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中文摘要：
在经典变分图像分解模型中，平衡参数通常依据图像振荡分量的先验信息进行选取。本文针对这一局限性，以更为一般的一类Meyer分解模型为出发点，首先讨论了该模型解的存在性和唯一性，然后给出一种能依据图像自身信息，自适应地确定平衡参数的分级分解框架，进而得到一种分级多尺度图像表示方法，最后，对其收敛性进行了理论分析。并利用Chambolle的投影方法给出具体算法。数值实验结果表明，该方法能较好地弥补单尺度分解模型在图像应用中存在的一些不足。
英文摘要：
In the image decomposition method based on the variational calculus, the classical selection method for the balance parameter is based on the information of the oscillating component of the image. However, this apriority can＇t be easily obtained in practice. To overcome this defect, we use a more general Meyer＇s decomposition model as start point, the existence and the uniqueness of this model are firstly examined. And then, under a hierarchical multiscale decomposition frame, the selecting for the balance parameter is adapted to the nature of the information of the image. Moreover, a hierarchical multi-scale representation of the image is achieved. Finally, following Chambolle＇s projection algorithm, the convergence of an iterative numerical implementation is proved. The experimental results show that above method can well complement the monoscale decomposition in the application of the image processing.
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