与控制》2017年第4期422-427,共6页Information and Control

基　　金：国家青年自然科学基金资助项目(11501401);太原科技大学校青年科技研究基金资助项目(20133011)

摘　　要：基于二阶微分方程的图像放大方法易出现边缘模糊及阶梯块效应的问题,利用高阶变分微分方程可以去除噪声及保护边缘的特点,提出了一种新的图像放大方法.首先,根据Chambolle提出的放大模型把低分辨的原图像投影到放大后图像所在空间的子空间上;其次,通过引入含有边缘检测函数的拉普拉斯变分正则项而构造出图像放大的泛函模型;最终,通过对新模型的分析,给出了一种快速有效的分裂Bregman算法对模型求解,得到了最终放大图像.实验表明,新模型以高阶变分泛函为基础,有效地去除了图像平滑部分的阶梯效应,更好地保持了图像边缘及纹理细节信息.To address edge blur and the blocky effects problem in the process of zooming in on an image on the basis of second-order differential equation,we propose a new image zooming method according to characteristic of denoising and edge protection for a high-order variation differential equation. First,in accordance with the Chambolle image zooming model,we regard the original low-resolution image as the subspace projection of a zoomed image to its own space. Second,we construct a new image zooming model by introducing a Laplace variation regular term that contains edge detection function. Finally,we introduce an efficient and fast split Bregman algorithm based on an analysis of the properties of the new model. The final zooming image is obtained. Experiments show that the proposed algorithm based on high-order variation can avoid blocky effects,thereby significantly enhancing the texture and the edges of a zoomed image and significantly improving visual effects as a result.

关 键 词：图像放大 高阶微分方程 变分 边缘检测函数 分裂Bregman算法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]