变分方法可以将图像分解为同类部分u和振荡部分v，但传统的图像分解方法会导致分解结果的对比度发生改变，并产生阶梯效应。为了更好地进行图像分解和去噪，提出了一种基于L1的可根据图像局部信息自适应的图像分解变分方法。该方法首先使用L1范数作为分解模型中的逼近项，以便使分解结果能保持原始图像边缘和保持对比度不变；然后通过引入图像局部特征的自适应函数来削减同类部分u的阶梯效应。实验证明，新方法比传统方法能更好地应用于图像分解和图像的噪声去除。

Image can be decomposed into homogenous components u and oscillatory components v by using variational methods. However the solution of traditional variational methods has contrast loss and staircasing effect. Now we propose a local adaptive variational decomposition method based on L1. Using L1-norm as the fidelity term, we can get the solution which preserves the edges of original images and the contrast invariant. At the same time, the adaptive function which we induced here can reduce the staircasing effect on homogenous component u. Numerical results are presented, showing that the new method works better on several various types of images for image decomposition and denoising than traditional methods.