非凸泛函的图像分解  

Image decomposition using the non-convex functional

作　　者：白键[1] 冯象初[1] 

机构地区：[1]西安电子科技大学理学院,陕西西安710071

出　　处：《西安电子科技大学学报》2013年第2期67-71,137,共6页Journal of Xidian University

基　　金：博士点新教师基金资助项目(20100203120010);国家自然科学基金资助项目(61105011)

摘　　要：提出了一种新的基于非凸泛函的图像分解模型.与经典的用Banach范数作为忠诚项的凸泛函模型相比,本文用残差图像的平方的积分除以它的梯度作为忠诚项.这种新的忠诚项对于纹理图像具有非常小的值,然而,对于几何图像有非常大的值,所以它很适合图像分解.应用梯度下降法求非凸泛函的极小值,这导致将一个新的非线性二阶偏微分方程演化到稳定的状态.与经典的总变差最小模型(TV)和四阶偏微分方程模型(OSV)相比,提出的模型可以更好地保持图像的边缘,所以纹理部分有更少的卡通信息.数值实验也证明了本文的模型比标准的TV和OSV模型具有更好的图像分解效果.This paper proposes a new model for image decomposition by non-convex functional minimization. Instead of using the Banach norm as the fidelity term, we use the integral of the square of residual component divided by its gradient as the fidelity term. This non-convex fidelity term has a very low value for the texture image and a high value for the geometric image, so it is appropriate for image decomposition. The gradient descent procedure is used to solve the proposed minimization problem, which leads to evolving a new nonlinear second-order partial differential equation （PDE） to a steady state. Compared with the total variation minimization（TV） model and the fourth-order PDE（OSV） model, the proposed nonlinear second-order PDE maintains many more sharp edges, so the texture part has less cartoon information. Experimental results also demonstrate that our model performs better than the standard TV and OSV models in image decomposition.

关 键 词：图像分解 总变差最小 泛函极小 非凸泛函 

分 类 号：TP751[自动化与计算机技术—检测技术与自动化装置]